question_answer 1)
If the equation \[4{{x}^{2}}+x(p+1)=0\] has exactly two equal roots, then one of the values of p is
A)
5 done
clear
B)
- 3 done
clear
C)
0 done
clear
D)
3 done
clear
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question_answer 2)
If a and b are the roots of the equation \[5{{x}^{2}}-x-2=0\], then the equation for which roots are\[\frac{2}{\alpha }\] and\[\frac{2}{\beta }\] is
A)
\[{{x}^{2}}-x+10=0\] done
clear
B)
\[{{x}^{2}}-x-10=0\] done
clear
C)
\[{{x}^{2}}+x+10=0\] done
clear
D)
\[{{x}^{2}}+x-10=0\] done
clear
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question_answer 3)
The sum of the coefficients of even powers of\[x\]a polynomial \[f(x)\] is
A)
\[f(1)\] done
clear
B)
\[f(0)\] done
clear
C)
\[\frac{f(1)+f(-1)}{2}\] done
clear
D)
\[\frac{f(1)-f(-1)}{2}\] done
clear
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question_answer 4)
The G.C.D. of \[{{x}^{3}}-{{x}^{2}}-4x-6\] and \[{{x}^{2}}-2x-3\] is
A)
\[3x+2\] done
clear
B)
\[x-3\] done
clear
C)
\[-x-3\] done
clear
D)
\[-2x-3\] done
clear
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question_answer 5)
The remainder when \[{{x}^{4}}-{{y}^{4}}\]is divided by x -y is
A)
0 done
clear
B)
\[x-3\] done
clear
C)
\[{{x}^{2}}-{{y}^{2}}\] done
clear
D)
\[2{{y}^{4}}\] done
clear
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question_answer 6)
If \[{{x}^{3}}-5x+7\] is divisible by \[(x+2)\], then the remainder is
A)
-21 done
clear
B)
-20 done
clear
C)
- 17 done
clear
D)
- 25 done
clear
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question_answer 7)
H.C.F. of \[{{x}^{3}}-1\] and \[{{x}^{4}}+{{x}^{2}}+1\] will be
A)
\[x-1\] done
clear
B)
\[{{x}^{2}}+x+1\] done
clear
C)
\[{{x}^{2}}-x+1\] done
clear
D)
\[{{x}^{2}}-x-1\] done
clear
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question_answer 8)
The L.C.M. of \[xy+yz+zx+{{y}^{2}}\] and \[{{x}^{2}}+xy+yz+zx\] is
A)
\[x+y\] done
clear
B)
\[y+z\] done
clear
C)
\[(x+y)(y+z)(z+x)\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}\] done
clear
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question_answer 9)
The solution of \[\frac{2x+3}{2x-1}=\frac{3x-1}{3x+1}\]is
A)
\[\frac{1}{8}\] done
clear
B)
\[-\frac{1}{8}\] done
clear
C)
\[\frac{8}{3}\] done
clear
D)
\[-\frac{8}{3}\] done
clear
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question_answer 10)
If \[x-\frac{1}{x}=2\], then the value of \[{{x}^{4}}+\frac{1}{{{x}^{4}}}\] is
A)
4 done
clear
B)
8 done
clear
C)
12 done
clear
D)
34 done
clear
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question_answer 11)
The equation whose roots are 4 and 5 is
A)
\[{{x}^{2}}+9x+20=0\] done
clear
B)
\[{{x}^{2}}-9x-20=0\] done
clear
C)
\[{{x}^{2}}-9x+20=0\] done
clear
D)
\[{{x}^{3}}+9x+20=0\] done
clear
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question_answer 12)
The value .of \[{{\left( \frac{{{x}^{b}}}{{{x}^{c}}} \right)}^{\frac{1}{bc}}}.{{\left( \frac{{{x}^{c}}}{{{x}^{a}}} \right)}^{\frac{1}{ca}}}.{{\left( \frac{{{x}^{a}}}{{{x}^{b}}} \right)}^{\frac{1}{ab}}}\] on simplifying is
A)
\[x\] done
clear
B)
\[\frac{1}{x}\] done
clear
C)
1 done
clear
D)
- 1 done
clear
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question_answer 13)
The value of \[x\], y and z respectively on simplifying the equations \[2x+3y=0,\]\[3y+4z=14,\]\[2x+4z=26,\] is
A)
3,-2, 5 done
clear
B)
-3,2,5 done
clear
C)
- 3, 2, - 5 done
clear
D)
3, 2, 5 done
clear
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question_answer 14)
If \[{{a}^{m}}.{{a}^{n}}={{a}^{mn}}\], then \[m(n-2)+n(m-2)\] is
A)
1 done
clear
B)
- 1 done
clear
C)
0 done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
question_answer 15)
If the difference of the squares of two numbers is 45, the square of the smaller number is 4 times the larger number, then the numbers are
A)
9, 6 or 9, - 6 done
clear
B)
5, 6 or 5, - 6 done
clear
C)
9, 5 or 9, - 5 done
clear
D)
none of these done
clear
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question_answer 16)
The value of \[{{x}^{2}}-6x+13\]can never be less than
A)
4 done
clear
B)
5 done
clear
C)
4.5 done
clear
D)
7 done
clear
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question_answer 17)
In n is a whole number greater than 1, then n \[\left( {{\text{n}}^{\text{2}}}\text{ }-\text{ 1} \right)\]is always divisible by
A)
12 done
clear
B)
12 and 24 done
clear
C)
24 done
clear
D)
36 done
clear
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question_answer 18)
In solving an equation of the form \[ax+b=0\] (a, b having only 1 as the common factor). A made a mistake in copying 6 and got \[\frac{7}{3}\] as the root whereas B made a mistake in copying a and got \[\frac{8}{5}\] as the root. The correct root is
A)
\[\frac{7}{5}\] done
clear
B)
\[\frac{3}{8}\] done
clear
C)
\[\frac{8}{3}\] done
clear
D)
\[\frac{8}{5}\] done
clear
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question_answer 19)
The polynomial (in \[x\]):\[{{x}^{6}}+18{{x}^{3}}+125\], admits
A)
No factor of degree between 2 and 5 done
clear
B)
\[{{x}^{2}}-3x+5\] as a factor done
clear
C)
\[x+1\] as a factor done
clear
D)
\[x-125\] as a factor done
clear
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question_answer 20)
If \[{{a}^{x}}=b,\,{{b}^{y}}=c,\,{{c}^{z}}=a\], then the value of \[xyz\] is
A)
0 done
clear
B)
1 done
clear
C)
\[\frac{1}{abc}\] done
clear
D)
abc done
clear
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question_answer 21)
If the index of any power function is zero, then the value of that function is
A)
0 done
clear
B)
1 done
clear
C)
- 1 done
clear
D)
None of these done
clear
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question_answer 22)
If \[f:R\to R,f(x)={{x}^{2}}+8\], then \[f(-3)\] is
A)
1 done
clear
B)
- 17 done
clear
C)
- 1 done
clear
D)
17 done
clear
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question_answer 23)
If \[f(x)={{x}^{2}},x>0\] then the function is
A)
not one to one function done
clear
B)
one to one function done
clear
C)
into function done
clear
D)
none of these done
clear
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question_answer 24)
Five tables and eight chairs cost Rs. 7,350 three tables and five chairs cost Rs. 4,475. The price of a table is
A)
Rs. 950 done
clear
B)
Rs. 325 done
clear
C)
Rs. 925 done
clear
D)
Rs. 350 done
clear
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question_answer 25)
If sum and difference of two expressions is \[5{{x}^{2}}-x-4\] and \[{{x}^{2}}+9x-10\] respectively, then the expressions are
A)
\[(4{{x}^{2}}+8x-6),(4{{x}^{2}}-10x+2)\] done
clear
B)
\[(2{{x}^{2}}+4x-3),(3{{x}^{2}}-10x-6)\] done
clear
C)
\[(3{{x}^{2}}+4x-7),(2{{x}^{2}}-5x+3)\] done
clear
D)
\[(3{{x}^{2}}+4x+7),(2{{x}^{2}}-5x-3)\] done
clear
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question_answer 26)
If the sum and the product of two numbers are 25 and 144 respectively, then the difference of the numbers must be
A)
3 done
clear
B)
5 done
clear
C)
7 done
clear
D)
11 done
clear
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question_answer 27)
Range of function \[f(x)=\frac{1}{1-x}\]is
A)
set of rational numbers done
clear
B)
set of real numbers except zero done
clear
C)
set of natural numbers done
clear
D)
set of integers done
clear
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question_answer 28)
If \[f(x)=|x|\,\,\,\forall x\in R\], then the function is
A)
not one to one function done
clear
B)
one to one function done
clear
C)
into function done
clear
D)
not into function done
clear
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question_answer 29)
If l\[\log (x+1)+\log (x-1)=\log 3\], then value of x is
A)
3 done
clear
B)
2 done
clear
C)
1 done
clear
D)
none of these done
clear
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question_answer 30)
\[{{3}^{x-y}}=27\] and \[{{3}^{x+y}}=243\], then \[x\] is equal to
A)
0 done
clear
B)
4 done
clear
C)
2 done
clear
D)
6 done
clear
View Solution play_arrow
question_answer 31)
If \[p+q=1\] and the ordered pair (p, q) satisfies \[3x+2y=1\], then it also satisfies
A)
\[3x+3y=3\] done
clear
B)
\[5x+4y=4\] done
clear
C)
\[5x+4y=4\] done
clear
D)
None of these done
clear
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question_answer 32)
The age of a father is twice that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the difference of ages of the two sons is 15 years, the age of the father is
A)
100 years done
clear
B)
70 years done
clear
C)
60 years done
clear
D)
50 years done
clear
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question_answer 33)
If \[{{\log }_{10}}a+{{\log }_{10}}b={{\log }_{10}}(a+b)\], then
A)
\[a=b=2\] done
clear
B)
\[~\text{a}=\text{b}=\text{1}\] done
clear
C)
\[a=\frac{{{b}^{2}}}{1-b}\] done
clear
D)
\[a=\frac{b}{b-1}\] done
clear
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question_answer 34)
If \[x=\frac{1}{5+\frac{1}{5+\frac{1}{5}}}\] , then
A)
\[{{x}^{2}}+5x-1=0\] done
clear
B)
\[{{x}^{2}}-5x-1=0\] done
clear
C)
\[{{x}^{2}}-5x+1=0\] done
clear
D)
\[{{x}^{2}}+5x+1=0\] done
clear
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question_answer 35)
The values of \[x\] and y satisfying the two equations \[32x+33y=31,33x+32y=34\] respectively will be
A)
-1,2 done
clear
B)
2, - 1 done
clear
C)
0, 0 done
clear
D)
2, 3 done
clear
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question_answer 36)
If \[2{{x}^{3}}+4{{x}^{2}}+2ax+b\] is exactly divisible by \[{{x}^{2}}-1\],then the value of a and b respectively will be
A)
1, 2 done
clear
B)
- 1, 4 done
clear
C)
1, - 2 done
clear
D)
-1, - 4 done
clear
View Solution play_arrow
question_answer 37)
The sum of \[\frac{1}{x+y}\]and \[\frac{1}{x-y}\]is
A)
\[\frac{2y}{{{x}^{2}}-{{y}^{2}}}\] done
clear
B)
\[\frac{2x}{{{x}^{2}}-{{y}^{2}}}\] done
clear
C)
\[\frac{2x}{{{y}^{2}}-{{x}^{2}}}\] done
clear
D)
\[\frac{-2y}{{{x}^{2}}-{{y}^{2}}}\] done
clear
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question_answer 38)
The greatest value assumed by the function \[f(x)=5-|x-3|\] is
A)
3 done
clear
B)
8 done
clear
C)
6 done
clear
D)
5 done
clear
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question_answer 39)
The value of \[\frac{{{2}^{m+3}}\times {{3}^{2m-n}}\times {{5}^{m+n+3}}\times {{6}^{n+1}}}{{{6}^{m+1}}\times {{10}^{n+3}}\times {{15}^{m}}}\]is equal to
A)
0 done
clear
B)
1 done
clear
C)
\[{{2}^{m}}\] done
clear
D)
None of these done
clear
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question_answer 40)
If \[x=2,\,y=1\] and \[z=-3\] then \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz\]is equal to
A)
6 done
clear
B)
0 done
clear
C)
2 done
clear
D)
8 done
clear
View Solution play_arrow
question_answer 41)
If \[{{3}^{4x-2}}=729\], then the value of \[x\] is
A)
3 done
clear
B)
1.2 done
clear
C)
2 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 42)
\[{{x}^{3}}+a{{x}^{2}}-7x-6\] can be factorised into 3 linear factors when
A)
a = 0 done
clear
B)
a = 1 done
clear
C)
a = 2 done
clear
D)
a = 3 done
clear
View Solution play_arrow
question_answer 43)
The number of prime numbers between 0 and 20 is
A)
7 done
clear
B)
8 done
clear
C)
6 done
clear
D)
9 done
clear
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question_answer 44)
The equation \[\frac{(x+2)(x-5)}{(x-3)(x+6)}=\frac{x-2}{x+4}\] has
A)
3 roots done
clear
B)
2 roots done
clear
C)
1 root done
clear
D)
no root done
clear
View Solution play_arrow
question_answer 45)
The sum of two numbers is 9 and the sum of their squares is 41. The numbers are
A)
4 and 5 done
clear
B)
1 and 8 done
clear
C)
3 and 6 done
clear
D)
2 and 7 done
clear
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question_answer 46)
If the sum of the squares of roots of the equation \[{{x}^{2}}+2x-p=0\] is 10, then the value of p will be
A)
- 3 done
clear
B)
3 done
clear
C)
6 done
clear
D)
- 6 done
clear
View Solution play_arrow
question_answer 47)
lf \[h(x)={{x}^{2}}-2\], then the value of \[\frac{1}{2}h\left( \frac{1}{2} \right)\] his
A)
0 done
clear
B)
1 done
clear
C)
\[-\frac{7}{8}\] done
clear
D)
\[\frac{7}{8}\] done
clear
View Solution play_arrow
question_answer 48)
If \[{{2}^{2x-y}}=32\] and \[{{2}^{x+y}}=16\] then \[{{x}^{2}}+{{y}^{2}}\] is equal to
A)
9 done
clear
B)
10 done
clear
C)
11 done
clear
D)
13 done
clear
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question_answer 49)
Factors of \[\text{2}\left( \text{a }+\text{ b} \right)\text{2}-\text{9}\left( \text{a }+\text{ b} \right)-\text{5}\] are
A)
\[a+b+5,2a+2b-1\] done
clear
B)
\[\text{a}+\text{b}-\text{5},\text{2a}+\text{2b}+\text{1}\] done
clear
C)
\[a-b+5,2a-2b+5\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 50)
If \[x-\frac{1}{x-2}=2-1\frac{1}{x-2}\] , then x is equal to
A)
1 done
clear
B)
2 done
clear
C)
1 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 51)
If\[\frac{1}{x}+\frac{1}{y}=\frac{1}{2z}\] then z is equal to
A)
\[\frac{x+y}{2xy}\] done
clear
B)
\[\frac{xy}{2(x+y)}\] done
clear
C)
\[\frac{xy}{(x+y)}\] done
clear
D)
\[\frac{x+y}{xy}\] done
clear
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question_answer 52)
If \[{{a}^{x}}={{b}^{y}}\]and \[{{b}^{2}}=ac\], then \[\frac{1}{x}+\frac{1}{z}\]
A)
\[\frac{2}{y}\] done
clear
B)
\[\frac{1}{y}\] done
clear
C)
\[\frac{1}{2}y\] done
clear
D)
\[2y\] done
clear
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question_answer 53)
If re, ,y, z are positive real numbers and a, b, c are rational numbers, then the value of \[\frac{1}{1+{{x}^{b-a}}+{{x}^{x-a}}}+\frac{1}{1+{{x}^{a-b}}+{{x}^{c-b}}}+\frac{1}{1+{{x}^{b-c}}+{{x}^{a-c}}}\]
A)
- 1 done
clear
B)
1 done
clear
C)
0 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 54)
The product\[\left( 1-\frac{1}{n} \right)\left( 1-\frac{1}{n+1} \right)\left( 1-\frac{1}{n+2} \right)......\left( 1-\frac{1}{2n} \right)\] equals
A)
\[\frac{n-1}{2n}\] done
clear
B)
\[\frac{1}{2n}\] done
clear
C)
\[\frac{2n}{n-1}\] done
clear
D)
\[\frac{1}{n}\] done
clear
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question_answer 55)
For which of the following function is : \[\frac{f-f}{a-b}\] Constant for all number a and b where \[a\ne b\]?
A)
\[f(x)=4x+7\] done
clear
B)
\[f(x)=x+{{x}^{2}}\] done
clear
C)
\[f(x)=\cos x\] done
clear
D)
\[f(x)={{\log }_{e}}x\] done
clear
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question_answer 56)
After travelling for 30 minutes a train meets an accident, due to which it has to stop for 45 minutes. Due to the accident its speed is also reduced to \[\frac{2}{3}\] of its former value and the train reaches its destination 1 hour 30 minutes late. Had the accident occurred 60 km later, the train would have reached 30 minutes earlier. The length of journey is
A)
90 km done
clear
B)
120 km done
clear
C)
150 km done
clear
D)
180 km done
clear
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question_answer 57)
If p, q and r are in A.R, then which of the following statements is correct?
A)
\[pq+qr-2{{q}^{2}}=0\] done
clear
B)
\[pq+qr-2{{p}^{2}}=0\] done
clear
C)
\[pq+qr-pqr=0\] done
clear
D)
\[pq+qr-2{{r}^{2}}=0\] done
clear
View Solution play_arrow
question_answer 58)
The value of \[{{1}^{2}}+{{2}^{2}}+{{3}^{2}}+.....+{{n}^{2}}\]is
A)
\[\frac{n(n+1)}{2}\] done
clear
B)
\[\frac{n(n+1)(2n+1)}{6}\] done
clear
C)
\[\frac{n(n+1)(2n-1)}{6}\] done
clear
D)
\[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\] done
clear
View Solution play_arrow
question_answer 59)
\[f(x),g(x)\] are two polynomial with integer coefficient such that their HCF is 1 and LCM is \[({{x}^{2}}-4)({{x}^{4}}-1)\]lf \[f(x)={{x}^{3}}-2{{x}^{2}}-x+2\] then \[g(x)\]is
A)
\[{{x}^{3}}-2{{x}^{2}}+x+2\] done
clear
B)
\[{{x}^{3}}-2{{x}^{2}}+x-2\] done
clear
C)
\[{{x}^{3}}+2{{x}^{2}}+x+2\] done
clear
D)
\[{{x}^{3}}-2{{x}^{2}}-x-2\] done
clear
View Solution play_arrow
question_answer 60)
If \[x-\frac{1}{x}=5\]then \[{{x}^{3}}-\frac{1}{{{x}^{3}}}\]equals
A)
125 done
clear
B)
130 done
clear
C)
135 done
clear
D)
140 done
clear
View Solution play_arrow
question_answer 61)
If \[{{c}_{0}},{{c}_{1}},{{c}_{2}}....,{{c}_{n}}\]denote the binomial coefficients in the expression of \[{{(1+x)}^{n}}\], then find the value of \[{{c}_{0}},+{{c}_{1}},+{{c}_{2}}+....,{{c}_{n}}+:\]
A)
\[{{2}^{n-1}}\] done
clear
B)
\[{{2}^{n}}\] done
clear
C)
\[{{2}^{n+1}}\] done
clear
D)
0 done
clear
View Solution play_arrow
question_answer 62)
The sum of the series\[1+{{\log }_{e}}2+\frac{{{({{\log }_{e}}2)}^{2}}}{2!}+\frac{{{({{\log }_{e}}2)}^{2}}}{3!}+.....\,\,\,to\,\,\infty \] is
A)
2 done
clear
B)
1 done
clear
C)
0 done
clear
D)
- done
clear
View Solution play_arrow
question_answer 63)
The expansion of log \[{{\log }_{e}}\frac{1}{(1-x)}\]is
A)
\[x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\,.....\] done
clear
B)
\[x+\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}+\,.....\] done
clear
C)
\[1-x+\frac{{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3}+\,.....\] done
clear
D)
\[1+x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\,.....\] done
clear
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question_answer 64)
If \[x\] and y are positive with \[x-y=2\] and \[xy=24\], then \[\frac{1}{x}+\frac{1}{y}\]is equal to
A)
\[\frac{5}{12}\] done
clear
B)
\[\frac{1}{12}\] done
clear
C)
\[\frac{1}{6}\] done
clear
D)
\[\frac{25}{6}\] done
clear
View Solution play_arrow
question_answer 65)
If \[f(x)=\frac{2x+5}{{{x}^{2}}+x+5}\], then \[f[f(-1)]\] is equal to
A)
\[\frac{149}{155}\] done
clear
B)
\[\frac{155}{147}\] done
clear
C)
\[\frac{155}{149}\] done
clear
D)
\[\frac{147}{155}\] done
clear
View Solution play_arrow
question_answer 66)
If\[x+\frac{1}{x}=2\] then, \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] is equal to
A)
2 done
clear
B)
0 done
clear
C)
4 done
clear
D)
6 done
clear
View Solution play_arrow
question_answer 67)
The expression \[\frac{5-x}{{{x}^{2}}-x-20}\]when simplified, equals
A)
\[\frac{1}{x+4}\] done
clear
B)
\[\frac{1}{x-4}\] done
clear
C)
\[\frac{1}{x+4}\] done
clear
D)
\[\frac{1}{x-5}\] done
clear
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question_answer 68)
The value of k, for which the system of equation \[kx+2y=5,3x+y=1\] has no solution, is
A)
5 done
clear
B)
\[\frac{2}{3}\] done
clear
C)
6 done
clear
D)
\[\frac{3}{2}\] done
clear
View Solution play_arrow
question_answer 69)
Mohan gets 3 marks for each correct sum and loses 2 marks for each wrong sum. He attempts 30 sums and obtains 40 marks. The number of sums solved correctly is
A)
10 done
clear
B)
15 done
clear
C)
20 done
clear
D)
25 done
clear
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question_answer 70)
If \[x\] satisfies \[|x-1|+|x-2|+|x-3|\,\,\,\ge 6\], then
A)
\[0\le 0\le 4\] done
clear
B)
\[x\le 0\,\,or\,\,x\ge 4\] done
clear
C)
\[x\le -2\,\,or\,\,x\ge 4\] done
clear
D)
\[x\ge -2\,\,or\,\,x\le 4\] done
clear
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question_answer 71)
If \[a+b+c=0\], the value of \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}\]is
A)
1 done
clear
B)
0 done
clear
C)
- 1 done
clear
D)
3 done
clear
View Solution play_arrow
question_answer 72)
Which one of the following statements is correct?
A)
The set of natural numbers has the distributive property of multiplication over subtraction done
clear
B)
The set of natural number is associative under subtraction done
clear
C)
The set of integers is not distributive under multiplication done
clear
D)
The set of natural number is finite done
clear
View Solution play_arrow
question_answer 73)
If \[{{2}^{x}}-{{2}^{x-1}}=4\], then \[{{x}^{x}}\] is equal to
A)
7 done
clear
B)
3 done
clear
C)
27 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 74)
A number other than one which is either divisible by 1 or itself is called a
A)
composite number done
clear
B)
prime number done
clear
C)
comprise number done
clear
D)
none of these done
clear
View Solution play_arrow
question_answer 75)
If \[x=2,\,y=3\], then \[{{x}^{2}}+{{y}^{3}}\]is equal to
A)
30 done
clear
B)
37 done
clear
C)
33 done
clear
D)
31 done
clear
View Solution play_arrow
question_answer 76)
If \[f(x)=\frac{{{x}^{2}}-5x+6}{x-2}\] ,\[x\ne 2\]then \[f(3)\] is equal to
A)
8 done
clear
B)
6 done
clear
C)
2 done
clear
D)
0 done
clear
View Solution play_arrow
question_answer 77)
The value of \[k\] for which the roots of equation \[(x-1)(x-5)+k=0\] differ by 2 is
A)
3 done
clear
B)
6 done
clear
C)
\[-3\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
question_answer 78)
The value of the expression\[\sqrt{6+\sqrt{6+\sqrt{6+....+upto\,\,\infty \,\,}}}\] is
A)
2 done
clear
B)
3 done
clear
C)
30 done
clear
D)
5 done
clear
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question_answer 79)
A lady has only 25 paise and 50-paise coins in her purse. She has a total of 120 coins and the total amount is Rs. 50. The number of coins of each type in her purse, respectively, is
A)
90, 30 done
clear
B)
60, 60 done
clear
C)
40, 80 done
clear
D)
70, 50 done
clear
View Solution play_arrow
question_answer 80)
The largest angle of a triangle is twice the sum of the other two and the smallest one is one fourth of the largest. The agles are
A)
\[120{}^\circ ,\text{ }40{}^\circ ,\text{ }20{}^\circ \] done
clear
B)
\[120{}^\circ ,\text{ }30{}^\circ ,\text{ }30{}^\circ \] done
clear
C)
\[90{}^\circ ,\text{ }45{}^\circ ,\text{ }45{}^\circ \] done
clear
D)
\[~90{}^\circ ,\text{ }60{}^\circ ,\text{ }30{}^\circ \] done
clear
View Solution play_arrow
question_answer 81)
Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will start ringing together after
A)
6 minutes done
clear
B)
12 minutes done
clear
C)
18 minutes done
clear
D)
24 minutes done
clear
View Solution play_arrow
question_answer 82)
A leap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of coconuts in the leap is
A)
11 done
clear
B)
21 done
clear
C)
31 done
clear
D)
41 done
clear
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question_answer 83)
If one root of \[{{x}^{2}}-4x+k=0\] is 6, then the value of k is
A)
12 done
clear
B)
2 done
clear
C)
-2 done
clear
D)
-12 done
clear
View Solution play_arrow
question_answer 84)
The number \[{{10}^{n}}-1\] is divisible by 11 for
A)
odd values of n done
clear
B)
even values of n done
clear
C)
all values of n done
clear
D)
n, a multiple of 11 done
clear
View Solution play_arrow
question_answer 85)
It costs Rs. 10 a kilometer to fly and Rs. 2 a kilometer to drive. If one travels 200 km covering fi \[x\] km of the distance by flying and the rest by driving, then the cost of the trip is
A)
Rs. 2,000 done
clear
B)
Rs. 24,000 done
clear
C)
Rs. (8\[x\] + 400) done
clear
D)
Rs. (12\[x\] + 400) done
clear
View Solution play_arrow
question_answer 86)
For the equation\[|x{{|}^{2}}+|x|-6=0\]
A)
there is only one root done
clear
B)
the sum of the roots is 1 done
clear
C)
the sum of the roots is 0 done
clear
D)
the product of the roots is 4 done
clear
View Solution play_arrow
question_answer 87)
If \[A=\{x:{{x}^{2}}-3x+2=0\}\]and \[B=\{x:{{x}^{2}}+4x-5=0\}\] then the value of A - B is
A)
\[\{1,2\}\] done
clear
B)
{2} done
clear
C)
\[\{1\}\] done
clear
D)
{5, 2} done
clear
View Solution play_arrow
question_answer 88)
The value of\[\frac{{{x}^{a+b}}.{{x}^{b+c}}.{{x}^{c+a}}}{{{({{x}^{a}}.{{x}^{b}}.{{x}^{c}})}^{2}}}\]
A)
\[{{x}^{2}}\] done
clear
B)
\[{{x}^{a+b+c}}\] done
clear
C)
\[{{x}^{abc}}\] done
clear
D)
\[{{x}^{0}}\] done
clear
View Solution play_arrow
question_answer 89)
The H.C.F. of 608, 544; 638, 783; and 425, 476 respectively is
A)
32,29, 17 done
clear
B)
17,32, 29 done
clear
C)
29,32, 17 done
clear
D)
32,17,29 done
clear
View Solution play_arrow
question_answer 90)
If one root of the equation \[3{{x}^{2}}-9x=kx-k\] is 2,then the value of k is
A)
4 done
clear
B)
3 done
clear
C)
- 6 done
clear
D)
- 8 done
clear
View Solution play_arrow
question_answer 91)
If the expression\[(125-{{x}^{3}}=(5-x)({{x}^{2}}+ax+b)\], then the value of 'a' is
A)
4 done
clear
B)
2 done
clear
C)
- 7 done
clear
D)
5 done
clear
View Solution play_arrow
question_answer 92)
The value of \[x\] satisfying the equation\[{{x}^{2}}+{{p}^{2}}={{(q-x)}^{2}}\] is
A)
\[\frac{{{p}^{2}}-{{q}^{2}}}{2}\] done
clear
B)
\[\frac{{{q}^{2}}-{{p}^{2}}}{2q}\] done
clear
C)
\[\frac{{{q}^{2}}-{{p}^{2}}}{2}\] done
clear
D)
\[\frac{{{p}^{2}}-{{q}^{2}}}{2q}\] done
clear
View Solution play_arrow
question_answer 93)
The equations \[3x-5y+2=0\] and \[6x+4=10y\] have
A)
No solution(s) done
clear
B)
A single solution done
clear
C)
Two solutions done
clear
D)
An infinite number of solutions done
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View Solution play_arrow
question_answer 94)
If \[\alpha \] and \[\beta \] be the roots of the equation \[{{x}^{2}}+px+q=0\], then the equation whose roots are \[{{\alpha }^{2}}+\alpha \beta \]and \[{{\beta }^{2}}+\alpha \beta \]is
A)
\[{{x}^{2}}+{{p}^{2}}x+{{P}^{2}}q=0\] done
clear
B)
\[{{x}^{2}}-{{q}^{2}}x+{{P}^{2}}q=0\] done
clear
C)
\[{{x}^{2}}+{{q}^{2}}x+{{P}^{2}}q=0\] done
clear
D)
\[{{x}^{2}}-{{p}^{2}}x+{{P}^{2}}q=0\] done
clear
View Solution play_arrow
question_answer 95)
The solution set of the equation \[{{x}^{\frac{2}{3}}}+{{x}^{\frac{1}{3}}}=2\] is
A)
\[\{-8,1\}\] done
clear
B)
{8,1} done
clear
C)
\[\text{ }\!\!\{\!\!\text{ 1},-\text{1}\}\] done
clear
D)
\[\{2,-2\}\] done
clear
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question_answer 96)
A student walks from his house at 4 km per hour and reaches his school late by 5 minutes. If his speed has been 5 km per hour then he would have reached 10 minutes early. The distance of the school from his house is
A)
\[\frac{5}{3}\]km done
clear
B)
5 km done
clear
C)
6 km done
clear
D)
4 km done
clear
View Solution play_arrow
question_answer 97)
The v.lu. of \[\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right).......\left( 1-\frac{1}{n} \right)\] is equal to
A)
\[\frac{1}{n}\] done
clear
B)
\[\frac{2}{n}\] done
clear
C)
\[\frac{3}{n}\] done
clear
D)
\[\frac{4}{n}\] done
clear
View Solution play_arrow
question_answer 98)
The equations representing in the adjoining graph are
A)
\[7x+2y=11;y-2x=3\] done
clear
B)
\[2x+7y=11;\,5x+\frac{35}{2}y=25\] done
clear
C)
\[3x-7y=10\,;8y-6x=4\] done
clear
D)
\[3x-4y=1\,;8y-6x=4\] done
clear
View Solution play_arrow
question_answer 99)
Factors of \[4{{x}^{2}}-{{y}^{2}}+2x-2y-3xy\] are
A)
\[(x+y)(4x+y-2)\] done
clear
B)
\[(x-y)(4x-y+2)\] done
clear
C)
\[(x+y)(4x-y-2)\] done
clear
D)
\[(xy+2)\] done
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View Solution play_arrow
question_answer 100)
If one factor of the expression \[{{x}^{3}}+7k{{x}^{2}}-4kx+12\]is \[(x+3)\], then the value of k is
A)
5 done
clear
B)
\[\frac{1}{5}\] done
clear
C)
\[-\frac{13}{17}\] done
clear
D)
\[-\frac{17}{13}\] done
clear
View Solution play_arrow
question_answer 101)
If \[f(x)=5x-10\]is divided by \[x-\sqrt{2}\], then the remainder will be
A)
a non-zero rational number done
clear
B)
an irrational number done
clear
C)
zero done
clear
D)
\[f\left( \frac{1}{\sqrt{2}} \right)\] done
clear
View Solution play_arrow
question_answer 102)
The value of m, in order that \[{{x}^{2}}-mx-2\] is the quotient when \[{{x}^{3}}+3{{x}^{2}}-4\]is divided by\[x+2\], is
A)
- 1 done
clear
B)
1 done
clear
C)
0 done
clear
D)
- 2 done
clear
View Solution play_arrow
question_answer 103)
The H.C.F. of two expressions is x and their L.C.M. is \[{{x}^{3}}-9x\]. If one of the expression is \[{{x}^{2}}+3x\], then the other expression is
A)
\[{{x}^{2}}-3x\] done
clear
B)
\[{{x}^{3}}-3x\] done
clear
C)
\[{{x}^{2}}+9x\] done
clear
D)
\[{{x}^{2}}-9x\] done
clear
View Solution play_arrow
question_answer 104)
If \[f(x)=2{{x}^{2}}-x+1\] and \[g(x)={{x}^{3}}-3x+1\] then the value of \[f(1)+g(-1)\] is
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
View Solution play_arrow
question_answer 105)
The smallest integral value of \[x\], for which \[\frac{5}{x}\] is an integer is
A)
1 done
clear
B)
- 1 done
clear
C)
- 5 done
clear
D)
5 done
clear
View Solution play_arrow
question_answer 106)
The factors of \[(2{{x}^{2}}-3x-2)(2{{x}^{2}}-3x)-63\]are
A)
\[(x-3)(2x+3)(x-1)(x-7)\] done
clear
B)
\[(x+3)(2x-3)(x-1)(x-7)\] done
clear
C)
\[(x+3)(2x+3)(2{{x}^{2}}-3x+7)\] done
clear
D)
\[(x-3)(2x+3)(2{{x}^{2}}-3x+7)\] done
clear
View Solution play_arrow
question_answer 107)
A man's age is six times that of his son's age. In six years the father's age will be three times of the son's age. The age of the father and the son are respectively
A)
18, 3 done
clear
B)
30, 5 done
clear
C)
24, 4 done
clear
D)
42, 7 done
clear
View Solution play_arrow
question_answer 108)
The remainder when \[{{x}^{3}}-6{{x}^{2}}+11x-6\] is divided by\[x+2\] is
A)
- 60 done
clear
B)
- 39 done
clear
C)
31 done
clear
D)
45 done
clear
View Solution play_arrow
question_answer 109)
The remainder when \[{{x}^{6}}-3{{x}^{5}}+2{{x}^{2}}+8\] is divided by \[x+1\] is
A)
24 done
clear
B)
14 done
clear
C)
8 done
clear
D)
18 done
clear
View Solution play_arrow
question_answer 110)
The value of k for which (\[x+1\]) is a factor of\[{{x}^{3}}-k{{x}^{2}}+11x-6\]is
A)
- 5 done
clear
B)
2 done
clear
C)
6 done
clear
D)
- 6 done
clear
View Solution play_arrow
question_answer 111)
The value of k for which x + k is a factor of \[k{{x}^{2}}-2x+k+4\]is
A)
\[\frac{-4}{3}\] done
clear
B)
-5 done
clear
C)
2 done
clear
D)
\[\frac{6}{7}\] done
clear
View Solution play_arrow
question_answer 112)
The L.C.M. of \[2x+2,\,3{{x}^{2}}-12\] and \[4{{x}^{2}}+12x+8\] is
A)
\[12(x+1)(x-3)(x+2)\] done
clear
B)
\[12(x+1)(x-2)(x+3)\] done
clear
C)
\[12(x+1)(x-3)(x+3)\] done
clear
D)
\[12(x+1)(x+2)(x+2)\] done
clear
View Solution play_arrow
question_answer 113)
If\[x-\frac{1}{x}=9\], the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] is
A)
83 done
clear
B)
79 done
clear
C)
11 done
clear
D)
7 done
clear
View Solution play_arrow
question_answer 114)
The product of the reciprocal of \[\frac{x+3}{x+2}\]and \[\frac{{{x}^{2}}-4}{{{x}^{2}}-9}\] is
A)
\[\frac{1}{(x-3)(x-2)}\] done
clear
B)
\[\frac{x-2}{x-3}\] done
clear
C)
\[\frac{x-3}{x-2}\] done
clear
D)
\[(x-3)(x-2)\] done
clear
View Solution play_arrow
question_answer 115)
The value of k, if the roots of the equation \[2k{{x}^{2}}+2kx+2=0\] are equal is
A)
\[\frac{4}{5}\] done
clear
B)
4 done
clear
C)
1 done
clear
D)
0 done
clear
View Solution play_arrow
question_answer 116)
If one root of the equation \[{{x}^{2}}-12x+3k=0\]is square of the other, then k is
A)
3 done
clear
B)
9 done
clear
C)
6 done
clear
D)
12 done
clear
View Solution play_arrow
question_answer 117)
If one root of the quadratic equation is \[\sqrt{3}+1\] the equation is
A)
\[{{x}^{2}}-2x-\sqrt{3}=0\] done
clear
B)
\[{{x}^{2}}-2\sqrt{3}x+2=0\] done
clear
C)
\[{{x}^{2}}-2x-2=0\] done
clear
D)
\[{{x}^{2}}+2\sqrt{3}x+23=0\] done
clear
View Solution play_arrow
question_answer 118)
It k be the ratio of the roots of the equation\[{{x}^{2}}-px+q=0\]the value of \[\frac{k}{1+{{k}^{2}}}\] is
A)
\[\frac{{{q}^{2}}-2p}{p}\] done
clear
B)
\[\frac{q}{{{p}^{2}}-2q}\] done
clear
C)
\[\frac{p}{{{q}^{2}}-2p}\] done
clear
D)
\[\frac{p}{{{p}^{2}}-2q}\] done
clear
View Solution play_arrow
question_answer 119)
If sum of the roots is p and the sum of their squares is\[{{\text{q}}^{\text{2}}}\], the equation is
A)
\[{{x}^{2}}-px+{{p}^{2}}{{q}^{3}}=0\] done
clear
B)
\[{{x}^{2}}-px+{{q}^{3}}=0\] done
clear
C)
\[{{x}^{2}}-px+\frac{{{p}^{2}}-{{q}^{2}}}{2}=0\] done
clear
D)
none of these done
clear
View Solution play_arrow
question_answer 120)
If \[a,b,c\in R\], then the roots of the equation\[(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0\] are equal if and only if
A)
\[a=0,b=1,c=1\] done
clear
B)
\[a=b=c\] done
clear
C)
a = 1, b = 0, c = 1 done
clear
D)
\[a\ne 1,b=1,c=1\] done
clear
View Solution play_arrow
question_answer 121)
A student divided a number by two when he was required to multiply it by 2. The answer he got was 2. The correct answer should have been
A)
8 done
clear
B)
12 done
clear
C)
6 done
clear
D)
4 done
clear
View Solution play_arrow
question_answer 122)
A number consists of two digits. The sum of the digits is 11, reversing the digits, the number decreases by 45. The number is
A)
38 done
clear
B)
65 done
clear
C)
74 done
clear
D)
83 done
clear
View Solution play_arrow
question_answer 123)
The perimeter of a rectangular plot is 48 m and its area is 108 m2. The dimensions of the plot are
A)
12 and 9 done
clear
B)
18 and 6 done
clear
C)
27 and 4 done
clear
D)
36 and 3 done
clear
View Solution play_arrow
question_answer 124)
For a journey the cost of a child ticket is \[\frac{1}{3}\]rd of the cost of an adult ticket. If the cost of tickets for 4 adults and 5 children is Rs. 85, the cost of a child ticket is
A)
Rs. 5 done
clear
B)
Rs. 6 done
clear
C)
Rs. 10 done
clear
D)
Rs. 15 done
clear
View Solution play_arrow
question_answer 125)
The equations \[3x-5y+2=0\] and \[6x+4=10y\] have
A)
an infinite number of solutions done
clear
B)
no solution done
clear
C)
two solutions done
clear
D)
a single solution done
clear
View Solution play_arrow
question_answer 126)
The value of \[{{x}^{2}}-6x+13\]can never be less than
A)
5 done
clear
B)
4 done
clear
C)
6 done
clear
D)
13 done
clear
View Solution play_arrow
question_answer 127)
The value of \[18-|-7|-|11-22|\]is equal to
A)
58 done
clear
B)
0 done
clear
C)
41 done
clear
D)
28 done
clear
View Solution play_arrow
question_answer 128)
\[\frac{(\log x-\log y)(\log {{x}^{2}}+\log {{y}^{2}})}{(\log {{x}^{2}}-\log {{y}^{2}})(\log x+\log y)}\]
A)
0 done
clear
B)
1 done
clear
C)
\[\log \frac{x}{y}\] done
clear
D)
\[\log xy\] done
clear
View Solution play_arrow
question_answer 129)
If \[{{\log }_{10}}(2{{x}^{2}}+7x+16)=1\], the value of \[x\] is
A)
\[-2\,or\frac{3}{2}\] done
clear
B)
\[-2\,or-\frac{3}{2}\] done
clear
C)
\[-2\,or\frac{2}{3}\] done
clear
D)
\[2\,or\frac{3}{2}\] done
clear
View Solution play_arrow
question_answer 130)
Given log 6 and log 8, then the only logarithm that cannot be obtained without using the table is
A)
log 64 done
clear
B)
log 21 done
clear
C)
\[\log \frac{8}{3}\] done
clear
D)
log 9 done
clear
View Solution play_arrow
question_answer 131)
The value of x and y respectively in the simultaneous equations\[2x-\frac{3}{y}=12\,\,and\,\,5x+\frac{7}{y}=1,y\ne 0\] is
A)
\[2,-\frac{1}{3}\] done
clear
B)
\[3,-\frac{1}{2}\] done
clear
C)
\[-3,\frac{1}{2}\] done
clear
D)
\[-2,\frac{1}{3}\] done
clear
View Solution play_arrow
question_answer 132)
For all \[a>0,b>0,c>0\]\[\log ({{a}^{a}}{{b}^{b}}{{c}^{c}})+\log \left( \frac{1}{abc} \right)\]is equal to
A)
\[\log ({{a}^{a+1}}{{b}^{b+1}}{{c}^{c+1}})\] done
clear
B)
\[\log \left( {{a}^{a}}{{b}^{b}}{{c}^{c}}+\frac{1}{abc} \right)\] done
clear
C)
\[\log ({{a}^{a-1}}{{b}^{b-1}}{{c}^{c-1}})\] done
clear
D)
\[\log a+\log b+\log c\] done
clear
View Solution play_arrow
question_answer 133)
If \[{{\log }_{10}}[{{\log }_{10}}(\log _{10}^{x})]=0\], then
A)
\[x={{10}^{3}}\] done
clear
B)
\[x={{10}^{10}}\] done
clear
C)
\[x={{10}^{5}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 134)
If \[f(x)=\log \left( \frac{1+x}{1-x} \right)\], then \[f\left( \frac{2x}{1+{{x}^{2}}} \right)\]is equal to
A)
\[2f(x)\] done
clear
B)
\[f(2x)\] done
clear
C)
\[2f(-x)\] done
clear
D)
\[f(x)\] done
clear
View Solution play_arrow
question_answer 135)
A farmer divides his herd of n cows among his four sons so that one son gets one-half the herd, the second, one-fourth, the third son, one-fifth and the fourth, 7 cows, then n is
A)
180 done
clear
B)
140 done
clear
C)
240 done
clear
D)
100 done
clear
View Solution play_arrow
question_answer 136)
The sum of two numbers is 20; their product is 40. The sum of their reciprocals is
A)
\[\frac{1}{10}\] done
clear
B)
4 done
clear
C)
2 done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
question_answer 137)
Consider the following statements : The system of equations \[2x-y=4\] and \[px-y=q\]
\[\text{I}\]has a unique solution if \[p\ne 2\]. \[\text{II}\]has infinitely many solutions if p = 2, q = 4 of these statements :
A)
\[\text{I}\] alone is correct. done
clear
B)
\[\text{II}\] alone is correct. done
clear
C)
\[\text{I}\] and \[\text{II}\] are correct. done
clear
D)
\[\text{I}\] and \[\text{II}\] are false. done
clear
View Solution play_arrow
question_answer 138)
If the roots of \[{{x}^{2}}-2mx+{{m}^{2}}-1=0\]lie between - 2 and 4, then
A)
\[-3\le m\le 4\] done
clear
B)
\[-3\le m\le 5\] done
clear
C)
\[-1\le m\le 5\] done
clear
D)
\[-1\le m\le 3\] done
clear
View Solution play_arrow
question_answer 139)
The value of \[7{{\log }_{a}}\frac{16}{15}+5{{\log }_{a}}\frac{25}{24}+3{{\log }_{a}}\frac{81}{80}\] is
A)
\[\log _{a}^{3}\] done
clear
B)
\[\log _{a}^{1}\] done
clear
C)
\[\log _{a}^{2}\] done
clear
D)
\[\log _{a}^{5}\] done
clear
View Solution play_arrow
question_answer 140)
\[\log ({{x}^{2}})+\log ({{y}^{2}})\]is equal to
A)
\[\log ({{x}^{2}}+{{y}^{2}})\] done
clear
B)
\[2\log (xy)\] done
clear
C)
\[2\log (x+y)\] done
clear
D)
\[\log \frac{{{x}^{2}}}{{{y}^{2}}}\] done
clear
View Solution play_arrow
question_answer 141)
If \[{{\log }_{8}}m+{{\log }_{8}}\frac{1}{6}=\frac{2}{3}\], then m is equal to
A)
12 done
clear
B)
48 done
clear
C)
18 done
clear
D)
24 done
clear
View Solution play_arrow
question_answer 142)
If \[{{\log }_{2}}({{x}^{3}}+{{x}^{2}})-{{\log }_{2}}(x+1)=5\], then \[{{\log }_{2}}x\] is
A)
\[\frac{5}{2}\] done
clear
B)
\[\frac{2}{5}\] done
clear
C)
5 done
clear
D)
2 done
clear
View Solution play_arrow
question_answer 143)
What is the condition for the roots of \[a{{x}^{2}}+bx+c=0\]to be in the ratio of p : q ?
A)
\[{{a}^{2}}{{c}^{2}}(p+q)={{p}^{2}}{{q}^{2}}b\] done
clear
B)
\[ac{{(p+q)}^{2}}=pq{{b}^{2}}\] done
clear
C)
\[pq{{(a+c)}^{2}}=pq{{b}^{2}}\] done
clear
D)
\[{{p}^{2}}{{q}^{2}}(a+c)={{a}^{2}}{{c}^{2}}b\] done
clear
View Solution play_arrow
question_answer 144)
The sum of the roots of \[\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}\]is zero. The product of the roots is
A)
\[-\frac{1}{2}({{a}^{2}}+{{b}^{2}})\] done
clear
B)
0 done
clear
C)
\[\frac{1}{2}(a+b)\] done
clear
D)
\[2({{a}^{2}}+{{b}^{2}})\] done
clear
View Solution play_arrow
question_answer 145)
One root of the equation \[a{{x}^{2}}+bx+c=0\] is square of the other if
A)
\[{{a}^{2}}c+{{b}^{3}}+a{{c}^{2}}=3abc\] done
clear
B)
\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] done
clear
C)
\[{{b}^{2}}c+{{c}^{2}}a+{{a}^{2}}b=abc\] done
clear
D)
\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca=0\] done
clear
View Solution play_arrow
question_answer 146)
The ratio of the ages of A and B ten years before was 3 : 5. The ratio of their present ages is 2 : 3. Their ages are respectively
A)
30, 50 done
clear
B)
20,30 done
clear
C)
40, 60 done
clear
D)
16, 24 done
clear
View Solution play_arrow
question_answer 147)
If a and b are any two such real numbers that ab = 0, then
A)
a =0, \[b\ne 0\] done
clear
B)
b=0, \[a\ne 0\] done
clear
C)
a = 0 or b = 0 or both done
clear
D)
a =b and b=0 done
clear
View Solution play_arrow
question_answer 148)
The value of \[{{(256)}^{0.16}}\times {{(256)}^{0.09}}\] is
A)
64 done
clear
B)
256.25 done
clear
C)
16 done
clear
D)
4 done
clear
View Solution play_arrow
question_answer 149)
If the roots of the equation \[a{{x}^{2}}+bx+c=0\] are reciprocal of each other; then
A)
a = b done
clear
B)
a = c done
clear
C)
b = c done
clear
D)
a = 0 done
clear
View Solution play_arrow
question_answer 150)
The value of k for which \[{{x}^{2}}-4x+k=0\] has coincident roots, is
A)
4 done
clear
B)
- 4 done
clear
C)
0 done
clear
D)
- 2 done
clear
View Solution play_arrow
question_answer 151)
\[{{9}^{\frac{3}{2}}}\div {{(243)}^{\frac{-2}{3}}}\]simplifies to
A)
\[{{3}^{\frac{10}{3}}}\] done
clear
B)
\[{{3}^{\frac{19}{3}}}\] done
clear
C)
\[{{3}^{\frac{1}{3}}}\] done
clear
D)
\[{{3}^{19}}\] done
clear
View Solution play_arrow
question_answer 152)
The solution of \[{{(25)}^{x-2}}={{(125)}^{2x-4}}\] is
A)
\[\frac{3}{4}\] done
clear
B)
0 done
clear
C)
2 done
clear
D)
\[-2\] done
clear
View Solution play_arrow
question_answer 153)
If \[{{a}^{x}}={{b}^{y}}={{c}^{z}}\]and \[\frac{b}{a}=\frac{c}{b}\], then \[\frac{2z}{x+z}\]is equal to
A)
\[\frac{y}{x}\] done
clear
B)
\[\frac{x}{y}\] done
clear
C)
\[\frac{x}{z}\] done
clear
D)
\[\frac{z}{x}\] done
clear
View Solution play_arrow
question_answer 154)
The condition that the roots of the equation \[l{{x}^{2}}+mx+n=0\] may be in the ratio 3: 4 is
A)
\[14{{n}^{2}}=49ml\] done
clear
B)
\[{{m}^{2}}=9nl\] done
clear
C)
\[12{{m}^{2}}=49nl\] done
clear
D)
\[4{{l}^{2}}=49nl\] done
clear
View Solution play_arrow
question_answer 155)
The condition for the roots of equation\[{{x}^{2}}-lx+m=0\] to differ by one is
A)
\[{{l}^{2}}=4m+1\] done
clear
B)
\[{{l}^{2}}+{{m}^{2}}=1\] done
clear
C)
\[{{m}^{2}}=4l+1\] done
clear
D)
\[l=m+1\] done
clear
View Solution play_arrow
question_answer 156)
Find k if one root of the equation \[{{x}^{2}}-6kx+8=0\] is twice the other.
A)
2 done
clear
B)
± 1 done
clear
C)
\[\pm \frac{1}{2}\] done
clear
D)
3 done
clear
View Solution play_arrow
question_answer 157)
If \[\alpha ,\beta \] are the roots of \[3{{x}^{2}}-4x+1=0\] the equation whose roots are\[\frac{\alpha }{\beta },\frac{\beta }{\alpha }\] is
A)
\[3{{x}^{2}}+10x+3=0\] done
clear
B)
\[3{{x}^{2}}+10x-3=0\] done
clear
C)
\[3{{x}^{2}}-10x-3=0\] done
clear
D)
\[3{{x}^{2}}-10x+3=0\] done
clear
View Solution play_arrow
question_answer 158)
The solution of the equation \[{{3}^{1+x}}+{{7}^{1-x}}=50\]is
A)
0 done
clear
B)
2 done
clear
C)
± 1 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 159)
The value of \[\frac{x+y+z}{{{x}^{-1}}{{y}^{-1}}+{{y}^{-1}}{{z}^{-1}}+{{z}^{-1}}{{x}^{-1}}}\] is
A)
\[\frac{1}{xyz}\] done
clear
B)
\[\frac{1}{xy}+\frac{1}{yz}+\frac{1}{xz}\] done
clear
C)
\[xyz\] done
clear
D)
\[xy+yz+zx\] done
clear
View Solution play_arrow
question_answer 160)
If \[x\] be real and positive, then the value of\[y=x+\frac{1}{x}\] satisfies
A)
\[0<y\le 0.5\] done
clear
B)
\[0.5<y\le 1\] done
clear
C)
\[1<y<2\] done
clear
D)
\[y\ge 2\] done
clear
View Solution play_arrow
question_answer 161)
If \[2x+y=3,xy=1\], then the value of \[8{{x}^{3}}+{{y}^{3}}\]is
A)
16 done
clear
B)
9 done
clear
C)
4 done
clear
D)
1 done
clear
View Solution play_arrow
question_answer 162)
a + b is a factor of
A)
\[{{a}^{4}}({{b}^{2}}-{{c}^{2}})+{{b}^{4}}({{c}^{2}}-{{b}^{2}})+{{c}^{4}}({{a}^{2}}-{{b}^{2}})\] done
clear
B)
\[a{{(b-c)}^{3}}+b{{(c-a)}^{3}}+c{{(a-b)}^{3}}\] done
clear
C)
\[{{(a+b+c)}^{3}}-{{(b+c-a)}^{3}}-{{(c+a-b)}^{3}}-{{(a+b-c)}^{3}}\] done
clear
D)
\[a({{b}^{4}}-{{c}^{4}})+b({{c}^{4}}-{{a}^{4}})+c({{a}^{4}}+{{b}^{4}})\] done
clear
View Solution play_arrow
question_answer 163)
The roots of the equation \[\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}\]are
A)
\[\frac{3}{13},\frac{2}{13}\] done
clear
B)
\[\frac{13}{6},\frac{11}{6}\] done
clear
C)
\[\frac{9}{13},\frac{4}{13}\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 164)
The roots of the equation \[{{x}^{-2}}+{{x}^{-1}}=12\] are
A)
\[\frac{1}{2},\frac{1}{3}\] done
clear
B)
\[\frac{1}{3},-\frac{1}{4}\] done
clear
C)
3, - 3 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 165)
The roots of the equation \[\sqrt{3y+1}=\sqrt{y-1}\] are
A)
0, - 1 done
clear
B)
2, 3 done
clear
C)
2, 1 done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 166)
State which of the following statements is true \[{{2}^{16}}-1\] is divisible by
A)
11 done
clear
B)
13 done
clear
C)
17 done
clear
D)
19 done
clear
View Solution play_arrow
question_answer 167)
State which of the following statements is true. For every integer \[n,(n+1)(n+2)\] is divisible by
A)
7 done
clear
B)
6 done
clear
C)
9 done
clear
D)
12 done
clear
View Solution play_arrow
question_answer 168)
\[a,b,c(a>c)\]are three digits from left to right, of a three digits number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digits 4 in its unit place. The other two digits from left to right are
A)
5 and 4 done
clear
B)
5 and 9 done
clear
C)
4 and 5 done
clear
D)
9 and 5 done
clear
View Solution play_arrow
question_answer 169)
If \[x+2\] is factor of \[{{\{{{(x+1)}^{5}}+2x+K)}^{3}}\}\], then the value of 'K' is
A)
1 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
View Solution play_arrow
question_answer 170)
The remainder obtained by dividing \[{{x}^{n}}-\frac{a}{b}\]by\[ax-b\] is
A)
\[\frac{{{b}^{n+1}}-{{a}^{n+1}}}{{{a}^{n-1}}.b}\] done
clear
B)
\[\frac{{{a}^{n}}-{{b}^{n}}}{ab}\] done
clear
C)
\[\frac{{{a}^{n}}-{{b}^{n}}}{{{a}^{n}}{{b}^{n}}}\] done
clear
D)
\[\frac{{{a}^{n+1}}-{{b}^{n+1}}}{a{{b}^{n}}}\] done
clear
View Solution play_arrow
question_answer 171)
HCF of\[6{{x}^{2}}y(x-y)({{x}^{2}}+xy+{{y}^{2}}),18x{{y}^{2}}{{(x-y)}^{2}}\] and \[12x(x-y)\]is
A)
\[6x(x-y)\] done
clear
B)
\[6(x-y)\] done
clear
C)
\[6x\] done
clear
D)
\[x(x-y)\] done
clear
View Solution play_arrow
question_answer 172)
LCM of the polynomials \[{{x}^{3}}y-x{{y}^{3}},\]\[{{x}^{4}}-2{{x}^{2}}{{y}^{2}}+{{y}^{4}}\]and\[{{x}^{4}}-{{y}^{4}}\]
A)
\[xy({{x}^{2}}-{{y}^{2}}){{(x+y)}^{2}}(x-y)\] done
clear
B)
\[xy({{x}^{2}}+{{y}^{2}}){{(x-y)}^{2}}{{(x+y)}^{2}}\] done
clear
C)
\[xy({{x}^{2}}+{{y}^{2}}){{(x-y)}^{2}}(x+y)\] done
clear
D)
\[xy({{x}^{2}}+{{y}^{2}})(x-y)(x+y)\] done
clear
View Solution play_arrow
question_answer 173)
The sum of a number and its reciprocal is \[\frac{125}{22}\]The number is
A)
\[\frac{2}{11}\] done
clear
B)
\[\frac{1}{11}\] done
clear
C)
\[\frac{3}{11}\] done
clear
D)
None of these done
clear
View Solution play_arrow
question_answer 174)
If \[x=\frac{y}{{{(1+p)}^{q}}}\],then o is equal to
A)
\[\log \left[ \frac{\frac{y}{x}}{1+p} \right]\] done
clear
B)
\[\frac{\log \left( \frac{y}{x} \right)}{\log (1+p)}\] done
clear
C)
\[\frac{\log (y-x)}{\log (1+p)}\] done
clear
D)
\[\frac{\log (y-x)}{\log (1+p)}\] done
clear
View Solution play_arrow
question_answer 175)
If \[x\] and y are any two positive real numbers then \[x<y\] implies,
A)
\[-x<-y\] done
clear
B)
\[-x>-y\] done
clear
C)
\[\frac{1}{x}>\frac{1}{y}\] done
clear
D)
\[-\frac{1}{x}>\frac{1}{y}\] done
clear
View Solution play_arrow
question_answer 176)
If a and b are any two real numbers such that\[ab=0\]
A)
a = 0 and b=0 done
clear
B)
a = 0 or b = 0 or both done
clear
C)
a = 0 and \[b\ne 0\] done
clear
D)
\[a\ne 0\] and b = 0 done
clear
View Solution play_arrow
question_answer 177)
\[{{x}^{2}}+4x>2x+8\] is true when
A)
\[x>\,or\,x<-2\] done
clear
B)
\[x>4\,\,or\,x<2\] done
clear
C)
\[x>2\,\,or\,x<-4\] done
clear
D)
\[x>-2\,\,or\,x<4\] done
clear
View Solution play_arrow
question_answer 178)
If \[y=\frac{{{x}^{2}}-2x+4}{{{x}^{2}}+2x+4}\]where \[x\]can take real values, then
A)
\[\frac{1}{3}\le y\le 3\] done
clear
B)
\[3<y\le 5\] done
clear
C)
\[5<y\le 7\] done
clear
D)
\[7<y\le 9\] done
clear
View Solution play_arrow
question_answer 179)
Solution of the equations\[\frac{x+3}{4}+\frac{2y+9}{3}=3\]and \[\frac{2x-1}{2}-\frac{y+3}{4}=4\frac{1}{2}\]
A)
\[x=-5,y=-3\] done
clear
B)
\[x=-5,y=3\] done
clear
C)
\[x=5,y=3\] done
clear
D)
\[x=5,y=-3\] done
clear
View Solution play_arrow
question_answer 180)
If \[{{(3)}^{x+y}}=81\] and \[{{(81)}^{x-y}}=3\], then the values of \[x\] and y are
A)
\[\frac{17}{8},\frac{9}{8}\] done
clear
B)
\[\frac{17}{8},\frac{11}{8}\] done
clear
C)
\[\frac{17}{8},\frac{15}{8}\] done
clear
D)
\[\frac{11}{8},\frac{15}{8}\] done
clear
View Solution play_arrow
question_answer 181)
The value of \[{{(625)}^{0.16}}\times {{(625)}^{0.09}}\]is
A)
4 done
clear
B)
5 done
clear
C)
25 done
clear
D)
625 done
clear
View Solution play_arrow
question_answer 182)
What must be added to \[\frac{x}{y}\] make it\[\frac{y}{x}\] ?
A)
\[\frac{y-x}{{{y}^{2}}{{x}^{2}}}\] done
clear
B)
\[\frac{{{y}^{2}}-{{x}^{2}}}{yx}\] done
clear
C)
\[\frac{xy}{x+y}\] done
clear
D)
\[\frac{{{x}^{2}}{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\] done
clear
View Solution play_arrow
question_answer 183)
\[{{(x+y)}^{3}}-{{(x-y)}^{3}}\] can be factorised as
A)
\[2y(3{{y}^{2}}+{{x}^{2}})\] done
clear
B)
\[2y(3{{x}^{2}}+{{y}^{2}})\] done
clear
C)
\[2x(3{{x}^{2}}+{{y}^{2}})\] done
clear
D)
\[2x{{({{x}^{2}}+3y)}^{2}}\] done
clear
View Solution play_arrow
question_answer 184)
If\[x=\frac{\sqrt{2}+1}{\sqrt{2}-1},y=\frac{\sqrt{2}-1}{\sqrt{2}+1}\], then\[{{x}^{2}}+xy+{{y}^{2}}\]is equal to
A)
39 done
clear
B)
35 done
clear
C)
38 done
clear
D)
36 done
clear
View Solution play_arrow
question_answer 185)
If\[f(x)=\frac{2x+3}{x-2},x\ne 2\] and \[x\in R\], then \[\frac{f(6)}{f\left( \frac{1}{2} \right)}\]is equal to
A)
\[\frac{35}{45}\] done
clear
B)
\[\frac{-35}{45}\] done
clear
C)
\[\frac{-45}{32}\] done
clear
D)
\[\frac{45}{35}\] done
clear
View Solution play_arrow
question_answer 186)
The perimeter of a rectangle whose length is twice the breadth is 24 cm. Then the area of the rectangle is
A)
28 sq. cm done
clear
B)
32 sq. cm done
clear
C)
36 sq. cm done
clear
D)
42 sq. cm done
clear
View Solution play_arrow
question_answer 187)
If 6 kg of sugar and 5 kg of tea together cost Rs. 209 and 4 kg of sugar and 3 kg of tea together cost Rs. 131, then the cost of 1 kg sugar and 1 kg tea are respectively
A)
Rs. 11 and Rs. 25 done
clear
B)
Rs. 12 and Rs. 20 done
clear
C)
Rs. 14 and Rs. 20 done
clear
D)
Rs. 14 and Rs. 25 done
clear
View Solution play_arrow
question_answer 188)
If \[\alpha ,\beta \] are the roots of the equation \[\alpha {{x}^{2}}+bx+c=\]0, then the value of \[\frac{1}{a\alpha +b}+\frac{1}{a\beta +b}\]is
A)
\[\frac{b}{ac}\] done
clear
B)
\[\frac{a}{bc}\] done
clear
C)
\[\frac{c}{ab}\] done
clear
D)
\[\frac{bc}{a}\] done
clear
View Solution play_arrow
question_answer 189)
If \[{{x}^{2}}+7ax+40=0\] and \[{{x}^{2}}+2ax-60=0\] have a common root, then the value of a is
A)
± 1 done
clear
B)
± 2 done
clear
C)
± 3 done
clear
D)
± 4 done
clear
View Solution play_arrow
question_answer 190)
If \[x=\frac{y}{{{(1+a)}^{p}}}\], then p is equal to
A)
\[\frac{{{\log }_{e}}\left( \frac{y}{x} \right)}{{{\log }_{e}}(1+a)}\] done
clear
B)
\[\log \left\{ \frac{y}{x(1+a)} \right\}\] done
clear
C)
\[\log \left\{ \frac{y-x}{1+a} \right\}\] done
clear
D)
\[\frac{\log y}{\log \{x(1+a)\}}\] done
clear
View Solution play_arrow
question_answer 191)
If \[x\] and y are any two positive real numbers, then \[x\] > y implies
A)
\[-x>-y\] done
clear
B)
\[-x<-y\] done
clear
C)
\[\frac{1}{x}>\frac{1}{y}\] done
clear
D)
\[-\frac{1}{x}>\frac{1}{y}\] done
clear
View Solution play_arrow
question_answer 192)
10 years ago the age of the father was 5 times that of the son. 20 years hence the age of the father will be twice that of the son. The present age of the father (in years) is
A)
40 done
clear
B)
45 done
clear
C)
60 done
clear
D)
70 done
clear
View Solution play_arrow
question_answer 193)
If 14 is the maximum of- \[-\lambda {{x}^{2}}+\lambda x+8\], then the value of \[\lambda \] is
A)
24 done
clear
B)
\[6\sqrt{3}\] done
clear
C)
\[-6\sqrt{3}\] done
clear
D)
- 12 done
clear
View Solution play_arrow
question_answer 194)
The expression\[{{x}^{2}}-x-30\]is positive for
A)
no value of \[x\] done
clear
B)
all values of \[x\] between - 5 and 6 done
clear
C)
all\[x\] done
clear
D)
\[x>6\,\,or\,\,x<-5\] done
clear
View Solution play_arrow
question_answer 195)
If \[a={{2}^{\frac{2}{3}}}+{{2}^{\frac{1}{3}}}\],then
A)
\[{{a}^{3}}-6a-6=0\] done
clear
B)
\[{{a}^{3}}-6a+6=0\] done
clear
C)
\[{{a}^{3}}+6a-6=0\] done
clear
D)
\[{{a}^{3}}+6a+6=0\] done
clear
View Solution play_arrow
question_answer 196)
The system of equations \[3x-4y=12\]and \[6x-8y=48\]has
A)
2 solution done
clear
B)
1 solution done
clear
C)
infinite number of solutions done
clear
D)
no solution done
clear
View Solution play_arrow
question_answer 197)
If \[{{56}^{2}}-{{51}^{2}}=5p\], then p is equal is
A)
106 done
clear
B)
107 done
clear
C)
105 done
clear
D)
104 done
clear
View Solution play_arrow
question_answer 198)
A farmer divides his herd of \[x\] cows among his 4 sons so that one son gets one half of the herd, the second gets one-fourth, the third son gets one-fifth and the fourth gets 7 cows. Then \[x\] is
A)
100 done
clear
B)
140 done
clear
C)
0 done
clear
D)
1 done
clear
View Solution play_arrow
question_answer 199)
The graph of \[x\] = 15 is a straight line
A)
intersecting both the axes done
clear
B)
parallel to y-axis done
clear
C)
parallel to : \[x\]-axis done
clear
D)
passing through the origin done
clear
View Solution play_arrow
question_answer 200)
\[{{x}^{m}}={{x}^{n}}\Rightarrow m\]
A)
> n done
clear
B)
= n done
clear
C)
<n done
clear
D)
none of these done
clear
View Solution play_arrow
question_answer 201)
If\[2x+y=3\]and \[xy=1\], the value of\[{{(x+y)}^{x-y}}\]is
A)
100 done
clear
B)
10 done
clear
C)
0 done
clear
D)
1 done
clear
View Solution play_arrow
question_answer 202)
The smaller value of n for which\[{{x}^{2}}-2x-3\]and\[{{x}^{3}}-2{{x}^{2}}-nx-3\]have an H.C.F. involving \[x\] is
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
View Solution play_arrow
question_answer 203)
If \[2{{x}^{2}}+xy-3{{y}^{2}}+x+ay-10=\]\[(2x+3y+b)\]\[(x-y-2)\],the value of a and b are
A)
11 and 5 done
clear
B)
1 and - 5 done
clear
C)
- 1 and - 5 done
clear
D)
- 11 and 5 done
clear
View Solution play_arrow
question_answer 204)
If a-b = 3 and \[{{a}^{3}}-{{b}^{3}}=117\] then a+b is equals
A)
5 done
clear
B)
7 done
clear
C)
9 done
clear
D)
11 done
clear
View Solution play_arrow
question_answer 205)
The value of n for which the expression \[9{{x}^{4}}-12{{x}^{2}}+n{{x}^{2}}-8x+4\]becomes a perfect square is
A)
12 done
clear
B)
16 done
clear
C)
18 done
clear
D)
24 done
clear
View Solution play_arrow
question_answer 206)
The solution of\[{{64}^{2x-5}}=4\times {{8}^{x-5}}\]is
A)
\[\frac{9}{17}\] done
clear
B)
\[\frac{17}{9}\] done
clear
C)
\[\frac{17}{10}\] done
clear
D)
\[\frac{20}{9}\] done
clear
View Solution play_arrow
question_answer 207)
The value of \[\frac{{{\left( x+\frac{1}{y} \right)}^{a}}{{\left( x-\frac{1}{y} \right)}^{b}}}{{{\left( y+\frac{1}{x} \right)}^{a}}{{\left( y-\frac{1}{x} \right)}^{b}}}\]is equal to
A)
\[{{\left( \frac{x}{y} \right)}^{a+b}}\] done
clear
B)
\[{{\left( \frac{y}{x} \right)}^{a+b}}\] done
clear
C)
\[{{(xy)}^{a+b}}\] done
clear
D)
\[\frac{{{x}^{n}}}{{{y}^{b}}}\] done
clear
View Solution play_arrow
question_answer 208)
If U = Set of all triangles, X = Set of isosceles triangles, Y = Set of equilateral triangles, Z = Set of right-angled triangles, W = Set of acute- angled triangles. Then \[Y\cap W\] is
A)
U done
clear
B)
Y done
clear
C)
Z done
clear
D)
X done
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question_answer 209)
If X = (multiples of 2), Y = (multiples of 5), Z = (multiples of 10), then\[X\cap (Y\cap Z)\] is equal to
A)
multiples of 10 done
clear
B)
multiples of 5 done
clear
C)
multiples of 2 done
clear
D)
multiples of 7 done
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question_answer 210)
Three bells, toll at intervals of 36 sec, 40 sec and sec respectively. They start ringing toll at particular time. They next toll together after
A)
18 minutes done
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B)
12 minutes done
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C)
6 minutes done
clear
D)
24 minutes done
clear
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question_answer 211)
Factors of\[16{{x}^{2}}-9{{(y+2x)}^{2}}\]are
A)
\[(2x+3y)(10x+3y)\] done
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B)
\[-(2x+3y)(10x+3y)\] done
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C)
\[(2x+10y)(x+3y)\] done
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D)
\[-(2x+10y)(x+3y)\] done
clear
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question_answer 212)
The G.C.D. of two whole numbers is 5 and their L.C.M. is 60. If one of the number is 20, then the other number would be
A)
25 done
clear
B)
13 done
clear
C)
16 done
clear
D)
15 done
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question_answer 213)
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is
A)
1 done
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B)
2 done
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C)
3 done
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D)
4 done
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question_answer 214)
Let\[f(x)=g(x)q(x)+r(x)\], where\[f(x)g(x)\]\[,g(x)\]and\[r(x)\]are polynomials, and degree of \[r(x)<\]deg.\[g(x)\]If deg.\[f(x)\]<deg\[g(x)\], then deg.\[g(x)\]is
A)
not defined done
clear
B)
0 done
clear
C)
\[\deg .f(x)-\deg .g(x)\] done
clear
D)
\[\deg .f(x)+\deg .g(x)\] done
clear
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question_answer 215)
If\[{{\log }_{10}}m+{{\log }_{10}}n={{\log }_{10}}(m+n)\]and\[m=7\], then the value of n is
A)
5 done
clear
B)
\[\frac{2}{3}\] done
clear
C)
\[\frac{7}{6}\] done
clear
D)
\[\frac{3}{4}\] done
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question_answer 216)
The value of\[\frac{{{(1.5)}^{2}}+{{(4.7)}^{3}}+{{(3.8)}^{3}}-3\times 1.5\times 4.7\times 3.8}{{{(1.5)}^{2}}+{{(4.7)}^{2}}+{{(3.8)}^{2}}-1.5\times 4.7\times -4.7\times 3.8-1.5\times 3.8}\]
A)
8 done
clear
B)
9 done
clear
C)
10 done
clear
D)
11 done
clear
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question_answer 217)
Consider the following statements : 1. \[X-2\]is a factor of \[{{X}^{3}}-3{{X}^{2}}+4X-4\] 2.\[X+1\]is a factor of \[2{{X}^{3}}+4X+6\] 3. \[X-1\] is a factor of\[{{X}^{6}}-{{X}^{5}}+{{X}^{4}}-{{X}^{3}}+{{X}^{2}}-X+1\] Of these statements
A)
1 and 2 are correct done
clear
B)
1, 2 and 3 are correct done
clear
C)
2 and 3 are correct done
clear
D)
1 and 3 are correct done
clear
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question_answer 218)
L.C.M. of 125, 175 and 225 is
A)
7875 done
clear
B)
7575 done
clear
C)
7075 done
clear
D)
1235 done
clear
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question_answer 219)
If\[{{2}^{X}}{{.3}^{2X}}=100\](Given log 2 = 0.3010 and log = 0.4771), then the value of \[X\]is
A)
1.49 done
clear
B)
1.59 done
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C)
1.69 done
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D)
1.79 done
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question_answer 220)
If\[{{\log }_{10}}a,{{\log }_{10}}b,{{\log }_{10}}c\]are in A.P., then a, b, c must be in
A)
A.P. done
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B)
G.P. done
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C)
h.p. done
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D)
None of these done
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question_answer 221)
The smallest number, which must be added to 803642 in order to obtain a multiple ot 9, is
A)
1 done
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B)
2 done
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C)
3 done
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D)
4 done
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question_answer 222)
The given table shows the bank transaction of
Month June July August Deposit (Rs.) \[2x+y+z\] \[x+2y+3z\] \[x+4z\] Withdrawal (Rs.) \[x-y-z\] \[x-2y+3z\] \[2x-3z\]
His balance for the month of September is
A)
2(3y + 4z) done
clear
B)
3(2y + 3z) done
clear
C)
\[2(3x+4y)\] done
clear
D)
\[8x+7z\] done
clear
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question_answer 223)
If \[a=\frac{1}{3-2\sqrt{2}},b=\frac{1}{3+2\sqrt{2}}\]. then the value of \[{{a}^{2}}+{{b}^{2}}\]is
A)
34 done
clear
B)
35 done
clear
C)
36 done
clear
D)
37 done
clear
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question_answer 224)
If \[a=\frac{1}{3-2\sqrt{2}},b=\frac{1}{3+2\sqrt{2}}\], then the value of \[{{a}^{3}}+{{b}^{3}}\]3 - 2V2 3 + 2^2
A)
194 done
clear
B)
196 done
clear
C)
198 done
clear
D)
200 done
clear
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question_answer 225)
If \[(7+4\sqrt{3})\]), then the value of\[{{x}^{2}}+\frac{1}{{{x}^{2}}}\]is
A)
193 done
clear
B)
194 done
clear
C)
195 done
clear
D)
196 done
clear
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question_answer 226)
Which one of the following statements is correct?
A)
If \[g(x)(\ne 0)\] and \[f(x)\] are two polynomials\[\in F(x)\], then there exists unique polynomials q\[q(x)\]and\[r(x)\in F(x)\]such that\[f(x)=g(x)q(x)+r(x)\], where deg.\[\deg .r(x),\deg .g(x)\]. done
clear
B)
If\[g(x)(\ne 0)\]and\[f(x)\]are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and\[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\]where deg. \[r(x)<\]: deg. \[g(x)\]. done
clear
C)
If \[g(x)(\ne ,0)\] and\[f(x)\] are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and \[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\], where either \[r(x)=0\] or deg. \[r(x)<\]deg. \[g(x)\] done
clear
D)
If \[g(x)(\ne ,0)\] and\[f(x)\] are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and \[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\], where either \[r(x)=0\] or deg. \[r(x)<\]deg. \[g(x)\] done
clear
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question_answer 227)
If \[X=7+4\sqrt{3}\], then the value of\[\sqrt{X}+\frac{1}{\sqrt{X}}\]is
A)
8 done
clear
B)
6 done
clear
C)
5 done
clear
D)
4 done
clear
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question_answer 228)
If \[\sqrt{5}\text{=2}.\text{236}\] and\[\sqrt{10}=\text{ 3}.\text{162}\], the value of\[\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}\]on simplifying is
A)
0.455 done
clear
B)
0.855 done
clear
C)
0.655 done
clear
D)
0.755 done
clear
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question_answer 229)
The equation\[{{x}^{3}}-3x+q=0\]will have two roots equal, if the value of q is
A)
±2 done
clear
B)
± 1 done
clear
C)
± 3 done
clear
D)
± 4 done
clear
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question_answer 230)
Consider the following statements : Assertion : \[x-3\] is a factor of \[\text{P}\left( \text{x} \right)\text{ }=\text{ x3 }-\text{ 3}{{\text{x}}^{\text{2}}}\text{ }+\text{ 4x }-\text{ 12}\] Reason (R): \[P(2)\ne 0\]Of these statements :
A)
Both A and R are true and R is the correct explanation of A. done
clear
B)
Both A and R are true but R is not a correct explanation of A. done
clear
C)
A is true, but R is false. done
clear
D)
A is false, but R is true. done
clear
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question_answer 231)
The value of \[{{\log }_{10}}2+16{{\log }_{10}}\frac{16}{15}+12{{\log }_{10}}\frac{25}{24}\]\[+7{{\log }_{10}}\frac{81}{80}\] is
A)
3 done
clear
B)
2 done
clear
C)
1 done
clear
D)
0 done
clear
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question_answer 232)
The value of\[5\sqrt{3}-3\sqrt{12}+2\sqrt{75}\]on simplify is
A)
\[5\sqrt{3}\] done
clear
B)
\[6\sqrt{3}\] done
clear
C)
\[\sqrt{3}\] done
clear
D)
\[9\sqrt{3}\] done
clear
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question_answer 233)
The product of \[\sqrt{3}\]and \[\sqrt[3]{5}\] is
A)
\[5\sqrt{3}\] done
clear
B)
\[6\sqrt{3}\] done
clear
C)
\[\sqrt{3}\] done
clear
D)
\[9\sqrt{3}\] done
clear
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question_answer 234)
The value of \[|-5-6|\times |-4+3|\]on simplification is
A)
13 done
clear
B)
12 done
clear
C)
11 done
clear
D)
10 done
clear
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question_answer 235)
The value of \[x\] on simplifying \[X-2|X|=-3\]
A)
-1 or 3 done
clear
B)
1 or -3 done
clear
C)
-1 or - 3 done
clear
D)
1, 3 done
clear
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question_answer 236)
The value of\[{{\log }_{3}}9+{{\log }_{5}}25+{{\log }_{2}}8\]is
A)
4 done
clear
B)
5 done
clear
C)
6 done
clear
D)
7 done
clear
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question_answer 237)
\[\left( 1-\frac{1}{3} \right)\left( 1-\frac{14}{{}} \right)\left( 1-\frac{1}{5} \right).....\left( 1-\frac{1}{n} \right)\]
A)
\[\frac{1}{n}\] done
clear
B)
\[\frac{2}{n}\] done
clear
C)
\[\frac{3}{n}\] done
clear
D)
\[\frac{4}{n}\] done
clear
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question_answer 238)
If \[\frac{X}{2}=\frac{Y}{3}\], then\[\left[ \frac{4}{5}+\frac{y-X}{y+X} \right]\]equals
A)
\[\frac{3}{5}\] done
clear
B)
\[\frac{4}{5}\] done
clear
C)
1 done
clear
D)
\[\frac{6}{5}\] done
clear
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question_answer 239)
The value of\[\frac{{{(119)}^{2}}+(119)(111)+{{(111)}^{2}}}{{{(119)}^{3}}-{{(111)}^{3}}}\] is
A)
8 done
clear
B)
\[\frac{1}{8}\] done
clear
C)
230 done
clear
D)
\[\frac{1}{230}\] done
clear
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question_answer 240)
The exponential form of\[\sqrt{\sqrt{2}\times \sqrt{3}}\]is
A)
\[{{6}^{-\frac{1}{2}}}\] done
clear
B)
\[{{6}^{\frac{1}{2}}}\] done
clear
C)
\[{{6}^{\frac{1}{4}}}\] done
clear
D)
\[6\] done
clear
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question_answer 241)
If\[\sqrt{5}=2.236\] and \[\sqrt{3}=1.732\].then ^e value of
A)
14 done
clear
B)
14.39 done
clear
C)
14.392 done
clear
D)
16 done
clear
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question_answer 242)
If \[\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}\], then the value of 'a' and 'b' is
A)
\[\text{a }=\text{2},\text{ b}=-\text{ 1}\] done
clear
B)
\[\text{a }=\text{2},\text{ b}=-\text{ 1}\] done
clear
C)
\[\text{a }=\text{ }-\text{ 2},\text{ b }=\text{ 1}\] done
clear
D)
\[~\text{a }=\text{ }-\text{ 2},\text{ b }=\text{ }-\text{ 1}\] done
clear
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