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question_answer1) If\[A=\left( \begin{matrix} \alpha -1 \\ 0 \\ 0 \\ \end{matrix} \right),B=\left( \begin{matrix} \alpha +1 \\ 0 \\ 0 \\ \end{matrix} \right)\]be two matrices, then \[A{{B}^{T}}\]is a non-zero matrix for |a| not equal to
JEE Main Online Paper (Held On 07 May 2012)
A)
2
done
clear
B)
0
done
clear
C)
1
done
clear
D)
3
done
clear
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question_answer2) If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of\[6\pi c{{m}^{2}}hr,\]then the rate (in mm/hr) at which the radius of the circular sheet increases is
JEE Main Online Paper (Held On 07 May 2012)
A)
1.0
done
clear
B)
0.1
done
clear
C)
1.1
done
clear
D)
2.0
done
clear
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question_answer3) The difference between the fourth term and the first term of a Geometrical Progresssion is 52. If the sum of its first three terms is 26, then the sum of the first six terms of the progression is
JEE Main Online Paper (Held On 07 May 2012)
A)
63
done
clear
B)
189
done
clear
C)
728
done
clear
D)
364
done
clear
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question_answer4) The value of k for which the equation\[(k-2){{x}^{2}}+8x+k+4=0\]has both roots real, distinct and negative is
JEE Main Online Paper (Held On 07 May 2012)
A)
6
done
clear
B)
3
done
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C)
4
done
clear
D)
1
done
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question_answer5) Let y (x) be a solution of \[\frac{\left( 2+\sin x \right)}{\left( 1+y \right)}\frac{dy}{dx}=\cos x.\] If \[y(0)=2,\]then \[y\left( \frac{\pi }{2} \right)\]equals
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\frac{5}{2}\]
done
clear
B)
2
done
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C)
\[\frac{7}{2}\]
done
clear
D)
3
done
clear
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question_answer6) If the eccentricity of a hyperbola \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]which passes through (k, 2), is \[\frac{\sqrt{13}}{3},\] then the value of \[{{k}^{2}}\] is
JEE Main Online Paper (Held On 07 May 2012)
A)
18
done
clear
B)
8
done
clear
C)
1
done
clear
D)
2
done
clear
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question_answer7) If \[\int\limits_{e}^{x}{tf(t)dt}=\sin x-x\cos x-\frac{{{x}^{2}}}{2},\]for all\[x\in R-\{0\},\]then the value of\[f\left( \frac{\pi }{6} \right)\] is
JEE Main Online Paper (Held On 07 May 2012)
A)
1/2
done
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B)
1
done
clear
C)
0
done
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D)
-1/2
done
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question_answer8) If the number of 5-element subsets of the set\[A=\{{{a}_{1}},{{a}_{2}},....,{{a}_{20}}\}\] of 20 distinct elements is k times the number of 5-element subsets containing\[{{a}_{4}},\]then k is
JEE Main Online Paper (Held On 07 May 2012)
A)
5
done
clear
B)
\[\frac{20}{7}\]
done
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C)
4
done
clear
D)
\[\frac{10}{3}\]
done
clear
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question_answer9) If the system of equations \[x+y+z=6\] \[x+2y+3z=10\] \[x+2y+\lambda z=0\] has a unique solution, then \[\lambda \] is not equal to
JEE Main Online Paper (Held On 07 May 2012)
A)
1
done
clear
B)
0
done
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C)
2
done
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D)
3
done
clear
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question_answer10) If the straight lines \[\text{x}+\text{3y}=\text{4},\text{3x}+\text{y}=\text{4}\]and \[\text{x}+\text{y}=0\]form a triangle, then the triangle is
JEE Main Online Paper (Held On 07 May 2012)
A)
scalene
done
clear
B)
equilateral triangle
done
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C)
isosceles
done
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D)
right angled isosceles
done
clear
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question_answer11) Let fix)be an indefinite integral of \[{{\cos }^{3}}x.\] Statement 1:f(x) is a periodic function of period\[\pi .\] Statement 2: \[{{\cos }^{3}}x\] is a periodic function.
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true, Statement 2 is false.
done
clear
B)
Both the Statements are true, but Statement2 is not the correct explanation of Statement1.
done
clear
C)
Both the Statements are true, and Statement2 is correct explanation of Statement 1.
done
clear
D)
Statement 1 is false, Statement 2 is true.
done
clear
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question_answer12) The parabola\[{{y}^{2}}=x\] divides the circle \[{{x}^{2}}+{{y}^{2}}=2\]into two parts whose areas are in the ratio
JEE Main Online Paper (Held On 07 May 2012)
A)
\[9\pi +2:3\pi -2\]
done
clear
B)
\[9\pi -2:3\pi +2\]
done
clear
C)
\[7\pi -2:2\pi -3\]
done
clear
D)
\[7\pi +2:3\pi +2\]
done
clear
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question_answer13) The equation of the circle passing through the point (1,2) and through the points of intersection of\[{{x}^{2}}+{{y}^{2}}-4x-6y-21=0\]and \[3x+4y+5=0\] is given by
JEE Main Online Paper (Held On 07 May 2012)
A)
\[{{x}^{2}}+{{y}^{2}}+2x=2y+11=0\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x+2y-7=0\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x-2y-3=0\]
done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+2x+2y-11=0\]
done
clear
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question_answer14)
The frequency distribution of daily working expenditure of families in a locality is as follows:
Expenditure in Rs. (x): |
0-50 |
50-100 |
100-150 |
150-200 |
200-250 |
No. of families (f): |
24 |
33 |
37 |
B |
25 |
If the mode of the distribution is " 140, then the value of b is
JEE Main Online Paper (Held On 07 May 2012)
A)
34
done
clear
B)
31
done
clear
C)
26
done
clear
D)
36
done
clear
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question_answer15) The sum of the series\[{{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\text{2}.{{\text{6}}^{\text{2}}}+....+\text{2(2m}{{\text{)}}^{\text{2}}}\]is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[m{{(2m+1)}^{2}}\]
done
clear
B)
\[{{m}^{2}}(m+2)\]
done
clear
C)
\[{{m}^{2}}(2m+1)\]
done
clear
D)
\[m{{(m+2)}^{2}}\]
done
clear
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question_answer16) The point of intersection of the lines\[({{a}^{3}}+3)x+ay+a-3=0\]and\[({{a}^{5}}+2)x+(a+2)y+2a+3=0\](a real) lies on they-axis for
JEE Main Online Paper (Held On 07 May 2012)
A)
no value of a
done
clear
B)
more than two values of a
done
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C)
exactly one value of a
done
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D)
exactly two values of a
done
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question_answer17) ABCD is parallelogram. The position vectors of A and C are respectively,\[3\hat{i}+3\hat{j}+5\hat{k}\] and\[\hat{i}-5\hat{j}-5\hat{k}\].If M is the midpoint of the diagonal\[\overset{\to }{\mathop{OM}}\,\]then the magnitude of the projection of on\[\overset{\to }{\mathop{OC}}\,,\] where O is the origin, is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[7\sqrt{51}\]
done
clear
B)
\[\frac{7}{\sqrt{50}}\]
done
clear
C)
\[7\sqrt{50}\]
done
clear
D)
\[\frac{7}{\sqrt{51}}\]
done
clear
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question_answer18) The range of the function \[f\left( x \right)=\frac{x}{1+|x|},x\in R,\]is
JEE Main Online Paper (Held On 07 May 2012)
A)
R
done
clear
B)
-1,1
done
clear
C)
R- {0}
done
clear
D)
[-1, 1]
done
clear
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question_answer19) If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m)of the point of intersection of the lines joining the top of each pole to the foot of other is
JEE Main Online Paper (Held On 07 May 2012)
A)
16
done
clear
B)
18
done
clear
C)
50
done
clear
D)
15
done
clear
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question_answer20) If \[\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+3\hat{j}-\hat{k}\]and\[\vec{c}=\lambda \hat{i}+\hat{j}+(2\lambda -1)\hat{k}\]are coplanar vectors, then\[\lambda \]is equal to
A)
0
done
clear
B)
-1
done
clear
C)
2
done
clear
D)
1
done
clear
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question_answer21) Statement 1:\[y=mx-\frac{1}{m}\]is always a tangent to the parabola, \[{{y}^{2}}=-4x\]for all non-zero values of w. Statement 2: Every tangent to the parabola, \[{{y}^{2}}=-4x\] will meet its axis at a point whose abscissa is non-negative.
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
done
clear
B)
Statement 1 is false, Statement 2 is true.
done
clear
C)
Statement 1 is true. Statement 2 is false.
done
clear
D)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
done
clear
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question_answer22) Let \[{{Z}_{1}}\]and \[{{Z}_{2}}\]be any two complex number. Statement1:\[\left| {{Z}_{1}}-{{Z}_{2}} \right|\ge \left| {{Z}_{1}} \right|-\left| {{Z}_{2}} \right|\] Statement 2: \[\left| {{Z}_{1}}+{{Z}_{2}} \right|\le \left| {{Z}_{1}} \right|+\left| {{Z}_{2}} \right|\]
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
done
clear
B)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
done
clear
C)
Statement 1 is true. Statement 2 is false.
done
clear
D)
Statement 1 is false. Statement 2 is true.
done
clear
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question_answer23) Let X and Y are two events such that\[P\left( X\cup Y \right)=P(X\cap Y).\] Statement1:\[P(X\cap Y')=P\left( X'\cap Y \right)=0\] Statement 2; \[P(X)+P=2P\left( X\cap Y \right)\]
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is false. Statement 2 is true. Statement 1 is true. Statement 2 is true,
done
clear
B)
Statement 2 is not a correct explanation of Statement 1.
done
clear
C)
Statement 1 is true. Statement 2 is false.
done
clear
D)
Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
done
clear
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question_answer24) If\[f(y)=1-(y-1)+{{(y-1)}^{2}}-{{(y-1)}^{3}}\]\[+...-{{(y-1)}^{17}},\]then the coefficient of \[{{y}^{2}}\] in it is
JEE Main Online Paper (Held On 07 May 2012)
A)
\[^{17}{{C}_{2}}\]
done
clear
B)
\[^{17}{{C}_{3}}\]
done
clear
C)
\[^{18}{{C}_{2}}\]
done
clear
D)
\[^{18}{{C}_{3}}\]
done
clear
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question_answer25) The values of a for which the two points (1, a, 1)and (-3, 0, a) lie on the opposite sides of the plane \[\text{3x}+\text{4y}-\text{12z}+\text{13}=0,\] satisfy
JEE Main Online Paper (Held On 07 May 2012)
A)
\[0<a<\frac{1}{3}\]
done
clear
B)
\[-1<a<0\]
done
clear
C)
\[a<-1\]or \[a<\frac{1}{3}\]
done
clear
D)
\[a=0\]
done
clear
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question_answer26) \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x-\sin x}{x} \right)\sin \left( \frac{1}{x} \right)\]
JEE Main Online Paper (Held On 07 May 2012)
A)
equals 1
done
clear
B)
equals 0
done
clear
C)
does not exist
done
clear
D)
equals? 1
done
clear
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question_answer27) A line with positive direction cosines passes through the point P (2, - 1, 2) and makes equal angles with the coordinate axes. If the line meets the plane \[2x+y+z=9\] at point Q, then the length PQ equals
JEE Main Online Paper (Held On 07 May 2012)
A)
\[\sqrt{2}\]
done
clear
B)
2
done
clear
C)
\[\sqrt{3}\]
done
clear
D)
1
done
clear
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question_answer28) Let\[f(x)=\sin x,g(x)=x.\] Statement1:\[f(x)\le g(x)\] for x in \[(0,\infty )\] Statement2:\[f(x)\le 1\] for x in \[(0,\infty )\] but \[g(x)\to \infty \]as\[x\to \infty .\]
JEE Main Online Paper (Held On 07 May 2012)
A)
Statement 1 is true, Statement 2 is false.
done
clear
B)
Statement 1 is true. Statement 2 is true Statement 2 is a correct explanation for Statement 1.
done
clear
C)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation for Statement!.
done
clear
D)
Statement 1 is false. Statement 2 is true.
done
clear
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question_answer29) The Statement that is TRUE among the following is
JEE Main Online Paper (Held On 07 May 2012)
A)
The contrapositive of\[3x+2=8\Rightarrow x=2\]is\[x\ne 2\]\[\Rightarrow \]\[3x+2\ne 8.\]
done
clear
B)
The converse of \[=0\Rightarrow x=0\] is \[x\ne 0\Rightarrow \tan x=0.\]
done
clear
C)
\[p\Rightarrow q\] is equivalent to\[p\vee \tilde{\ }q.\]
done
clear
D)
\[p\vee q\]and\[p\wedge q\] have the same truth table.
done
clear
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question_answer30) If\[x+|y|=2y,\] then y as a function of x, at x = 0 is
A)
differentiable but not continuous
done
clear
B)
continuous but not differentiable
done
clear
C)
continuous as well as differentiable
done
clear
D)
neither continuous nor differentiable
done
clear
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