A) \[a=\frac{4}{7},\,r=\frac{3}{7}\] done clear
B) \[a=2,\,r=\frac{3}{8}\] done clear
C) \[a=\frac{3}{2},\,r=\frac{1}{2}\] done clear
D) \[a=3,\,r=\frac{1}{4}\] done clear
E) None of these done clear
View Answer play_arrowA) 5 done clear
B) \[\frac{1}{5}\] done clear
C) \[-\,5\] done clear
D) \[-\frac{1}{5}\] done clear
E) None of these done clear
View Answer play_arrowColumn ? I | Column - II | ||
a. | \[\sin (x+y)\sin (x-y)\] | i. | \[{{\cos }^{2}}x-{{\sin }^{2}}y\] |
b. | \[\cos (x+y)\cos (x-y)\] | ii. | \[\frac{1-\tan \theta }{1+\tan \theta }\] |
c. | \[\cot \left( \frac{\pi }{4}+\theta \right)\] | iii. | \[\frac{1+\tan \theta }{1-\tan \theta }\] |
d. | \[\tan \left( \frac{\pi }{4}+\theta \right)\] | iv. | \[{{\sin }^{2}}x-{{\sin }^{2}}y\] |
A) a - i, b - ii, c - iii, d - iv done clear
B) a - ii, b- iv, c - iii, d -i done clear
C) a - iv, b- ii, c- i, d - iii done clear
D) a - iii, b - ii, c - iv, d - i done clear
E) None of these done clear
View Answer play_arrowA) 40 done clear
B) 60 done clear
C) 80 done clear
D) 100 done clear
E) None of these done clear
View Answer play_arrowA) \[{{(-1)}^{n/2}}\,(n+1)\] done clear
B) \[{{(-1)}^{n}}\,(n+1)\] done clear
C) \[{{(-1)}^{n/2}}\,(n+2)\] done clear
D) \[{{(-1)}^{n}}\,(n+2)\] done clear
E) None of these done clear
View Answer play_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) An equivalence relation done clear
E) None of these done clear
View Answer play_arrowquestion_answer7) A={1,2,3} and B = {3,8}, then \[(A\cup B)\times (A\cap B)\] is
A) {(3, 1), (3, 2), (3, 3), (3, 8)} done clear
B) {(1, 3), (2, 3), (3, 3), (8, 3)} done clear
C) {(1, 2), (2, 2), (3, 3), (8, 8)} done clear
D) {(8, 3), (8, 2). (8, 1), (8, 8)} done clear
E) None of these done clear
View Answer play_arrowA) 128 done clear
B) 216 done clear
C) 140 done clear
D) 160 done clear
E) None of these done clear
View Answer play_arrowA) Two real roots done clear
B) Two positive roots done clear
C) Two negative roots done clear
D) One positive and one negative root done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{132}{12\,\sqrt{3}+5}\] done clear
B) \[\frac{132}{12\,\sqrt{3}-5}\] done clear
C) \[\frac{132}{5\,\sqrt{3}+12}\] done clear
D) \[\frac{132}{5\sqrt{3}-12}\] done clear
E) None of these done clear
View Answer play_arrowA) \[[0,1]\] done clear
B) \[\left[ -\frac{1}{4},\frac{1}{3} \right]\] done clear
C) \[\left[ 0,\frac{1}{3} \right]\] done clear
D) \[(0,\infty )\] done clear
E) None of these done clear
View Answer play_arrowA) 5 done clear
B) 6 done clear
C) 7 done clear
D) 8 done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{n-5}{6}\] done clear
B) \[\frac{n-4}{6}\] done clear
C) \[\frac{5}{n-4}\] done clear
D) \[\frac{n-4}{5}\] done clear
E) None of these done clear
View Answer play_arrowA) \[x=3\] done clear
B) \[x=4\sqrt{3}\] done clear
C) \[x=9\] done clear
D) \[x=\sqrt{3}\] done clear
E) None of these done clear
View Answer play_arrowA) a, c done clear
B) b, c done clear
C) a, b done clear
D) a + c, b + c done clear
E) None of these done clear
View Answer play_arrowA) \[{{p}^{3}}-(3p-1)\,q+{{q}^{2}}=0\] done clear
B) \[{{p}^{3}}-q\,(3p+1)-{{q}^{2}}=0\] done clear
C) \[{{p}^{3}}+q\,(3p+1)+{{q}^{2}}=0\] done clear
D) \[{{p}^{3}}-q\,(3p+1)+{{q}^{2}}=0\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer17) If A.M and G.M of x and y are in the ratio p: q, then x : y is
A) \[p-\sqrt{{{p}^{2}}+{{q}^{2}}}:p+\sqrt{{{p}^{2}}+{{q}^{2}}}\] done clear
B) \[p+\sqrt{{{p}^{2}}-{{q}^{2}}}:p+\sqrt{{{p}^{2}}-{{q}^{2}}}\] done clear
C) \[p:q\] done clear
D) \[p+\sqrt{{{p}^{2}}+{{q}^{2}}}:p-\sqrt{{{p}^{2}}+{{q}^{2}}}\] done clear
E) \[q+\sqrt{{{p}^{2}}-{{q}^{2}}}:q-\sqrt{{{p}^{2}}-{{q}^{2}}}\] done clear
View Answer play_arrowA) Are in A.P. done clear
B) Are in G.P. done clear
C) Are in H.P. done clear
D) Both (A) and (B) done clear
E) None of these done clear
View Answer play_arrowA) \[{{\tan }^{-1}}\left( \frac{2k}{{{k}^{2}}+1} \right)\] done clear
B) \[{{\tan }^{-1}}\left( \frac{2k}{1-{{k}^{2}}} \right)\] done clear
C) \[-2{{\tan }^{-1}}k\] done clear
D) \[2{{\tan }^{-1}}k\] done clear
E) None of these done clear
View Answer play_arrowA) \[3x-4\] done clear
B) \[4x-3\] done clear
C) \[4x+3\] done clear
D) \[3x+4\] done clear
E) None of these done clear
View Answer play_arrowA) 216 done clear
B) 240 done clear
C) 600 done clear
D) 3125 done clear
E) None of these done clear
View Answer play_arrowquestion_answer22) Solution set of inequality \[{{\log }_{10}}({{x}^{2}}-2x-2)\le 0\]
A) \[[-1,\,1-\sqrt{3}]\] done clear
B) \[[1+\sqrt{3},3]\] done clear
C) \[[-1,\,1-\sqrt{3})\,\cup (1+\sqrt{3},3]\] done clear
D) \[[1-\sqrt{3},3)\,\cup (1+\sqrt{3},2]\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{405}{256}\] done clear
B) \[\frac{504}{259}\] done clear
C) \[\frac{450}{263}\] done clear
D) \[\frac{445}{256}\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{23}{17}\left( \frac{\sqrt{3}-1}{2}+\frac{1}{\sqrt{2}} \right)\] done clear
B) \[\frac{23}{17}\left( \frac{\sqrt{3}+1}{2}+\frac{1}{\sqrt{2}} \right)\] done clear
C) \[\frac{23}{17}\left( \frac{\sqrt{3}-1}{2}-\frac{1}{\sqrt{2}} \right)\] done clear
D) \[\frac{23}{17}\left( \frac{\sqrt{3}+1}{2}-\frac{1}{\sqrt{2}} \right)\] done clear
E) None of these done clear
View Answer play_arrowA) \[{{(x-y)}^{2}}=24\,(x+y-4)\] done clear
B) \[{{(x+y)}^{2}}=6\,(x+y-4)\] done clear
C) \[{{(x-y)}^{2}}=12\,(x+y-4)\] done clear
D) \[{{(x+y)}^{2}}=24\,(x-y+4)\] done clear
E) None of these done clear
View Answer play_arrowA) No real value of b and c done clear
B) \[0<c<b\sqrt{2}\] done clear
C) \[|c|\,<\,|b|\sqrt{2}\] done clear
D) \[|c|\,>\,|b|\sqrt{2}\] done clear
E) None of these done clear
View Answer play_arrowA) \[(-\infty \,-1)\cup (1,\,4]\] done clear
B) \[(-\infty \,-1)\cup (1,\,4]\] done clear
C) \[(-\infty \,-1)\cup [1,\,4]\] done clear
D) \[(-\infty \,-1)\cup [1,\,4)\] done clear
E) None of these done clear
View Answer play_arrowA) \[\sqrt{1+{{\cos }^{2}}\alpha }\] done clear
B) \[\sqrt{1+{{\sin }^{2}}\alpha }\] done clear
C) \[\sqrt{2+{{\sin }^{2}}\alpha }\] done clear
D) \[\sqrt{2+{{\cos }^{2}}\alpha }\] done clear
E) None of these done clear
View Answer play_arrowA) 535 done clear
B) 601 done clear
C) 728 done clear
D) 835 done clear
E) None of these done clear
View Answer play_arrowA) Mutually exclusive and independent done clear
B) Equally likely but not independent done clear
C) Independent but not equally likely done clear
D) Independent and equally likely done clear
E) None of these done clear
View Answer play_arrowquestion_answer31) Consider the following statements:
I. All artists are whimsical. |
II. Some artists are drug addicts. |
III. Frustrated people are prone to become drug addicts. |
From the above three statements it may be concluded that |
A) Artists are frustrated. done clear
B) All frustrated people are drug addicts. done clear
C) Some drug addicts are whimsical done clear
D) Whimsical people are generally frustrated. done clear
E) None of these done clear
View Answer play_arrowA) Apple done clear
B) Pineapple done clear
C) Grapes done clear
D) Oranges done clear
E) None of these done clear
View Answer play_arrowA) 3 km east, then 2 km south done clear
B) 3 km east, then 1 km north done clear
C) 1 km north, then 2 km west done clear
D) 3 km south, then 1 km north done clear
E) None of these done clear
View Answer play_arrowquestion_answer34) Arrange the following in a meaningful order:
(i) Plan | (ii) Revise |
(iii) Publish | (iv) Think |
(v) Write |
A) (v), (iv), (iii), (ii), (i) done clear
B) (i), (ii), (iii), (iv), (v) done clear
C) (iv), (i), (v), (ii), (iii) done clear
D) (iv), (i), (v), (iii), (ii) done clear
E) None of these done clear
View Answer play_arrowA) 5 done clear
B) 18 done clear
C) 10 done clear
D) 3 done clear
E) None of these done clear
View Answer play_arrowquestion_answer36) Consider the following statements:
1. Either A and B are of the same age or A is older than B |
2. Either C or D are of the same age or D is older than C |
3. B is older than C |
Which of the following conclusions can be drawn from the above statements? |
A) A is older than B done clear
B) B and D are of the same age done clear
C) D is older than C done clear
D) A is older than C done clear
E) None of these done clear
View Answer play_arrowA) 10 done clear
B) 18 done clear
C) 26 done clear
D) 32 done clear
E) None of these done clear
View Answer play_arrowA) CARFTION done clear
B) FRACNOIT done clear
C) NOITCARF done clear
D) CARFNOIT done clear
E) None of these done clear
View Answer play_arrowDirections: Study the information below and answer questions based on it. Each of the six friends. A, B, C, D, E and F scored different marks in an examination. C scored more than only A and E. D scored less than only B. E did not score the least. The one who scored the third highest marks scored 81 marks. E scored 62 marks. |
A) 70 done clear
B) 94 done clear
C) 86 done clear
D) 61 done clear
E) None of these done clear
View Answer play_arrowDirections: Study the information below and answer questions based on it. Each of the six friends. A, B, C, D, E and F scored different marks in an examination. C scored more than only A and E. D scored less than only B. E did not score the least. The one who scored the third highest marks scored 81 marks. E scored 62 marks. |
A) 94 done clear
B) 60 done clear
C) 89 done clear
D) 78 done clear
E) None of these done clear
View Answer play_arrowA) \[1+\sqrt{5}\] done clear
B) \[-1+\sqrt{5}\] done clear
C) \[-1+\sqrt{2}\] done clear
D) \[1+\sqrt{2}\] done clear
E) None of these done clear
View Answer play_arrowA) 0 done clear
B) \[-\,1\] done clear
C) 1 done clear
D) 2 done clear
E) None of these done clear
View Answer play_arrowquestion_answer43) The function \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\] increases, if:
A) \[0<\times <\frac{\pi }{8}\] done clear
B) \[\frac{\pi }{4}<\times <\frac{3\pi }{8}\] done clear
C) \[\frac{3\pi }{8}<\times <\frac{5\pi }{8}\] done clear
D) \[\frac{5\pi }{8}<\times <\frac{3\pi }{4}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer44) If \[f(x)=x{{e}^{x(1-x)}}\], then f (x) is:
A) Increasing on \[\left[ -\,1/2,1 \right]\] done clear
B) Decreasing on R done clear
C) Increasing on R done clear
D) Decreasing on \[\left[ -\,1/2,1 \right]\] done clear
E) None of these done clear
View Answer play_arrowA) Neither a maximum nor a minimum done clear
B) Only one maximum done clear
C) Only one minimum done clear
D) Only one maximum and only one minimum. done clear
E) None of these done clear
View Answer play_arrowA) 40 m done clear
B) 50 m done clear
C) 150 m done clear
D) 75 m done clear
E) None of these done clear
View Answer play_arrowA) \[4{{x}^{2}}+4{{y}^{2}}-30x-10y=25\] done clear
B) \[5{{x}^{2}}+5{{y}^{2}}+27x-23y=42\] done clear
C) \[5{{x}^{2}}+5{{y}^{2}}-27x+23y-42=0\] done clear
D) \[5{{x}^{2}}+5{{y}^{2}}-21x-14y=42=0\] done clear
E) None of these done clear
View Answer play_arrowA) \[{{x}^{2}}+{{y}^{2}}+8x-10y+40=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+8x-10y+30=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+8x-10y-40=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+8x-10y-30=0\] done clear
E) None of these done clear
View Answer play_arrowA) 0 done clear
B) 7 done clear
C) 8 done clear
D) 9 done clear
E) None of these done clear
View Answer play_arrowA) \[n-m+1:m\] done clear
B) \[n-m+1:~n\] done clear
C) \[n:n-m+\text{1}\] done clear
D) \[m:n-m+\text{1}\] done clear
E) None of theses done clear
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