question_answer1) If \[A={{\sin }^{2}}+{{\cos }^{4}}x\], then for all real x
A) \[\frac{13}{16}\le A\le 1\] done clear
B) \[1\le A\le 2\] done clear
C) \[\frac{3}{4}\le A\le \frac{13}{16}\] done clear
D) \[\frac{3}{4}\le A\le 1\] done clear
E) None of these done clear
View Answer play_arrowA) \[\,132\] done clear
B) \[\,144\] done clear
C) 132 done clear
D) 144 done clear
E) None of these done clear
View Answer play_arrowA) equals \[\sqrt{2}\] done clear
B) equals \[-\,\sqrt{2}\] done clear
C) equals \[\frac{1}{\sqrt{2}}\] done clear
D) does not exist done clear
E) None of these done clear
View Answer play_arrowA) \[P(C|D)\ge P(C)\] done clear
B) \[P(C|D)<P(C)\] done clear
C) \[P(C|D)=\frac{P(D)}{P(C)}\] done clear
D) \[P(C|D)=P(C)\] done clear
E) None of these done clear
View Answer play_arrowA) (1, 1) done clear
B) (1, 0) done clear
C) \[\left( -\,1,1 \right)\] done clear
D) (0, 1) done clear
E) None of these done clear
View Answer play_arrowA) \[P({{A}^{c}})-P(B)\] done clear
B) \[P(A)-P({{B}^{c}})\] done clear
C) \[P({{A}^{c}})+P({{B}^{c}})\] done clear
D) \[P({{A}^{c}})-P({{B}^{c}})\] done clear
E) None of these done clear
View Answer play_arrowA) \[-3{{x}^{2}}+{{y}^{2}}=3\] done clear
B) \[{{x}^{2}}-3{{y}^{2}}=3\] done clear
C) \[3{{x}^{2}}-{{y}^{2}}=3\] done clear
D) \[-{{x}^{2}}+3{{y}^{2}}=3\] done clear
E) None of these done clear
View Answer play_arrowA) \[\left( -\,1,\text{1} \right)\] done clear
B) \[(0,\infty )\] done clear
C) \[(1,\infty )\] done clear
D) \[(-1,\infty )\] done clear
E) None of these done clear
View Answer play_arrowA) \[3\sqrt{5}\] done clear
B) \[10\sqrt{3}\] done clear
C) \[5\sqrt{3}\] done clear
D) \[3\sqrt{10}\] done clear
E) None of these done clear
View Answer play_arrowA) 0 done clear
B) 1 done clear
C) 2 done clear
D) \[\infty \] done clear
E) None of these done clear
View Answer play_arrowA) 24 min done clear
B) 34 min done clear
C) 125 min done clear
D) 135 min done clear
E) None of these done clear
View Answer play_arrowA) y = 0 done clear
B) y = l done clear
C) y = 2 done clear
D) y = 3 done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{25}{16}\] done clear
B) \[\frac{56}{33}\] done clear
C) \[\frac{19}{12}\] done clear
D) \[\frac{20}{7}\] done clear
E) None of these done clear
View Answer play_arrowA) There is a regular polygon with \[\frac{r}{R}=\frac{1}{2}\] done clear
B) There is a regular polygon with \[\frac{r}{R}=\frac{1}{\sqrt{2}}\] done clear
C) There is a regular polygon with \[\frac{r}{R}=\frac{2}{3}\] done clear
D) There is a regular polygon with \[\frac{r}{R}=\frac{\sqrt{3}}{2}\] done clear
E) None of these done clear
View Answer play_arrowA) A = C done clear
B) B = C done clear
C) \[A\cap B=\phi \] done clear
D) A = B done clear
E) None of these done clear
View Answer play_arrowquestion_answer16) If \[\left| z-\frac{4}{z} \right|=2,\] then the maximum value of |z| is equal to
A) \[\sqrt{3}+1\] done clear
B) \[\sqrt{5}+1\] done clear
C) 2 done clear
D) \[2+\sqrt{2}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer17) The remainder left out when \[{{8}^{2n}}-{{(62)}^{2n+1}}\]is divided by 9 is
A) 0 done clear
B) 2 done clear
C) 7 done clear
D) 8 done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{8}{3}\] done clear
B) \[\frac{2}{3}\] done clear
C) \[\frac{4}{3}\] done clear
D) \[\frac{5}{3}\] done clear
E) None of these done clear
View Answer play_arrowA) \[-\frac{1}{i-1}\] done clear
B) \[\frac{1}{i+1}\] done clear
C) \[-\frac{1}{i+1}\] done clear
D) \[\frac{1}{i-1}\] done clear
E) None of these done clear
View Answer play_arrowA) \[{}^{4}{{P}_{4}}\] done clear
B) \[{}^{4}{{P}_{3}}\] done clear
C) \[{}^{4}{{P}_{1}}+{}^{4}{{P}_{2}}+{}^{4}{{P}_{3}}\] done clear
D) \[{}^{4}{{P}_{1}}+{}^{4}{{P}_{2}}+{}^{4}{{P}_{3}}+{}^{4}{{P}_{4}}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer21) Match the column in the table given below:
S. No. | Sets | Roster Form | |
1. | {\[x:{{x}^{2}}-3=0\] and x is a rational number} | a. | {4} |
2. | {\[x:x\] is an even prime number} | b. | \[\left\{ -\,5,5 \right\}\] |
3. | {\[x:3<x<5,\] x is a natural number} | c. | {*} |
4. | {\[x:{{x}^{2}}=25,\] and x is an odd integer} | d. | {2} |
A) 1 - c, 2 - d, 3 - a, 4 - b done clear
B) 1 - d, 2 - c, 3 - a, 4 - b done clear
C) 1 - c, 2 - a, 3 - d, 4 - b done clear
D) 1 - b, 2 - d, 3 - a, 4 - c done clear
E) None of these done clear
View Answer play_arrowquestion_answer22) Angle between the lines \[2x-y-15=0\] and \[~3x+y+4=0\] is
A) \[60{}^\circ \] done clear
B) \[180{}^\circ \] done clear
C) \[90{}^\circ \] done clear
D) \[45{}^\circ \] done clear
E) None of these done clear
View Answer play_arrowA) \[-\,1\] done clear
B) 3 done clear
C) 5 done clear
D) \[-\,5\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer24) If a, b, c are in G.P, then
A) \[{{a}^{2}},{{b}^{2}},{{c}^{2}}\] are in G.P done clear
B) \[{{a}^{2}}(b+c),{{c}^{2}}(a+b),{{b}^{2}}(a+c)\] are in G.P done clear
C) \[\frac{a}{a+b},\frac{b}{c+a},\frac{c}{a+b}\] are in G.P done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowquestion_answer25) The distance between the lines \[3x-2y=1\] and \[6x+9=4y\] is
A) \[\frac{1}{\sqrt{52}}\] done clear
B) \[\frac{11}{\sqrt{52}}\] done clear
C) \[\frac{4}{\sqrt{13}}\] done clear
D) \[\frac{6}{\sqrt{13}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[{{m}_{1}}+{{m}_{2}}=\,\frac{2h}{b}\,\,and\,\,{{m}_{1}}{{m}_{2}}=-\frac{a}{b}\] done clear
B) \[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\,\,and\,\,{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] done clear
C) \[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\,\,and\,\,{{m}_{1}}{{m}_{2}}=-ab\] done clear
D) \[{{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}\,\,and\,\,{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] done clear
E) None of these done clear
View Answer play_arrowA) 500 done clear
B) 560 done clear
C) 580 done clear
D) 520 done clear
E) None of these done clear
View Answer play_arrowA) Equilateral done clear
B) Isosceles done clear
C) Right angled done clear
D) Right angled isosceles done clear
E) None of these done clear
View Answer play_arrowquestion_answer29) Argument and modulus of \[\frac{1+i}{1-i}\] are respectively
A) \[\frac{-\pi }{2}\,and\,\,1\] done clear
B) \[\frac{\pi }{2}\,\,and\,\,\sqrt{2}\] done clear
C) \[\frac{\pi }{2}\,\,and\,\,1\] done clear
D) \[0\,\,and\,\,\sqrt{2}\] done clear
E) None of these done clear
View Answer play_arrowA) 23 done clear
B) 5 done clear
C) 15 done clear
D) 18 done clear
E) None of these done clear
View Answer play_arrowquestion_answer31) If \[\frac{3x+4}{{{x}^{2}}-3x+2}=\frac{A}{x-2}-\frac{B}{x-1},\] then(A, B)=
A) (7, 10) done clear
B) (10, 7) done clear
C) \[\left( 10,-\,7 \right)\] done clear
D) \[\left( -\,10,7 \right)\] done clear
E) None of these done clear
View Answer play_arrowA) \[(n+2)\,{{2}^{n-1}}\] done clear
B) \[(n+1)\,{{2}^{n}}\] done clear
C) \[(n+1)\,{{2}^{n-1}}\] done clear
D) \[(n+2)\,{{2}^{n}}\] done clear
E) None of these done clear
View Answer play_arrowA) 1 : 2 internally done clear
B) 1 : 2 externally done clear
C) 2 : 1 internally done clear
D) 2 : 1 externally done clear
E) None of these done clear
View Answer play_arrowA) 3 done clear
B) 5 done clear
C) 0 done clear
D) \[-\,3\] done clear
E) None of these done clear
View Answer play_arrowA) Town B done clear
B) 45 km from town A done clear
C) Town A done clear
D) 45 km from town B done clear
E) None of these done clear
View Answer play_arrowquestion_answer36) If \[{}^{n-1}{{C}_{r}}={{({{k}^{2}}-3)}^{n}}{{C}_{r+1}},\] then k \[\in \]
A) \[(-\,\infty ,-\,2]\] done clear
B) \[[2,\infty ]\] done clear
C) \[[-\,\sqrt{3},\sqrt{3}]\] done clear
D) \[(\sqrt{3},2]\] done clear
E) None of these done clear
View Answer play_arrowA) \[7+12\sqrt{3}\] done clear
B) \[12-7\sqrt{3}\] done clear
C) \[12+7\sqrt{3}\] done clear
D) \[4\pi \] done clear
E) None of these done clear
View Answer play_arrowDirection: Read the given passage carefully and answer the questions that follow. |
A, B, C, D, E, F are members of a family. They are engineer, stenographer, doctor, draughtsman, lawyer and judge (not in order). A, the engineer is married to the lady stenographer. The judge is married to the lawyer. F, the draughtsman is the son of B and brother of E. C, the lawyer is the daughter-in-law of D. E is the unmarried doctor. D is the grandmother of F. There are two married couples in the family. |
A) Judge done clear
B) Lawyer done clear
C) Draughtsman done clear
D) Cannot be determined done clear
E) None of these done clear
View Answer play_arrowDirection: Read the given passage carefully and answer the questions that follow. |
A, B, C, D, E, F are members of a family. They are engineer, stenographer, doctor, draughtsman, lawyer and judge (not in order). A, the engineer is married to the lady stenographer. The judge is married to the lawyer. F, the draughtsman is the son of B and brother of E. C, the lawyer is the daughter-in-law of D. E is the unmarried doctor. D is the grandmother of F. There are two married couples in the family. |
A) AD only done clear
B) BC only done clear
C) Both AD and BC done clear
D) Both AC and BD done clear
E) None of these done clear
View Answer play_arrowDirection: Read the given passage carefully and answer the questions that follow. |
A, B, C, D, E, F are members of a family. They are engineer, stenographer, doctor, draughtsman, lawyer and judge (not in order). A, the engineer is married to the lady stenographer. The judge is married to the lawyer. F, the draughtsman is the son of B and brother of E. C, the lawyer is the daughter-in-law of D. E is the unmarried doctor. D is the grandmother of F. There are two married couples in the family. |
A) Judge done clear
B) Stenographer done clear
C) Doctor done clear
D) Cannot be determined done clear
E) None of these done clear
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