A) \[{{2}^{99}}\] done clear
B) \[{{99}^{2}}\] done clear
C) \[{{100}^{99}}\] done clear
D) \[{{18}^{99}}\] done clear
E) None of these done clear
View Answer play_arrowA) 6 done clear
B) 8 done clear
C) 10 done clear
D) 12 done clear
E) None of these done clear
View Answer play_arrowA) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} done clear
B) {(2, 2), (3, 2), (4, 2), (2, 4)} done clear
C) {(3, 3), (3, 4), (5, 4), (4, 3), (3, 1)} done clear
D) {(1, 1), (2, 2), (3, 4), (5, 1), (5, 2)} done clear
E) None of these done clear
View Answer play_arrowA) \[[f{{(x)}^{2}}+[g{{(x)}^{2}}]=0\] done clear
B) \[\frac{f(x)}{g(x)}\] done clear
C) \[\frac{g\,(x)}{f\,(x)}\] done clear
D) \[f{{(x)}^{2}}>g{{(x)}^{2}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[(-\infty ,2)\] done clear
B) \[[2,\,\,4]\] done clear
C) \[(4,\,\,\infty ]\] done clear
D) \[[1,\,\,-\infty )\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer6) If \[z=3-4i,\] then \[{{z}^{4}}-3{{z}^{3}}+3{{z}^{2}}+99z-95\] is equal to
A) 5 done clear
B) 6 done clear
C) \[-\,5\] done clear
D) \[-\,4\] done clear
E) None of these done clear
View Answer play_arrowA) \[|z-a|\,\,=a\] done clear
B) \[\left| z-\frac{1}{1-a} \right|=\,|1-a|\] done clear
C) \[\left| z-\frac{1}{1-a} \right|=\frac{1}{|1-a|}\] done clear
D) \[|z-(1-a)|\,=\,|1-a|\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer8) If tan (u + iv) = i, then the value of v is
A) 0 done clear
B) \[\infty \] done clear
C) 1 done clear
D) 3 done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{2\sqrt{6}}{5}+\frac{24i}{5}\] done clear
B) \[\frac{24}{5}+\frac{2\,\sqrt{6}\,i}{5}\] done clear
C) \[\frac{2\sqrt{6}}{5}-\frac{24\,i}{5}\] done clear
D) Both (A) and (B) done clear
E) None of these done clear
View Answer play_arrowA) \[\left( 3+\frac{p}{n} \right)\] done clear
B) \[\left( 3-\frac{p}{n} \right)\] done clear
C) \[\left( 3+\frac{n}{p} \right)\] done clear
D) \[\left( 3-\frac{n}{p} \right)\] done clear
E) None of these done clear
View Answer play_arrowA) 6 done clear
B) 8 done clear
C) 10 done clear
D) 11 done clear
E) None of these done clear
View Answer play_arrowquestion_answer12) The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is
A) 2489 done clear
B) 4735 done clear
C) 2317 done clear
D) 2632 done clear
E) None of these done clear
View Answer play_arrowA) \[{{c}^{3}}a={{b}^{3}}d\] done clear
B) \[c{{a}^{3}}=b{{d}^{3}}\] done clear
C) \[{{a}^{3}}b={{c}^{3}}d\] done clear
D) \[a{{b}^{3}}=c{{d}^{3}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[1-\sqrt{3}:2:1+\sqrt{3}\] done clear
B) \[1:\sqrt{2}:-\,\sqrt{3}\] done clear
C) \[1:-\,\sqrt{2}:\sqrt{3}\] done clear
D) \[1\mp \sqrt{3}:-\,2:1\pm \sqrt{3}\] done clear
E) None of these done clear
View Answer play_arrowA) 11 done clear
B) 12 done clear
C) 13 done clear
D) 15 done clear
E) None of these done clear
View Answer play_arrowquestion_answer16) If \[^{n+2}{{C}_{8}}:{}^{n-2}{{P}_{4}}=57:16\] find n.
A) 21 done clear
B) 19 done clear
C) 17 done clear
D) 8 done clear
E) None of these done clear
View Answer play_arrowA) a = b done clear
B) a > b done clear
C) a < b done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[-\,560\] done clear
B) 498 done clear
C) 516 done clear
D) \[-\,168\] done clear
E) None of these done clear
View Answer play_arrowA) 1 or 2 done clear
B) 2 or 3 done clear
C) 3 or 1 done clear
D) Both (A) and (B) done clear
E) None of these done clear
View Answer play_arrowA) nS = 1 done clear
B) 1/S is an integer done clear
C) \[1/{{S}^{2}}\] is an integer done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[x=n\pi +{{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\] done clear
B) \[x=2n\pi -{{\tan }^{-1}}(b/a)\] done clear
C) \[x=2n\pi -{{\tan }^{-1}}\left( \frac{b}{a} \right)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\] done clear
D) \[x=2n\pi -{{\tan }^{-1}}(b/a)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\] done clear
E) None of these done clear
View Answer play_arrowA) a, b, c are in A.P done clear
B) \[{{a}^{2}},\,{{b}^{2}},\,{{c}^{2}}\] are in A.P done clear
C) \[{{a}^{2}},\,{{b}^{2}},\,{{c}^{2}}\]are in G.P done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[5{{x}^{2}}-5{{y}^{2}}-72x+54y+225=0\] done clear
B) \[5{{x}^{2}}-5{{y}^{2}}+72x+54y+225=0\] done clear
C) \[5{{x}^{2}}+5{{y}^{2}}+72x+54y+225=0\] done clear
D) \[5{{x}^{2}}+5{{y}^{2}}-72x+54y+225=0\] done clear
E) None of these done clear
View Answer play_arrowA) \[(\alpha +\beta )(x+y)=2\,\alpha \beta xy\] done clear
B) \[\alpha \beta \,(x+y)=xy\,(\alpha +\beta )\] done clear
C) \[\alpha \beta \,(x+y)=2xy\,(\alpha +\beta )\] done clear
D) \[\alpha \beta \,(x-y)=2xy\,(\alpha -\beta )\] done clear
E) None of these done clear
View Answer play_arrowA) A.P done clear
B) G.P done clear
C) H.P done clear
D) Both (A) and (B) done clear
E) None of these done clear
View Answer play_arrowA) \[7,\frac{1}{7}\] done clear
B) \[3,\frac{1}{3}\] done clear
C) \[-7,\frac{1}{7}\] done clear
D) \[-7,\frac{-1}{7}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer27) The lines \[{{(lx+my)}^{2}}-3\,{{(mx-ly)}^{2}}=0\] and \[lx+my+n=0\] form
A) An isosceles triangle done clear
B) A right angled triangle done clear
C) An equilateral triangle done clear
D) Both (A) and (B) done clear
E) None of these done clear
View Answer play_arrowA) \[(a,\,\,-a)\] done clear
B) \[(a/2,\,\,a/2)\] done clear
C) \[(a/2,\,\,\pm a)\] done clear
D) \[(\pm \,a,\,\,a/2)\] done clear
E) None of these done clear
View Answer play_arrowDirection: In a music school 28 students learn trumpet 30 students learn violin and 32 students learn guitar. 6 students learn trumpet and violin 8 students learn violin and guitar 10 students learn guitar and trumpet. The number of students who learn only one instrument is 54. Also 20 students learn only violin. Every student learn at least one instrument out of the three instruments. |
A) 45 done clear
B) 55 done clear
C) 60 done clear
D) 70 done clear
E) None of these done clear
View Answer play_arrowDirection: In a music school 28 students learn trumpet 30 students learn violin and 32 students learn guitar. 6 students learn trumpet and violin 8 students learn violin and guitar 10 students learn guitar and trumpet. The number of students who learn only one instrument is 54. Also 20 students learn only violin. Every student learn at least one instrument out of the three instruments. |
A) 8 done clear
B) 6 done clear
C) 4 done clear
D) 2 done clear
E) None of these done clear
View Answer play_arrowquestion_answer31) Find the next term in the series: 3, 20, 63, 144, 275, ?
A) 354 done clear
B) 468 done clear
C) 548 done clear
D) 554 done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{9}{32}\] done clear
B) \[\frac{10}{17}\] done clear
C) \[\frac{9}{34}\] done clear
D) \[\frac{12}{35}\] done clear
E) None of these done clear
View Answer play_arrowA) std done clear
B) dim done clear
C) bro done clear
D) cus done clear
E) None of these done clear
View Answer play_arrowquestion_answer34) How many triangles are there in the figure given below?
A) 24 done clear
B) 27 done clear
C) 25 done clear
D) 26 done clear
E) None of these done clear
View Answer play_arrowDirection: Read the information carefully and answer the question based on it. Five persons are sitting in a row. One of the two persons at the extreme ends is intelligent and other one is fair. A fat person is sitting to the right of a weak person. A tall person is too left of the fair person and the weak person is sitting between the intelligent and the fat person. |
A) First done clear
B) Second done clear
C) Third done clear
D) Fourth done clear
E) None of these done clear
View Answer play_arrowDirection: Read the information carefully and answer the question based on it. Five persons are sitting in a row. One of the two persons at the extreme ends is intelligent and other one is fair. A fat person is sitting to the right of a weak person. A tall person is too left of the fair person and the weak person is sitting between the intelligent and the fat person. |
A) Intelligent done clear
B) fat done clear
C) Fair done clear
D) weak done clear
E) None of these done clear
View Answer play_arrowDirection: Read the information carefully and answer the question based on it. Five persons are sitting in a row. One of the two persons at the extreme ends is intelligent and other one is fair. A fat person is sitting to the right of a weak person. A tall person is too left of the fair person and the weak person is sitting between the intelligent and the fat person. |
A) Intelligent done clear
B) fat done clear
C) Fair done clear
D) tall done clear
E) None of these done clear
View Answer play_arrowDirection: In each question given below certain symbols are used with the following meaning. |
P ?Q means 'P is greater than Q'. |
P @ Q, means 'P is either greater than or equal to Q'. |
P * Q means 'P is equal to Q'. |
P # Q. means 'P is either smaller than or equal to Q'. |
P $ Q means 'P is smaller than Q'. |
Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I & II given below them is/are definitely true. |
Statements: A # B, C * A, D $ C, B " F | |
Conclusions | I. B @ C |
II. F" C |
A) Only Conclusion I is true. done clear
B) Only Conclusion II is true. done clear
C) Either Conclusion I or II is true. done clear
D) Neither Conclusion I nor II is true. done clear
E) Both Conclusions I & II are true. done clear
View Answer play_arrowDirection: In each question given below certain symbols are used with the following meaning. |
P ?Q means 'P is greater than Q'. |
P @ Q, means 'P is either greater than or equal to Q'. |
P * Q means 'P is equal to Q'. |
P # Q. means 'P is either smaller than or equal to Q'. |
P $ Q means 'P is smaller than Q'. |
Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I & II given below them is/are definitely true. |
Statements: A * B, C # D, A " F, B @ C | |
Conclusions | I. F" B |
II. A @ C |
A) Only Conclusion I is true. done clear
B) Only Conclusion II is true. done clear
C) Either Conclusion I or II is true. done clear
D) Neither Conclusion I nor II is true. done clear
E) Both Conclusions I & II are true. done clear
View Answer play_arrowDirection: In each question given below certain symbols are used with the following meaning. |
P ?Q means 'P is greater than Q'. |
P @ Q, means 'P is either greater than or equal to Q'. |
P * Q means 'P is equal to Q'. |
P # Q. means 'P is either smaller than or equal to Q'. |
P $ Q means 'P is smaller than Q'. |
Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I & II given below them is/are definitely true. |
Statements: A @ B, B * C, D "A, E # D | |
Conclusions | I. B * E |
II. C $ A |
A) Only Conclusion I is true. done clear
B) Only Conclusion II is true. done clear
C) Either Conclusion I or II is true. done clear
D) Neither Conclusion I nor II is true. done clear
E) Both Conclusions I & II are true. done clear
View Answer play_arrowquestion_answer41) If \[x=3-\sqrt{5},\] then \[\frac{\sqrt{x}}{\sqrt{2}+\sqrt{(3x-2)}}=\]
A) 5 done clear
B) \[\sqrt{5}\] done clear
C) \[\frac{1}{5}\] done clear
D) \[\frac{1}{\sqrt{5}}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer42) If \[|z-25\,i|\,\,\le 15,\] the \[|\max .\,\,amp(z)-\,\min .\,\,amp(z)|\]
A) \[{{\cos }^{-1}}\left( \frac{3}{5} \right)\] done clear
B) \[\pi -2{{\cos }^{-1}}\left( \frac{3}{5} \right)\] done clear
C) \[\frac{\pi }{2}+{{\cos }^{-1}}\left( \frac{3}{5} \right)\] done clear
D) \[{{\sin }^{-1}}\left( \frac{3}{5} \right)-{{\cos }^{-1}}\left( \frac{3}{5} \right)\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer43) The value of n if
a. | \[{}^{n+4}{{C}_{n+1}}-{}^{n+3}{{C}_{n}}=15\left( n+2 \right)\] | (p) | 6 |
b. | \[11({}^{n}{{P}_{4}})=20({}^{n-2}{{P}_{4}})\] | (q) | 18 |
c. | \[{}^{2n}{{C}_{3}}=11{}^{n}{{C}_{3}}\] | (r) | 16 |
d. | If p(n,r) = 1680 and C(n,r) = 70 | (s) | 27 |
A) a\[\to \]p, b\[\to \]q, c\[\to \]r, d\[\to \]s done clear
B) a\[\to \]r, b\[\to \]p, c\[\to \]s, d\[\to \]q done clear
C) a\[\to \]s, b\[\to \]c, c\[\to \]q, d\[\to \]p done clear
D) a\[\to \]s, b\[\to \]r, c\[\to \]p, d\[\to \]q done clear
E) None of these done clear
View Answer play_arrowa. | The number of permutations the word ENDEA is | (p) | 5! |
b. | The number of permutations in Which the letter E occurs in the first and the last positions is | (q) | \[2\times 5!\] |
c. | The number of permutations in Which none of the letters D, L, N occurs in the last five positions is | (r) | \[7\times 5!\] |
d. | The number of permutations in Which the letters A, E, 0 occur only in odd position is | (s) | \[21\times 5!\] |
A) a - p, b - q, c - r, d - s done clear
B) a - p, b - s, c - q, d - r done clear
C) a - q, b - s, c - r, d - p done clear
D) a - s, b - r, c - q, d - p done clear
E) None of these done clear
View Answer play_arrowA) \[\sqrt{2}\] done clear
B) \[\sqrt{3}\] done clear
C) 1 done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[1<e<2\text{/}\sqrt{3}\] done clear
B) \[e=2\text{/}\sqrt{3}\] done clear
C) \[e=\frac{\sqrt{3}}{2}\] done clear
D) \[e>2\text{/}\sqrt{3}\] done clear
E) None of these done clear
View Answer play_arrowA) \[\left( \frac{-16}{5},\frac{27}{10} \right)\] done clear
B) \[\left( \frac{-16}{7},\frac{53}{10} \right)\] done clear
C) \[\left( \frac{-16}{5},\frac{53}{10} \right)\] done clear
D) \[\left( \frac{16}{5},\frac{-53}{10} \right)\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{b}{a}\] done clear
B) \[1-\frac{b}{a}\] done clear
C) \[\frac{{{b}^{2}}}{{{a}^{2}}}\] done clear
D) \[\frac{a}{b}\] done clear
E) None of these done clear
View Answer play_arrowA) \[A=\frac{13}{2}\] done clear
B) \[B=-\,2\] done clear
C) A+B+C =5 done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) P (only one of them occurs)\[=P\,({{\bar{E}}_{1}}{{E}_{2}}{{E}_{3}}+{{E}_{1}}{{\bar{E}}_{2}}{{E}_{3}}+{{E}_{1}}{{E}_{2}}{{\bar{E}}_{3}})\] done clear
B) P (none of them occurs)\[=P\,({{\bar{E}}_{1}}+{{\bar{E}}_{2}}+{{\bar{E}}_{3}})\] done clear
C) P (at least one of them occurs)\[=P\,({{E}_{1}}+{{E}_{2}}+{{E}_{3}})\] done clear
D) P (all three occurs)\[=P\,({{E}_{1}}+{{E}_{2}}+{{E}_{3}})\] done clear
E) None of these done clear
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