A) Mutually exclusive done clear
B) Independent as well as mutually exhaustive done clear
C) Independent done clear
D) Dependent only on A done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{4}{9}\] done clear
B) \[\frac{7}{16}\] done clear
C) \[\frac{3}{7}\] done clear
D) \[\frac{8}{15}\] done clear
E) None of these done clear
View Answer play_arrowA) \[1\] done clear
B) \[\frac{5}{13}\] done clear
C) \[\frac{7}{13}\] done clear
D) \[\frac{13}{7}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer4) 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) 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) \[\frac{(n-5)}{6}\] done clear
B) \[\frac{(n-4)}{5}\] done clear
C) \[\frac{5}{(n-4)}\] done clear
D) \[6\,(n-5)\] done clear
E) None of these done clear
View Answer play_arrowA) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\] done clear
B) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\] done clear
C) \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\] done clear
D) \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[\sqrt{13}\] done clear
B) \[\frac{\sqrt{13}}{3}\] done clear
C) \[\frac{\sqrt{13}}{4}\] done clear
D) \[\frac{\sqrt{13}}{2}\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{1}{4}\,\,{{n}^{2}}\,{{(n+1)}^{2}}+n\] done clear
B) \[\frac{1}{4}\,\,{{n}^{2}}\,{{(n+1)}^{2}}-n\] done clear
C) \[\frac{1}{4}\,\,n\,\,{{(n+1)}^{2}}-n\] done clear
D) \[\frac{1}{4}\,\,{{n}^{2}}\,{{(n-1)}^{2}}-n\] done clear
E) None of these done clear
View Answer play_arrowA) \[{}^{11}{{C}_{6}}\,{{(0.2)}^{5}}\,{{(0.4)}^{3}}\] done clear
B) \[{}^{11}{{C}_{6}}\,{{(0.4)}^{6}}\,{{(0.6)}^{5}}\] done clear
C) \[{}^{11}{{C}_{6}}\,{{(0.6)}^{6}}\,{{(0.4)}^{5}}\] done clear
D) \[{}^{11}{{C}_{6}}{{(0.24)}^{7}}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer11) If \[\frac{{{(a+ib)}^{2}}}{a-ib}-\frac{{{(a-ib)}^{2}}}{a+ib}=x+iy\] then x =.....
A) \[\frac{-2{{b}^{3}}}{{{({{a}^{2}}+{{b}^{2}})}^{2}}}\] done clear
B) \[\frac{6{{a}^{2}}b}{{{({{a}^{2}}+{{b}^{2}})}^{2}}}\] done clear
C) 0 done clear
D) \[\frac{5{{a}^{2}}b}{{{a}^{2}}+{{b}^{2}}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{8}{13}\] done clear
B) \[\frac{7}{13}\] done clear
C) \[\frac{6}{13}\] done clear
D) \[\frac{4}{13}\] 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) 0 done clear
B) 1 done clear
C) \[\frac{1}{6}\] done clear
D) \[\frac{-1}{6}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer15) If \[f(x)=\frac{x-1}{x+1},\] then f(2x) is equal to:
A) \[\frac{f(x)+1}{f(x)+3}\] done clear
B) \[\frac{3f(x)+1}{f(x)+3}\] done clear
C) \[\frac{f(x)+3}{f(x)+1}\] done clear
D) \[\frac{f(x)+3}{3f(x)+1}\] done clear
E) None of these done clear
View Answer play_arrowA) \[R-\left\{ 0 \right\}\] done clear
B) \[R-\left\{ 1 \right\}\] done clear
C) \[R-\left\{ -\,1 \right\}\] done clear
D) \[R-\left\{ -\,1,1 \right\}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer17) If \[{}^{n}{{C}_{12}}={}^{n}{{C}_{8}},\] then\[{}^{n}{{C}_{17}}\] is equal to
A) 1140 done clear
B) 1130 done clear
C) 1120 done clear
D) 1110 done clear
E) None of these done clear
View Answer play_arrowA) 120 done clear
B) 540 done clear
C) 150 done clear
D) 250 done clear
E) None of these done clear
View Answer play_arrowA) Continuous at x = 1 done clear
B) Differentiable at x = 1 done clear
C) Continuous at x= 3 done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{\pi }{6}\] done clear
B) \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{4} \right)\] done clear
C) \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\] done clear
D) \[\frac{\pi }{3}\] done clear
E) None of these done clear
View Answer play_arrowA) 4 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
E) None of these done clear
View Answer play_arrowA) 380 done clear
B) 320 done clear
C) 260 done clear
D) 95 done clear
E) None of these done clear
View Answer play_arrowA) \[2(\sec \theta -\tan \theta )\] done clear
B) \[2\sec \theta \] done clear
C) \[-2\tan \theta \] done clear
D) \[cosec\theta +\tan \theta \] done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{8}{5}\] done clear
B) \[\frac{4}{3}\] done clear
C) \[\frac{7}{4}\] done clear
D) \[1\] s done clear
E) None of these done clear
View Answer play_arrowquestion_answer25) If \[g(f(x))=\,\,|\sin x|\] and \[f(g(x))={{(\sin \sqrt{x})}^{2}},\] then
A) \[f(x)={{\sin }^{2}}x,\,g(x)=\sqrt{x}\] done clear
B) \[f(x)=\sin x,\,g(x)=\,\,|x|\] done clear
C) \[f(x)=\,\,{{x}^{2}},\,g(x)=\,\,\sin \sqrt{x}\] done clear
D) f and g cannot be determined. done clear
E) None of these done clear
View Answer play_arrowA) \[-\,4\] done clear
B) 6 done clear
C) 5 done clear
D) 3 done clear
E) None of these done clear
View Answer play_arrowA) 20 done clear
B) 10 done clear
C) 6 done clear
D) 5 done clear
E) None of these done clear
View Answer play_arrowA) \[s>t\,and\,{{a}_{101}}>{{b}_{101}}\] done clear
B) \[s>t\,and\,{{a}_{101}}<{{b}_{101}}\] done clear
C) \[s<t\,and\,{{a}_{101}}>{{b}_{101}}\] done clear
D) \[s<t\,and\,{{a}_{101}}<{{b}_{101}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[\left( -\,3,-\,8 \right)\] done clear
B) \[\left( \frac{1}{3},-\frac{8}{3} \right)\] done clear
C) \[\left( -\frac{10}{3},-\frac{7}{3} \right)\] done clear
D) \[\left( -\,3,-\,9 \right)\] done clear
E) None of these done clear
View Answer play_arrowA) \[\sqrt{2}\] done clear
B) \[\sqrt{5}\] done clear
C) \[\sqrt{3}\] done clear
D) \[2\sqrt{3}\] done clear
E) None of these done clear
View Answer play_arrowDirections: Study the following information to answer the given questions. Five Women Madhu, Kanchan, Chandni, Sheela and Rekha are married to Doctor, Naval Officer, Lawyer, Sales Manager and Engineer. The ladies are Accountant, Teacher and Doctor by Profession, while two are Housewives. |
(i) One husband and Wife have the same profession. |
(ii) Madhu and Kanchan are neither Housewives nor they are married to Doctor or Lawyer. |
(iii) Sheela and Rekha are neither Teacher nor Accountant and their Husbands are neither the Engineer nor are in Navy. |
(iv) The Sales Manager is not Madhu's or Chandni's husband. His Wife is an Accountant. |
(v) Rekha is not a Doctor |
(vi) Chandni is not a Teacher and the Teacher's husband is naval officer |
A) Sheela done clear
B) Rekha done clear
C) Madhu done clear
D) Chandni done clear
E) None of these done clear
View Answer play_arrowDirections: Study the following information to answer the given questions. Five Women Madhu, Kanchan, Chandni, Sheela and Rekha are married to Doctor, Naval Officer, Lawyer, Sales Manager and Engineer. The ladies are Accountant, Teacher and Doctor by Profession, while two are Housewives. |
(i) One husband and Wife have the same profession. |
(ii) Madhu and Kanchan are neither Housewives nor they are married to Doctor or Lawyer. |
(iii) Sheela and Rekha are neither Teacher nor Accountant and their Husbands are neither the Engineer nor are in Navy. |
(iv) The Sales Manager is not Madhu's or Chandni's husband. His Wife is an Accountant. |
(v) Rekha is not a Doctor |
(vi) Chandni is not a Teacher and the Teacher's husband is naval officer |
A) Naval Officer - Kanchan done clear
B) Sales Manager - Madhu done clear
C) Lawyer - Sheela done clear
D) Engineer ? Chandni done clear
E) None of these done clear
View Answer play_arrowDirections: Study the following information to answer the given questions. Five Women Madhu, Kanchan, Chandni, Sheela and Rekha are married to Doctor, Naval Officer, Lawyer, Sales Manager and Engineer. The ladies are Accountant, Teacher and Doctor by Profession, while two are Housewives. |
(i) One husband and Wife have the same profession. |
(ii) Madhu and Kanchan are neither Housewives nor they are married to Doctor or Lawyer. |
(iii) Sheela and Rekha are neither Teacher nor Accountant and their Husbands are neither the Engineer nor are in Navy. |
(iv) The Sales Manager is not Madhu's or Chandni's husband. His Wife is an Accountant. |
(v) Rekha is not a Doctor |
(vi) Chandni is not a Teacher and the Teacher's husband is naval officer |
A) Chandni and Rekha done clear
B) Sheela and Chandni done clear
C) Madhu and Rekha done clear
D) Chandni and Madhu done clear
E) None of these done clear
View Answer play_arrowDirections: Some statements are given followed by some conclusions. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the following conclusions if any follow from the given statements: |
Statements: |
All boys are girls. Some girls are men. No men is a women |
Conclusion: |
(i) Some girls are not women. |
(ii) Some girls being women is a possibility. |
(iii) Some boys are not women. |
A) Only (i) follow done clear
B) Either (ii) or (iii) follow done clear
C) Either (i) or (ii) follow done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowDirections: Some statements are given followed by some conclusions. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the following conclusions if any follow from the given statements: |
Statements |
Some birds are animals. Some animals are idiots, |
All idiots are humans. No idiot is bat. Some bats are animals. |
Conclusion: |
(i) Some animals are not bats. |
(ii) Some humans being bat is a possibility. |
(iii) Some humans are definitely not bat. |
A) Only (i) follow done clear
B) Either (ii) or (iii) follow done clear
C) Either (i) or (ii) follow done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowDirections: Some statements are given followed by some conclusions. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the following conclusions if any follow from the given statements: |
Statements: |
All boys are girls. Some girls are not men. No men is a women. Some women are girls. No woman is human. |
Conclusion: |
(i) Some girls are not human. |
(ii) Some girls being men is a possibility. |
(iii) All boys being men is a possibility. |
A) Only (i) follow done clear
B) Either (ii) or (iii) follow done clear
C) Either (i) or (ii) follow done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowquestion_answer37) Following questions are based on the information given below:
I. '\[P\times Q\]' means 'P is father of Q' |
II. '\[P-Q\]' means 'P is sister of Q' |
III. '\[P+Q\]' means 'P is mother of Q' |
IV. '\[P\div Q\]' means 'P is the brother of Q' |
Which of the following represents 'R' is niece of 'M'? |
A) \[M\div K\times T-R\] done clear
B) \[M-J+R-N\] done clear
C) \[R-M\times T\div W\] done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) 175 done clear
B) 165 done clear
C) 145 done clear
D) 121 done clear
E) None of these done clear
View Answer play_arrowquestion_answer39) Consider the following figures:
Which of the following group(s) of figures fit/fits into the same class? |
1. (1, 7, 8) |
2. (4, 5, 6) |
3. (2, 3, 9) |
Select the correct answer using the code given below: |
A) 1 and 2 only done clear
B) 2 and 3 only done clear
C) 1, 2 and 3 done clear
D) 3 only done clear
E) None of these done clear
View Answer play_arrowquestion_answer40) Consider the following figures :
Change in positions of beads in the four figures above follows a sequence. Following the same sequence, which of the figures below should appear as the fifth figure above? |
A) done clear
B) done clear
C) done clear
D) done clear
E) None of these done clear
View Answer play_arrowA) \[SP=2\sqrt{5}\] done clear
B) \[SQ:QP=(\sqrt{5}+1):4\] done clear
C) The slope of the tangent to the circle at Q is \[\frac{1}{2}\] done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) Area of the triangle XYZ is \[6\sqrt{6}\] done clear
B) The radius of circumcircle of the triangle XYZ is \[\frac{35}{4}\sqrt{6}\] done clear
C) \[\sin \,\,\frac{X}{2}\,\,\sin \,\,\frac{Y}{2}\,\,\sin \,\,\frac{Z}{2}=\,\,\frac{4}{35}\] done clear
D) \[{{\sin }^{2}}\,\,\left( \frac{X+Y}{2} \right)=\frac{3}{5}\] done clear
E) All of these done clear
View Answer play_arrowLet a, \[\lambda ,\] \[\mu \in R\]. Consider the system of linear equations |
\[ax+2y=\lambda \] |
\[3x-2y=\mu \] |
Which of the following statement(s) is (are) correct? |
A) If \[a\ne -\,3,\] then the system has a unique solution for all values of \[\lambda \] and \[\mu \] done clear
B) If \[\lambda +\mu =0\], then the system has infinitely many solutions for \[a=-\,3\] done clear
C) If \[\lambda +\mu \ne 0,\] then the system has no solution for \[a=-\,3\] done clear
D) AII of these done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{1}{2}\] done clear
B) \[\frac{2}{9}\] done clear
C) \[\frac{-1}{2}\] done clear
D) \[\frac{-2}{9}\] done clear
E) None of these done clear
View Answer play_arrowA) \[3-\sqrt{3}\] done clear
B) \[2\,(3-\sqrt{3})\] done clear
C) \[2(\sqrt{3}-1)\] done clear
D) \[2\,(2+\sqrt{3})\] done clear
E) None of these done clear
View Answer play_arrowA) 0 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
E) None of these done clear
View Answer play_arrowA) \[{{R}_{2}}{{R}_{3}}=4\sqrt{6}\] done clear
B) Area of the triangle \[O{{R}_{2}}{{R}_{3}}\] is \[6\sqrt{2}\] done clear
C) Area of the triangle \[P{{Q}_{2}}{{Q}_{3}}\] is \[6\sqrt{2}\] done clear
D) All of these done clear
E) None of these done clear
View Answer play_arrowA) \[\frac{2}{3},{{e}^{2/3}}\] done clear
B) \[\frac{4}{3},{{e}^{4/3}}\] done clear
C) \[\frac{3}{2},{{e}^{3/2}}\] done clear
D) \[\frac{1}{2},{{e}^{1/2}}\] done clear
E) None of these done clear
View Answer play_arrowA) \[ab\,(r-1)\,\,(s-1)\,\,(s-r)\] done clear
B) \[\frac{1}{2}\,\,ab\,(r+1)\,\,(s+1)\,\,(s-r)\] done clear
C) \[\frac{1}{2}\,\,ab\,(r-1)\,\,(s-1)\,\,(s-r)\] done clear
D) \[ab\,(r+1)\,\,(s+1)\,\,(r-s)\] done clear
E) None of these. done clear
View Answer play_arrowquestion_answer50) The standard deviation of the numbers 31, 32, 33, ....... 46, 47 is
A) \[\sqrt{\frac{47}{12}}\] done clear
B) \[\sqrt{\frac{{{47}^{2}}-1}{12}}\] done clear
C) \[2\,\sqrt{6}\] done clear
D) \[4\,\sqrt{3}\] done clear
E) None of these done clear
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