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
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View Answer play_arrow
A)
\[\frac{4}{9}\]
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_arrow
A)
\[1\]
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
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View Answer play_arrow
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
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View Answer play_arrow
A)
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
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View Answer play_arrow
A)
\[\frac{(n-5)}{6}\]
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
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View Answer play_arrow
A)
\[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]
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
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View Answer play_arrow
A)
\[\sqrt{13}\]
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
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View Answer play_arrow
If \[\omega \] is an imaginary cube root of unity. then value of the expression \[2\,(1+\omega )\,\,(1+{{\omega }^{2}})+3\,(2+\omega )\,\,(2+{{\omega }^{2}})\]\[+.....+(n\,+1)\,\,(n\,+\omega )\,\,(n\,+{{\omega }^{2}})\]
A)
\[\frac{1}{4}\,\,{{n}^{2}}\,{{(n+1)}^{2}}+n\]
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
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View Answer play_arrow
A)
\[{}^{11}{{C}_{6}}\,{{(0.2)}^{5}}\,{{(0.4)}^{3}}\]
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
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View Answer play_arrow
A)
\[\frac{-2{{b}^{3}}}{{{({{a}^{2}}+{{b}^{2}})}^{2}}}\]
done
clear
B)
\[\frac{6{{a}^{2}}b}{{{({{a}^{2}}+{{b}^{2}})}^{2}}}\]
done
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C)
0
done
clear
D)
\[\frac{5{{a}^{2}}b}{{{a}^{2}}+{{b}^{2}}}\]
done
clear
E)
None of these
done
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View Answer play_arrow
A)
\[\frac{8}{13}\]
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
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View Answer play_arrow
A)
\[\left( \frac{-16}{5},\frac{27}{10} \right)\]
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
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View Answer play_arrow
A)
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_arrow
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
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View Answer play_arrow
The domain of the derivative of the function \[f(x)=\left\{ \begin{matrix} {{\tan }^{-1}}x, & if\,\,x||\,\le \,1 \\ \frac{1}{2}(|x|-1), & if\,\,|x|\,\le \,1 \\ \end{matrix} \right.\] is
A)
\[R-\left\{ 0 \right\}\]
done
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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
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View Answer play_arrow
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_arrow
A)
120
done
clear
B)
540
done
clear
C)
150
done
clear
D)
250
done
clear
E)
None of these
done
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View Answer play_arrow
A)
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
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View Answer play_arrow
A)
\[\frac{\pi }{6}\]
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
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View Answer play_arrow
A)
4
done
clear
B)
3
done
clear
C)
2
done
clear
D)
1
done
clear
E)
None of these
done
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View Answer play_arrow
A)
380
done
clear
B)
320
done
clear
C)
260
done
clear
D)
95
done
clear
E)
None of these
done
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View Answer play_arrow
A)
\[2(\sec \theta -\tan \theta )\]
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
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View Answer play_arrow
A)
\[\frac{8}{5}\]
done
clear
B)
\[\frac{4}{3}\]
done
clear
C)
\[\frac{7}{4}\]
done
clear
D)
\[1\] s
done
clear
E)
None of these
done
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View Answer play_arrow
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
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View Answer play_arrow
A)
\[-\,4\]
done
clear
B)
6
done
clear
C)
5
done
clear
D)
3
done
clear
E)
None of these
done
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View Answer play_arrow
A)
20
done
clear
B)
10
done
clear
C)
6
done
clear
D)
5
done
clear
E)
None of these
done
clear
View Answer play_arrow
Let \[{{b}_{i}}>1\] for i =1, 2 ... 101. Suppose\[\log {}_{e}{{b}_{1}}\], \[\log {}_{e}{{b}_{2}},.....,\,\,log{}_{e}{{b}_{101}}\]are in Arithmetic progression (A.P) with the common difference \[\log {}_{e}\] 2. Suppose \[{{a}_{1}},\,{{a}_{2}},\,.....,\,{{a}_{101}}\] are in A.P. such that \[{{a}_{1}}={{b}_{1}}\]and\[{{a}_{51}}={{b}_{51}}\]. If \[t={{b}_{1}}+{{b}_{2}}+.......+{{b}_{51}}\] and \[s={{a}_{1}}+{{a}_{2}}+.....+{{a}_{51}}\] then
A)
\[s>t\,and\,{{a}_{101}}>{{b}_{101}}\]
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_arrow
A)
\[\left( -\,3,-\,8 \right)\]
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
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View Answer play_arrow
A)
\[\sqrt{2}\]
done
clear
B)
\[\sqrt{5}\]
done
clear
C)
\[\sqrt{3}\]
done
clear
D)
\[2\sqrt{3}\]
done
clear
E)
None of these
done
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View Answer play_arrow
Directions: 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
Who among the following is engaged in Doctor's Profession with her husband?
A)
Sheela
done
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B)
Rekha
done
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C)
Madhu
done
clear
D)
Chandni
done
clear
E)
None of these
done
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View Answer play_arrow
Directions: 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
Which of the following pair is the correct match of husband - wife?
A)
Naval Officer - Kanchan
done
clear
B)
Sales Manager - Madhu
done
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C)
Lawyer - Sheela
done
clear
D)
Engineer ? Chandni
done
clear
E)
None of these
done
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View Answer play_arrow
Directions: 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
Who among the followings are Housewives?
A)
Chandni and Rekha
done
clear
B)
Sheela and Chandni
done
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C)
Madhu and Rekha
done
clear
D)
Chandni and Madhu
done
clear
E)
None of these
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View Answer play_arrow
Directions: 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
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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
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View Answer play_arrow
Directions: 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
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View Answer play_arrow
Directions: 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
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View Answer play_arrow
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
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View Answer play_arrow
A)
175
done
clear
B)
165
done
clear
C)
145
done
clear
D)
121
done
clear
E)
None of these
done
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View Answer play_arrow
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
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B)
2 and 3 only
done
clear
C)
1, 2 and 3
done
clear
D)
3 only
done
clear
E)
None of these
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View Answer play_arrow
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
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B)
done
clear
C)
done
clear
D)
done
clear
E)
None of these
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View Answer play_arrow
A)
\[SP=2\sqrt{5}\]
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
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View Answer play_arrow
A)
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
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View Answer play_arrow
Let 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
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View Answer play_arrow
Find the derivative of f(x) \[\left\{ \begin{matrix} \frac{x-1}{2{{x}^{2}}-7x+5}\,\,\,, & when\,x\ne 1 \\ -\frac{1}{3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,, & when\,x=1 \\ \end{matrix} \right.\] at x=1
A)
\[\frac{1}{2}\]
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
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View Answer play_arrow
A)
\[3-\sqrt{3}\]
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_arrow
A)
0
done
clear
B)
1
done
clear
C)
2
done
clear
D)
3
done
clear
E)
None of these
done
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View Answer play_arrow
A)
\[{{R}_{2}}{{R}_{3}}=4\sqrt{6}\]
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
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View Answer play_arrow
\[Let\,\,f(x)\,\,\,=\left[ \begin{matrix} {{\{1+|\sin x|\}}^{a/|\sin x|}}\,\,\,\,\,, & \frac{\pi }{6}<x<0 \\ b\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,, & x=0 \\ {{e}^{\tan 2x/\tan 3x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}}, & 0<x<\frac{\pi }{6} \\ \end{matrix} \right.\]. Determine a and b such that f(x) is continuous at x = 0.
A)
\[\frac{2}{3},{{e}^{2/3}}\]
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
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View Answer play_arrow
Area of the triangle with vertices (a, b),\[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}}),\] where \[a,\,{{x}_{1}}\] and \[{{x}_{2}},\] are in G.P. with common ratio r and b, \[{{y}_{1}}\] and \[{{y}_{2}}\] are in G.P. with common ratio s, is given by
A)
\[ab\,(r-1)\,\,(s-1)\,\,(s-r)\]
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
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View Answer play_arrow
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
View Answer play_arrow