\[Sin\left[ co{{t}^{-1}}\left\{ \cos \left( {{\tan }^{-1}}x \right) \right\} \right]\]is equal to:
A)
\[\sqrt{\frac{1+{{x}^{2}}}{2+{{x}^{2}}}}\]
done
clear
B)
\[\sqrt{\frac{2+{{x}^{2}}}{2+{{x}^{2}}}}\]
done
clear
C)
\[\sqrt{\frac{1+{{x}^{2}}}{2-{{x}^{2}}}}\]
done
clear
D)
\[\sqrt{\frac{1-{{x}^{2}}}{2+{{x}^{2}}}}\]
done
clear
View Answer play_arrow
\[\mathbf{y}=\mathbf{sinx}+\sqrt{3}.\mathbf{cosx}\]is maximum when
A)
\[x={{60}^{{}^\circ }}\]
done
clear
B)
(b)\[x={{30}^{{}^\circ }}\]
done
clear
C)
\[x={{45}^{{}^\circ }}\]
done
clear
D)
\[x={{75}^{{}^\circ }}\]
done
clear
View Answer play_arrow
\[\int{\sqrt{\frac{{{e}^{x}}-1}{{{e}^{x}}+1}}.}\mathbf{dx}\]is equal to:
A)
\[\int{\frac{\cos 2x-1}{\cos 2x+1}}.\mathbf{dx}\]
done
clear
B)
\[\log \left( {{e}^{x}}+\sqrt{{{e}^{2x}}-1} \right)-{{\sec }^{-1}}({{e}^{x}})+c\]
done
clear
C)
\[\log \left( {{e}^{x}}-\sqrt{{{e}^{2x}}-1} \right)-{{\sec }^{-1}}({{e}^{x}})+c\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
The value of the integral flog \[\int\limits_{0}^{\infty }{\log \left( x+\frac{1}{x} \right)}.\frac{dx}{1+{{x}^{2}}}\]is:
A)
\[\frac{\pi }{2}.log2\]
done
clear
B)
\[\pi .log2\]
done
clear
C)
\[-\pi .log2\]
done
clear
D)
\[-\frac{\pi }{2}.log2\]
done
clear
View Answer play_arrow
Lf \[\mathbf{A}=\left[ \begin{align} & 1\,\,\,2 \\ & 2\,\,\,1 \\ \end{align} \right]\]then adj. of A is equal to:
A)
\[\left[ \begin{align} & -1\,\,\,2 \\ & 2\,\,\,-1 \\ \end{align} \right]\]
done
clear
B)
\[\left[ \begin{align} & -1\,\,\,-2 \\ & -2\,\,\,-1 \\ \end{align} \right]\]
done
clear
C)
\[\left[ \begin{align} & 2\,\,\,1 \\ & 1\,\,\,1 \\ \end{align} \right]\]
done
clear
D)
\[\left[ \begin{align} & 1\,\,\,-2 \\ & -2\,\,\,1 \\ \end{align} \right]\]
done
clear
View Answer play_arrow
The value of the determinant
is
A)
\[-2\]
done
clear
B)
2
done
clear
C)
0
done
clear
D)
1
done
clear
View Answer play_arrow
If \[\left| \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}} \right|=\left| \overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}} \right|\] then angle between \[\overrightarrow{\mathbf{a}}\] and\[\overrightarrow{\mathbf{b}}\] is:
A)
\[{{0}^{{}^\circ }}\]
done
clear
B)
\[{{45}^{{}^\circ }}\]
done
clear
C)
\[{{60}^{{}^\circ }}\]
done
clear
D)
\[{{90}^{{}^\circ }}\]
done
clear
View Answer play_arrow
The acute angle between two lines whose direction ratio are 1, 3, 6 and 1, 2, 2 is;
A)
\[{{\cos }^{-1}}\left( \frac{17}{21} \right)\]
done
clear
B)
\[{{\cos }^{-1}}\left( \frac{18}{21} \right)\]
done
clear
C)
\[{{\cos }^{-1}}\left( \frac{20}{21} \right)\]
done
clear
D)
\[{{\cos }^{-1}}\left( \frac{23}{21} \right)\]
done
clear
View Answer play_arrow
\[\mathbf{4ta}{{\mathbf{n}}^{-1}}\left( \frac{1}{5} \right)-\mathbf{tan}9\frac{1}{239}\]is equal to:
A)
\[\pi \]
done
clear
B)
\[\frac{\pi }{2}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{\pi }{4}\]
done
clear
View Answer play_arrow
If \[P(A)=0.3,P(B)=0.6,P\left( \frac{B}{A} \right)=0.5\], then \[P(A\cup B)=\]
A)
0.60
done
clear
B)
0.15
done
clear
C)
0.75
done
clear
D)
0.65
done
clear
View Answer play_arrow
A random variable X has the following probability distribution: X: 0 1 2 3 4 5 6 7 8 P(X=x): a 3a 5a 7a 9a 11a 13a 15a 17a Then the value of a is:
A)
\[\frac{7}{81}\]
done
clear
B)
\[\frac{5}{81}\]
done
clear
C)
\[\frac{2}{81}\]
done
clear
D)
\[\frac{1}{81}\]
done
clear
View Answer play_arrow
\[\int\limits_{\frac{\pi }{6}}^{\frac{\pi }{3}}{\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}.dx}\]
A)
\[\frac{\pi }{6}\]
done
clear
B)
\[\frac{\pi }{12}\]
done
clear
C)
\[\frac{2\pi }{3a}\]
done
clear
D)
\[\frac{\pi }{4}\]
done
clear
View Answer play_arrow
The equation of the normal to the curve \[\mathbf{y}=\mathbf{sinx}\] at \[\left( \mathbf{0},\mathbf{0} \right)\] is:
A)
\[x+y=0\]
done
clear
B)
\[x=y\]
done
clear
C)
\[x=0\]
done
clear
D)
\[y=0\]
done
clear
View Answer play_arrow
The degree of the differential equation of which \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4a}\left( \mathbf{x}+\mathbf{a} \right)\]is a solution be:
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
None of these
done
clear
View Answer play_arrow
Let \[\phi \left( \mathbf{x} \right)=~\left\{ \begin{align} & \frac{1-\cos \lambda x}{x\sin x},x\ne 0 \\ & \frac{1}{2},x=0 \\ \end{align} \right.\] If \[\phi \left( \mathbf{x} \right)\]is continuous at \[\mathbf{x}=\mathbf{0}\], then\[\lambda \]=
A)
0
done
clear
B)
±1
done
clear
C)
2
done
clear
D)
\[-2\]
done
clear
View Answer play_arrow
If f(x) is an even function, then \[\int\limits_{0}^{x}{\mathbf{f}\left( \mathbf{t} \right).\mathbf{dt}}\] is:
A)
odd
done
clear
B)
even
done
clear
C)
neither even nor odd
done
clear
D)
None of these
done
clear
View Answer play_arrow
A man is known to speak truth 3 out of 4 times. He throws a dice and report that it is five. The probability that it is actually five is:
A)
\[\frac{3}{5}\]
done
clear
B)
\[\frac{1}{6}\]
done
clear
C)
\[\frac{2}{3}\]
done
clear
D)
\[\frac{3}{8}\]
done
clear
View Answer play_arrow
The corner points of the feasible region determined by the system of linear constraints are\[\left( \mathbf{0},\mathbf{10} \right),\left( \mathbf{5},\mathbf{5} \right),\left( \mathbf{15},\mathbf{15} \right),\left( \mathbf{0},\mathbf{20} \right)\]. Let\[\mathbf{Z}=\mathbf{px}+\mathbf{qy}\], where\[\mathbf{p},\mathbf{q}>\mathbf{0}\]. Condition on p and q so that the maximum of Z occur sat both the points \[\left( \mathbf{15},\mathbf{15} \right)\] and (0, 20) is
A)
\[p=q\]
done
clear
B)
\[p=2q\]
done
clear
C)
\[q=2p\]
done
clear
D)
\[q=3p\]
done
clear
View Answer play_arrow
\[\mathbf{cot}\left( \frac{\pi }{4}-\mathbf{2}.c\mathbf{o}{{\mathbf{t}}^{-\mathbf{1}}}\mathbf{3} \right)=\]
A)
5
done
clear
B)
6
done
clear
C)
7
done
clear
D)
None of these
done
clear
View Answer play_arrow
The area bounded by the parabola\[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4ax}\], latus rectum and x-axis is:
A)
\[\frac{2}{3}{{a}^{2}}\]
done
clear
B)
\[\frac{4}{3}{{a}^{2}}\]
done
clear
C)
\[\frac{1}{3}{{a}^{2}}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow