1. What is the value of, ∫01sin−1x1−x2dx \int_{0}^{1} \frac{\sin ^{-1} x}{\sqrt{1-x^{2}}} d x ∫011−x2sin−1xdx ?
π216 \frac{\pi^{2}}{16} 16π2
π28 \frac{\pi^{2}}{8} 8π2
π24 \frac{\pi^{2}}{4} 4π2
π2 \frac{\pi}{2} 2π
2. If y=sin2x y=\sin 2 x y=sin2x then
i. y1=2cos2x y_{1}=2 \cos 2 x y1=2cos2x
ii. y2+4y=0 y_{2}+4 y=0 y2+4y=0
iii. y3−4y1=0 y_{3}-4 y_{1}=0 y3−4y1=0
Which one of the following is correct?
i and ii
i and iii
ii and iii
i, ii and iii
3. Which of the following is a skew symmetric matrix?
[a00−a] \left[\begin{array}{cc}a & 0 \\ 0 & -a\end{array}\right] [a00−a]
[a0−a0] \left[\begin{array}{cc}a & 0 \\ -a & 0\end{array}\right] [a−a00]
[0a−a0] \left[\begin{array}{cc}0 & a \\ -a & 0\end{array}\right] [0−aa0]
[0−a0a] \left[\begin{array}{cc}0 & -a \\ 0 & a\end{array}\right] [00−aa]
4. What is the value of limx→01−cos2xx \lim _{x \rightarrow 0} \frac{\sqrt{1-\cos 2 x}}{x} limx→0x1−cos2x ?
22 2 \sqrt{2} 22
2 \sqrt{2} 2
12 \frac{1}{\sqrt{2}} 21
0
5. If the slope of a straight line is 23 \frac{2}{3} 32 and its length of intercept from y y y-axis is −5 \mathbf{- 5} −5, Then the equation of the straight line is -
2x + 3y = 15
3x + 2y = 15
2x - 3y = 15
3x - 2y = 15