1. If y=e−32x y=e^{-\frac{3}{2} x} y=e−23x, then the value of dydxis− \frac{d y}{d x} i s- dxdyis−
−32e−3x2 -\frac{3}{2} \mathrm{e}^{-\frac{3 x}{2}} −23e−23x
32e−3x2 \frac{3}{2} \mathrm{e}^{-\frac{3 \mathrm{x}}{2}} 23e−23x
23e−3x2 \frac{2}{3} e^{-\frac{3 x}{2}} 32e−23x
−23e−3x2 -\frac{2}{3} e^{-\frac{3 x}{2}} −32e−23x
2. C=(1324) C=\left(\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right) C=(1234)
C−1 \mathrm{C}^{-1} C−1 is equal to -
(−2321−12) \left(\begin{array}{cc}-2 & \frac{3}{2} \\ 1 & -\frac{1}{2}\end{array}\right) (−2123−21)
(2−3−11) \left(\begin{array}{cc}2 & -3 \\ -1 & 1\end{array}\right) (2−1−31)
12(4−3−21) \frac{1}{2}\left(\begin{array}{cc}4 & -3 \\ -2 & 1\end{array}\right) 21(4−2−31)
−12(4321) -\frac{1}{2}\left(\begin{array}{ll}4 & 3 \\ 2 & 1\end{array}\right) −21(4231)
3. The value of ∫0π2cosxdx \int_{0}^{\frac{\pi}{2}} \cos x d x ∫02πcosxdx is
−1 -1 −1
0 0 0
1 1 1
π2 \frac{\pi}{2} 2π
4. The equation of straight line passing through the origin making an angle 30∘ 30^{\circ} 30∘ with the positive direction of x x x axis is -
x+3y=0 x+\sqrt{3} y=0 x+3y=0
3x+y=0 \sqrt{3} x+y=0 3x+y=0
−3x+y=0 -\sqrt{3} x+y=0 −3x+y=0
x−3y=0 x-\sqrt{3} y=0 x−3y=0
5. If the value of (3,2)thi (3,2)^{\text {thi }} (3,2)thi minor of the determinant ∣254y6x−37−1∣ \left|\begin{array}{ccc}2 & 5 & 4 \\ y & 6 & x \\ -3 & 7 & -1\end{array}\right| 2y−35674x−1 is 2 , then the relation between x x x and y y y is-
2x+5y=2 2 x+5 y=2 2x+5y=2
3x+y=2 3 x+ y=2 3x+y=2
x−2y=2 x-2 y=2 x−2y=2
x−2y=1 x-2 y=1 x−2y=1