1. Which of the following is the area of shaded region in the figure?
163 \frac{16}{3} 316
43 \frac{4}{3} 34
83 \frac{8}{3} 38
323 \frac{32}{3} 332
2. For which value of ' k k k ' the straight lines 4x−y+3=0 4 x-y+3=0 4x−y+3=0 and 2x+ky−1=0 2 x+k y-1=0 2x+ky−1=0 are perpendicular to each other?
8
18 \frac{1}{8} 81
−18 -\frac{1}{8} −81
-8
3. Which one is the value of ∫1+tan2x(1−tanx)2 \int \frac{1+\tan ^{2} x}{(1-\tan x)^{2}} ∫(1−tanx)21+tan2x dx \mathrm{dx} dx ?
−11+tanx+c \frac{-1}{1+\tan x}+c 1+tanx−1+c
−11−tanx+c \frac{-1}{1-\tan x}+c 1−tanx−1+c
11−tanx+c \frac{1}{1-\tan x}+c 1−tanx1+c
11+tanx+c \frac{1}{1+\tan x}+c 1+tanx1+c
4. Which one is the equation of the circle whose center is at (−2,4) (-2,4) (−2,4) and touches the x x x-axis?
x2+y2+4x−8y+4=0 x^{2}+y^{2}+4 x-8 y+4=0 x2+y2+4x−8y+4=0
x2+y2−4x+8y+4=0 x^{2}+y^{2}-4 x+8 y+4=0 x2+y2−4x+8y+4=0
x2+y2−4x−8y+4=0 x^{2}+y^{2}-4 x-8 y+4=0 x2+y2−4x−8y+4=0
x2+y2+4x+8y+4=0 x^{2}+y^{2}+4 x+8 y+4=0 x2+y2+4x+8y+4=0
5. If A=[31−2−1] A=\left[\begin{array}{rr}3 & 1 \\ -2 & -1\end{array}\right] A=[3−21−1], then find A−1= A^{-1}= A−1= ?
[11−2−3] \left[\begin{array}{rr}1 & 1 \\ -2 & -3\end{array}\right] [1−21−3]
[−1−123] \left[\begin{array}{rr}-1 & -1 \\ 2 & 3\end{array}\right] [−12−13]
[3−12−1] \left[\begin{array}{ll}3 & -1 \\ 2 & -1\end{array}\right] [32−1−1]
[−11−23] \left[\begin{array}{ll}-1 & 1 \\ -2 & 3\end{array}\right] [−1−213]