1. The sum of the squares of the distance of the points (−3,0) (-3,0) (−3,0) and (3,0) (3,0) (3,0) from the point P(x,y) P(x, y) P(x,y) is always 40 , then the locus of the point will be \qquad
circle
parabola
ellipse
hyperbola
2. The value of sin(A−30∘)+sin(150∘+A) \sin \left(\mathrm{A}-30^{\circ}\right)+\sin \left(150^{\circ}+\mathrm{A}\right) sin(A−30∘)+sin(150∘+A) is -
−12cosA -\frac{1}{2} \cos \mathrm{A} −21cosA
0
cosA \cos \mathrm{A} cosA
sinA \sin \mathrm{A} sinA
3. If A=[1−111] A=\left[\begin{array}{rr}1 & -1 \\ 1 & 1\end{array}\right] A=[11−11], then A−1= A^{-1}= A−1= ?
12[11−11] \frac{1}{2}\left[\begin{array}{rr}1 & 1 \\ -1 & 1\end{array}\right] 21[1−111]
12[1−111] \frac{1}{2}\left[\begin{array}{rr}1 & -1 \\ 1 & 1\end{array}\right] 21[11−11]
[11−11] \left[\begin{array}{rr}1 & 1 \\ -1 & 1\end{array}\right] [1−111]
[1−111] \left[\begin{array}{rr}1 & -1 \\ 1 & 1\end{array}\right] [11−11]
4.
Ltx→0(1+3x)4x=? \underset{x \rightarrow 0}{\operatorname{Lt}}\left(1+\frac{3}{x}\right)^{4 x}=? x→0Lt(1+x3)4x=?
e43 \mathrm{e}^{\frac{4}{3}} e34
e12 \mathrm{e}^{12} e12
3e12 3 \mathrm{e}^{12} 3e12
1
5. The equation of the straight line AB A B AB is-
3x−y=23 \sqrt{3} x-y=2 \sqrt{3} 3x−y=23
3x+y=23 \sqrt{3} x+y=2 \sqrt{3} 3x+y=23
x+3y=23 x+\sqrt{3} y=2 \sqrt{3} x+3y=23
x−3y=22 x-\sqrt{3} y=2 \sqrt{2} x−3y=22