Property 6

Q.

The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is

1. $5x^2+3y^2=32$

2. $3x^2+5y^2=32$

3. $5x^2-3y^2=32$

4. $3x^2+5y^2+32$

Q. 45. How to find the value of trigonometric ratio having angle more than 90 degree say sin 120 or cos 270

Q. Prove that:
${\cos }^{3}2x+3\cos 2x=4\left({\cos }^{6}x-{\sin }^{6}x\right)$

Q. If tan alpha and tan beta are the roots of equation X square - PX + Q is equal to zero then find cos 2 alpha + beta

Q. If f(x) = cos [π²]x + cos [−π²] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).

Q. Let $A=\{1,3,5,7\},$ $B=\{2,4,6,8\}$ and $f:A\to B.$ Then number of functions $f$ such that $f\left(i\right)\ne i+1,\forall i=1,3,5,7$ is

1. $81$
2. $64$
3. $256$
4. $24$

Q.

Find the equation for the ellpse that satisfies the given conditions
Vertices $(0,\pm 13),Foci(0,\pm 5)$

Q. The area bounded by $x-$axis, the curve $y=(1+\frac{8}{x^2})$ and the ordinates at $x=2$ and $x=4$ is divided into two equal parts at $x=a$. Then $a^2-\sqrt{2}a-2=$

Q. If $A_n=\underset{0}{\overset{\pi /2}{\int }}\frac{\sin (2n-1)x}{\sin x}dx,B_n=\underset{0}{\overset{\pi /2}{\int }}{\left(\frac{\sin nx}{\sin x}\right)}^{2}dx,$ for $n\in N,$ then

1. $A_{n+1}=A_n$
2. $B_{n+1}=B_n$
3. $A_{n+1}-A_n=B_{n+1}$
4. $B_{n+1}-B_n=A_{n+1}$

Q. Find the area enclosed by the curve $x=y^2+2$, ordinates y = 0 & y = 3 and the Y - axis.

1. 5
2. 10
3. 15
4. 20

Q. Compute the derivative of f(x)=sin²​x

Q. Area enclosed by curve $y^3-9y+x=0$ and Y - axis is -

1. $\frac{9}{2}$
2. $9$
3. $\frac{81}{2}$
4. $81$

Q. $I_1=\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{\sin x-\cos x}{1+\sin x\cos x}dx,I_2=\underset{0}{\overset{2\pi }{\int }}{\cos }^{6}xdx$,
$I_3=\underset{-\frac{\pi }{2}}{\overset{\frac{\pi }{2}}{\int }}{\sin }^{3}xdx,I_4=\underset{0}{\overset{1}{\int }}\ln (\frac{1}{x}-1)dx$, then

Q. The value of ${\int }_0^{2\pi }{\sin }^{100}x{\cos }^{99}x\mathrm{dx}$is equal to

Q.

Find derivative of sin2x, cos2x and tan2x using first principle