List of practice Questions

The general solution of \(\sqrt3\cos x+\sin x=\sqrt2\), for any integer “n” is
The imaginary part of conjugate of \((\frac{1+i}{1-i})^5\) is
The area enclosed between the parabolas y2 = 16x and x2 = 16y is
The solution of y' = ex-y + x2e-y is
The value of \(4\tan^{-1}(\frac{1}{5})-\frac{\pi}{4}=\)
If the function f(x) defined by
\(f(x)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+...+\frac{x^2}{2}+x+1,\)
then f'(0)=
The value of the integral
∫ex{f(x) + f'(x)} dx is
The value of the integral \(\int\limits^{\pi}_{-\pi}\frac{\cos^2x}{1+a^x}dx,\)
a > 0 is
The value of the integral
\(\int\frac{e^x(x^2+1)}{(x+1)^2}\ dx=\)
A man 6' tall moves away from a source of light 20′ above the ground level, his rate of walking being 4 m.p.h. At what rate is the tip of his shadow moving ?
The maximum area of a rectangle that can be inscribed in a circle of radius 2 units is
If \(y=x^{x^x}\), then y' =
If \(\cos^{-1}(\frac{y}{b})=\log(\frac{x}{n})^x\), then x2y2 + xy1 =
The angle between the curves
x2 + y2 = 25 and
x2 + y2 - 2x + 3y - 43 = 0 at (-3, 4) is
If \(f(x)=\begin{cases} xe^{-(\frac{1}{|x|}+\frac{1}{x})}; & \text{if } x\ne0 \text{ then} \\ 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ ; & \text{if }x=0\end{cases}\)
which of the following is correct ?
If \(y=\sin^{-1}\frac{1}{2}(\sqrt{1+x}+\sqrt{1-x})\) then y' =
If xmyn = (x + y)m+n then y' =
Which of the following is false ?
If \(f=\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 3 & 2 & 4 & 5 & 1 & 6 \end{pmatrix}\in S_6\) then f-1 is
In a group G, the equations ax = b and ya = b have
If x + y = tan-1 y and y" = f(y)y' then f(y) =
The digit in the unit place of 7291 is
If a ≡ b (mod m) and x is an integer, then which of the following is incorrect ?
If a and b are positive integers such that (a2 - b2) is a prime number, then
The distance of the point A(a, b, c) from the x-axis is