List of practice Questions

\(\int\frac{1}{1+3\sin^2 x+8 \cos^2 x}\ dx=\)
If f(x) and g(x) are two functions with g(x) = \(x-\frac{1}{x}\) and fog(x) = \(x^3-\frac{1}{x^3}\) then f'(x) =
\(\int\limits_{2}^{8}\frac{5^{\sqrt{10-x}}}{5^{\sqrt{x}}+5^{\sqrt{10-x}}}\ dx=\)
A circular plate of radius 5 cm is heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. The rate at which its area is increasing when the radius is 5.2 cm is
If A = \(\begin{bmatrix}     1 & \tan\ \alpha/2 \\     -\tan\ \alpha/2 & 1 \end{bmatrix}\) and AB=I then B =
If f(x) = 1 + nx + \(\frac{n(n-1)}{2}x^2+\frac{n(n-1)(n-2)}{6}x^3+...+x^n\) then f"(1) =
If the function of f(x) = \(\frac{1}{x+2}\), then the point of discontinuity of the composite function y = f(f(x)) is
The function f(x) = cot x is discontiuous on every point of the set
If \(u=\sin^{-1}(\frac{2x}{1+x^2})\) and \(v=\tan^{-1}(\frac{2x}{1-x^2})\) then \(\frac{du}{dv}\) is
If \(\Delta=\begin{vmatrix}     1 & a & a^2 \\     1 & b & b^2 \\     1 & c & c^2 \end{vmatrix}\) and \(\Delta_1=\begin{vmatrix}     1 & 1 & 1 \\     bc & ca & ab \\     a & b & c \end{vmatrix}\) then
The area of a triangle with vertices(-3,0),(3, 0) and (0, k) is 9 sq.units, the value of k is
If A =\(\begin{bmatrix}   2-k & 2 \\     1 & 3-k \end{bmatrix}\) is a singular matrix, then the value of 5k - k2 is equal to
The value of
\(\cot^{-1}[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}]\) where x ∈ \((0,\frac{\pi}{4})\) is
The contrapositive of the statement
“If two lines do not intersect in the same plane then they are parallel.” is
Let the relation R be defined in N by aRb if 3a + 2b = 27 then R is
Let f : R→R be defined by f(x)= 3x2-5 and g : R→R by g(x)=\(\frac{x}{x^2+1}\) then gof is
f : R → R and g : [0, ∞) → R are defined by f(x) = x2 and g(x)=\(\sqrt{x}\). Which one of the following is not true ?
The mean of 100 observations is 50 and their standard deviation is 5. Then the sum of squares of all observations is
If n is even and the middle term in the expansion of \((x^2+\frac{1}{x})^n\) is 924 x6, then n is equal to
The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
A sinusoidal voltage of amplitude 25 V and frequency 50 Hz is applied to a half-wave rectifier using a P-N junction diode. No filter is used, and the load resistor is \( 1000\Omega \). The forward resistance \( R_f \) of the ideal diode is \( 10\Omega \). The percentage rectifier efficiency is:
A parallel plate air capacitor of capacitance \( C \) is connected to a cell of emf \( V \) and then disconnected from it. A dielectric slab of dielectric constant \( K \), which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?
If \(\lim\limits_{x \rightarrow 0} \frac{\sin(2+x)-\sin(2-x)}{x}\)= A cos B, then the values of A and B respectively are
The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt2\). Its equation is
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is