List of practice Questions

The component of \(\hat{i}\) in the direction of the vector \(\hat{i}+\hat{j}+2\hat{k}\) is
If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) then
The degree of the differential equation
\(1+(\frac{dy}{dx})^2+(\frac{d^2y}{dx^2})^2= \sqrt[3]{\frac{d^2y}{dx^2}+1}\) is
If a curve passes through the point (1, 1) at any point (x, y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point, then the curve also passes through the point
The area of the region bounded by the line y = x +1, and the lines x = 3 and x = 5 is
\(\int\sqrt{5-2x+x^2}\ dx=\)
\(\int\limits^{\pi}_{0}\frac{x\tan x}{\sec x.\cosec x}\ dx=\)
\(\int\limits_{-2}^{0}(x^3+3x^2+3x+3+(x+1)\cos(x+1))\ dx=\)
\(\int\frac{1}{1+3\sin^2 x+8 \cos^2 x}\ dx=\)
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 y = a sin x + b cos x, then y2 + \((\frac{dy}{dx})^2\) is a
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
If A and B are two matrices such that AB=B and BA=A then A2 + B2 =
If \(x\begin{bmatrix}     3 \\  2 \end{bmatrix}+y\begin{bmatrix}     1 \\     -1 \end{bmatrix}=\begin{bmatrix}     15 \\     5\end{bmatrix}\) then the value of x and y are
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