List of practice Questions

The function f(x) - x³ , x ∈ R has :

If \(f(x)=\begin{cases} 2x+8, & 1\le x\le2 \\ 6x, & 2\lt x \lt4\end{cases}\), then \(\int_1^4f(x)\) is :

The area of the region bounded by the line 2y = 5x +7, x-axis and the lines x - 1 and x -3 is :

The integrating factor of the differential equation (1 +y²)dx - (tan^-1 y - x)dy = 0, is :

The order and the degree of the differential equation
\(\frac{d^2y}{dx^2}=(1+\frac{dy}{dx})^{\frac{1}{2}}\)
respectively are :

Which of the following is correct ?

The corner points of feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy where p, q > 0. The condition on p and q so that, minimum of Z occurs at (3, 0) and (1, 1) is :

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces, and 5 on 1 face is :

If \(P(A)=\frac{3}{10},P(B)=\frac{2}{5}\), and P(A ∪ B) = \(\frac{3}{5}\), then \(P(\frac{B}{A})+P(\frac{A}{B})\) is equal to :

The relation R in the set A = {1, 2, 3, 4} is given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} is :

If f(x) - 27x³ and g(x) = \((x)^{\frac{1}{3}}\), then gof(x) is :

Principal value of \(\tan^{-1}(\sqrt3)+\tan^{-1}(1)\) is :

The principal value of \(\sin^{-1}(\frac{1}{2})\) is :

If A is an invertible matrix, such that A² - A + I = 0, then the inverse of A is :

The determinant \(\begin{vmatrix} x & \sin\theta & \cos\theta \\ -\sin\theta & -x & 1 \\ \cos\theta & 1 & x \end{vmatrix}\) is :

The value of k for which the matrix \(\begin{pmatrix} 0 & 2 & 4 \\ 2 & 0 & 5 \\ -3 & 5 & 0 \end{pmatrix}\) is a symmetric matrix is given by :

The value of λ for which the matrix \(\begin{pmatrix} 1 & 0 & λ \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix}\) is a singular matrix is :

If the order of a matrix A is 2 × 3, the order of matrix B is 3 × 4 and the order of matrix C is 3 × 4, then the order of the matrix (A, B).C^T is

The value of the determinant \(\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}\) is :

Match List I with List II

List I (Functions)		List II (Derivatives)
A.	f(x)=sin-1x	I.	\(\frac{1}{1+x^2}\), x ∈ R
B.	f(x)=tan-1x	II.	\(\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
C.	f(x)=cos-1x	III.	\(-\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
D.	f(x)=sin-1x	IV.	\(-\frac{1}{1+x^2}\), x ∈ R

Choose the correct answer from the options given below :

If y = Asinx + Bcosx, Where A and B are constants, then \(\frac{d^2y}{dx^2}\) is equal to :

The slope of the normal to the curve y = 2x² + 3sinx at x = 0, is :

If the function \(f(x)=\frac{k \sin x+2\cos x}{\sin x+\cos x}\) is increasing for all values of x, then

For fencing of flower bed with 100 cm long wire in the form of circular sector, the maximum area of the flower bed is :

Match List I with List II

List I		List II
A.	\(\int\limits^{\frac{\pi}{2}}_0\frac{\sin^{\frac{7}{2}}x}{\sin^{\frac{7}{2}}+\cos^{\frac{7}{2}}}dx\)	I.	\(\frac{\pi}{4}-\frac{1}{2}\)
B.	\(\int\limits_0^{\pi}\frac{x\sin x}{1+\cos^2x}dx\)	II.	0
C.	\(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}x\cos x\ dx\)	III.	\(\frac{\pi}{4}\)
D.	\(\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^2x\ dx\)	IV.	\(\frac{\pi^2}{4}\)

Choose the correct answer from the options given below :