List of practice Questions

If \(\begin{bmatrix}        x+4 & 2x & 2x           \\[0.3em]        2x & x+4           & 2x\\[0.3em]        2x   & 2x & x+4      \end{bmatrix}=\lambda(4-x)^2\),then value of \(\lambda \) is

for which value of \(\lambda\) is the function ,\(f(x) = \begin{cases} \lambda(x^2-2x) & \text{if } x \leq 0 \\ 4x+1& \text{if } x > 0 \end{cases}\) continuous at \(x=0 ?\)

The derivative \(\frac{\mathrm dy}{\mathrm d x}\) ,if \(x=a(\theta -sin\theta),y=a(1+cos\theta)\) is :

If \(y=sin^{-1}x \) and \((1-x^2)\frac{d^2y}{dx^2} -x \frac{dy}{dx}=K\),then value of K is:

If \(y=log[\frac{x^2}{e^2}]\) then value of \(\frac{d^2y}{dx^2}\) is:

The condition on a and b, such that for \(y = \frac{a}{x}-\frac{b}{x²}\), \(\frac{dy}{dx} =0\) at x=1 is:

The interval in which the function \(f(x) = 10-6x-2x²\) is decreasing is:

Area of the region bounded by the curve |x|+|y|=1 and x-axis is :

The value of the integral \(\int\limits_2^4 \frac{x}{x^2+1} dx\) is:

The sum of order and degree of the differential equation\[\frac{\{1+(\frac{dy}{dx})^2\}^\frac{5}{2}}{\frac{d^2y}{dx^2}}=p\]is:

The solution of the differential equation\(\frac{dy}{dx}= \frac{6}{x^2}; y(1) = 3\) is:

The mean of the number of heads in a simultaneous toss of three coins is :

For the LPP
Maximise z=x+y
subject to x-y≤-1, x+y≤2, x, y≥0, z has:

Choose the wrong statement from the following:

Let f: R→R defined by f(x)=2x³-7 for x∈R. Then:
(A) f is one-one function
(B) f is many to one function
(C) f is bijective function
(D) f is into function
Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

Let \(tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^2})\). Then y is:

The value of 2y-3x, if
\(2\begin {bmatrix}x &5\\ 7&y-3\end{bmatrix}+\begin{bmatrix}3&-4\\ 1&2\end{bmatrix}=\begin{bmatrix}7&6 \\15&14\end{bmatrix}\) is:

Match List - I with List II. If \(A = \begin{vmatrix}3&-2&3 \\2 &1 &-1 \\4 &-3 &2\end{vmatrix}\)

Choose the correct answer from the options given below:

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is:

Let \(\begin{vmatrix}3x&-7\\1&4\end{vmatrix}=\begin{vmatrix}3&2\\ 4&x\end{vmatrix}\), then value of x is:

The value of the determinant \(\begin{vmatrix}acosθ&bsinθ&0 \\-bsinθ&acosθ&0\\ 0&0&c\end{vmatrix}\) is:

The points of discontinuity of the function \(f\) defined by \(f(x) = \begin{cases} x+2 & x≤1 \\ x-2 &1<x<2\\ 0& x≥2\end{cases}\) are:

If \( f(x) = \begin{cases} x \left( 1 + \frac{1}{2} \sin(\log x^2) \right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \)

If \( f(x) = \begin{cases} \sqrt{\pi - \cos^{-1} x}, & x = -1 \\ \frac{\sqrt{2(1 + x)}}{\pi + \cos^{-1} x}, & x \neq -1 \end{cases} \) is right continuous at \( x = -1 \), then \( \lambda = \)