List of practice Questions

A card is drawn at random from a standard deck of 52 cards. Then, the probability of getting either an ace or a club is:

A cyclist covers first five kilometers at an average speed of 10 k.m. per hour, another three kilometers at 8 k.m. per hour and the last two kilometers at 5 k.m. per hour. Then, the average speed of the cyclist during the whole journey, is

It is given that at x = 1, the function \(f(x) = x^4 - 62x^2 + ax + 9\), attains its maximum value in the interval \([0, 2]\). Then, the value of 'a' is

Function, \(f(x) = -|x-1|+5, \forall x \in R\) attains maximum value at x =

The limit of the sequence,
\(\{b_n; b_n = \frac{n^n}{(n+1)(n+2)...(n+n)}; n>0\}\), is

The area of the surface generated by revolving the curve \(X = \sqrt{9-Y^2}, -2 \leq Y \leq 2\) about the y-axis, is

The volume of the solid for the region enclosed by the curves \(X = \sqrt{Y}\), \(X = \frac{Y}{4}\) revolve about x-axis, is

The value of \( \lim_{h \to 0} \left(\frac{1}{h} \int_{4}^{4+h} e^{t^2} dt \right) \) is

Consider a 2x2 matrix \(A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\). If \(a+d=1\) and \(ad-bc=1\), then \(A^3\) is equal to

For Lagrange's mean value theorem, the value of 'c' for the function \(f(x) = px^2+qx+r, p\neq 0\) in the interval \([1, b]\) and \(c \in ]1, b[\), is:

Which of the following statement is true about the geometric series \(1+r+r^2+r^3+.............; (r>0)\) ?

The value of \(\lim_{x \to 1} \frac{x^3-1}{x-1}\) is

If \(f'(x) = 3x^2 - \frac{2}{x^2}\), \(f(1) = 0\) then, \(f(x)\) is

The system of equations given by \( \begin{bmatrix} 1 & 1 & 1 & : & 3 \\ 0 & -2 & -2 & : & 4 \\ 1 & -5 & 0 & : & 5 \end{bmatrix} \) has the solution:

Let P and Q be two square matrices such that PQ = I, where I is an identity matrix. Then zero is an eigen value of

A is a, \(n \times n\) matrix of real numbers and \(A^3 - 3A^2 + 4A - 6I = 0\), where I is a, \(n \times n\) unit matrix. If \(A^{-1}\) exists, then

If \(f(x)\) and \(g(x)\) are differentiable functions for \(0 \leq x \leq 1\) such that, \(f(1)-f(0) = k(g(1)-g(0))\), \(k \neq 0\), and there exists a 'c' satisfying \(0<c<1\). Then, the value of \(\frac{f'(c)}{g'(c)}\) is equal to

If, \(y = x^{\tan(x)}\), then \(\frac{dy}{dx}\) at \(x = \frac{\pi}{4}\), is

The maximum values of the function
\(\sin(x)+\cos(2x)\), are

The solution of the differential equation,
\((x^2 + 1)\frac{dy}{dx} + 2xy = \sqrt{x^2 + 4}\), is

The sequence \(\{a_n = \frac{1}{n^2}; n>0\}\) is

In India, birth weight of less than 2.5 kg is considered low birth weight:

The proportion of frequencies lying on either side of the mean in a normal distribution curve within a range of +1 to -1 standard deviation is approximately:

Which of the mosquitoes is easily distinguished by white stripes on the black body?

Best sampling method where every unit in the population has an equal chance of being included in the sample is: