List of practice Questions

Let, random variable \(X \sim \text{Bernoulli}(p)\). Then, \(\beta_1\) is

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:

The value of \( \lim_{h \to 0} \left(\frac{1}{h} \int_{4}^{4+h} e^{t^2} dt \right) \) 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 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 limit of the sequence,
\(\{b_n; b_n = \frac{n^n}{(n+1)(n+2)...(n+n)}; n>0\}\), is

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

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

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

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

The values of 'm' for which the infinite series,
\(\sum \frac{\sqrt{n+1}+\sqrt{n}}{n^m}\) converges, are:

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

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

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:

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

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

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

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

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

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

Measures of variations or dispersion of data are: A. Interquartile Range B. Mode C. Standard Deviation D. Weighted Mean

Arrange the various methods of mosquito control according to life history of mosquitoes from egg to adult stages: A. Source reduction through engineering methods like filling, levelling B. Screening of buildings with bronze gauge C. Biological control through fish D. Residual sprays with Malathion

Waste water from kitchens and bathrooms NOT containing excreta is called:

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

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