List of practice Questions

As the particle size reduces, the optical absorption spectra shifts towards:

Carbon nanotube shows magneto-resistive effects:

Lithography is:

Scanning Tunneling Microscopy is based on:

Which statement is true for Scanning Tunneling Microscopy:

Atomic Force Microscopy is a modified version of:

Atomic Force Microscopy monitors:

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

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

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:

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:

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

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:

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

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