List of practice Questions

$\int\limits^{-\pi/2}_{{-3\pi/2}}$$\left[\left(x+\pi\right)^{3}+cos^{2} \left(x+3\pi\right)\right]dx$ is equal to :

The value of $\displaystyle \sum_{k=1}^{10}$$\left(sin\, \frac{2k\pi}{11}+i\,cos\, \frac{2k\pi}{11}\right)$ is :

All the values of m for which both roots of the equation $x^{2}-2mx+m^{2}-1=0$ are greater than -2but less than 4 lie in the interval :

The value of the integral $I=\int\limits^{6}_{{3}}$$\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}dx$ is :

any three vectors such that $\vec{a}\cdot\vec{b} \ne 0, \vec{b}\cdot\vec{c} \ne 0,$ then $\vec{a}$ and $\vec{c}$ are :

If x is real, the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?

$A B C$ is a triangle, right angled at $A .$ The resultant of the forces acting along $\overline{A B}, \overline{B C}$ with magnitudes $\frac{1}{A B}$ and $\frac{1}{A C}$ respectively is the force along $\overline{A D},$ where $D$ is the foot of the perpendicular from $A$ onto $B C$. The magnitude of the resultant is

A wire is cut into four pieces, which are put together by sides to obtain one conductor. If the original resistance of wire was $ R $ , the resistance of the bundle will be:

A wire mesh consisting of very small squares is viewed at a distance of $8 \,cm$ through a magnifying converging lens of focal length $10\, cm$, kept close to the eye. The magnification produced by the lens is

A uniform rod of length $\ell$ and mass $m$ is free to rotate in a vertical plane about $A$. The rod initially in horizontal position is released. The initial angular acceleration of the rod is (Moment of inertia of rod about $A$ is $\frac{m \ell^{2}}{3}$ ):

Which of the following is secondary pollutant?

Which of the following is the most basic oxide ?

When sound waves travel from air to water, which one of the following remains constant?

In methane the bond angle is:

If $a_{r}$ and $a_{t}$ represent radial and tangential accelerations, the motion of a particle will be uniformly circular if:

How many isomers are possible for the alkane $C_{4}H_{10}$ ?

Dipole moment is shown by:

Cyanide process is used for the extraction of

The action of enzymes in living system is to:

Correct gas equation is:

Which combinations of quantum numbers $n, l, m$ and $s$ for the electron in an atom does not provide a permissible solution of the wave equation?

$ Ca^{2+}$ is isoelectronic with:

Consider the following equation of Bernoulli's theorem. $P+\frac{1}{2} \rho v^{2}+\rho g h=K \text { (constant) }$ The dimensions of $K / P$ are same as that of which of the following ?

Which of the following compounds is carborundum?