List of practice Questions

Given that $ \int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)} $ dx = $ \frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'} $ then $ \int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)} $ is

The length of the perpendicular drawn from $(1,2,3)$ to the line $ \frac{x-6}{3} = \frac {y-7}{2} = \frac {z-7}{-2} $ is

$ lim_{n\rightarrow \infty} \frac {(n!)^{1/n}}{n} $ equals

The equation $ \sqrt{\left(x-2\right)^{2}+y^{2}}+\sqrt{\left(x+2\right)^{2}+y^{2}}=4 $ represents

If $ C_o, C_1,C_2,....C_{15} $ are the binomial coefficients in the expansion of $ (1+x)^{15} $ then $ \frac {C_1}{C_o} +\frac {2C_2}{C_1}+\frac {3C_3}{C_2} +....+\frac {15C_{15}}{C_{14}} $ is equal to

From a solid sphere of mass $M$ and radius $R$, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

For an amplitude modulated wave the maximum amplitude is found to be $ 10\,V $ while the minimum amplitude is found to be $ 2V $ , the modulation index is

Floral formula of family-Fabaceae is

Examples of secondary air pollutants is /are

During meiosis $ -I,$ the number of chromosomes is

DNA replication takes place during

$Fe^{3+}$ is reduced to $Fe^{2+}$ by using -

The correct statement(s) about $Cr^{2+}$ and $Mn^{3+}$ is (are) - [Atomic numbers of $Cr = 24$ and $Mn = 25$]

Consider a ray of light travelling from a denser to a rarer medium. If it is incident at the critical angle then

Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If $f$ is the focal length of bi-convex lens then, the focal length of the plano-convex lens is

Concentration of the urine is controlled by

Chalazogamy is shown by

At a certain time a particle has a speed of $18\, m/s$ in positive x-direction and $2.4\, s$ later its speed was $30\, m/s$ in the opposite direction. What is the magnitude of the average acceleration of the particle during the $2.4\, s$ interval?

Astronomical unit $(Au)$ is the average distance between the earth and sun approximately $1.5 \times 10^{8} km$. The speed of light is about $3.0 \times 10^{8} m / s$. The speed of light in astronomical unit per minute is

Conditions of a karyotype $2n \pm 1$ and $2n\pm 2$ are called

Evolution of different species in a given area starting from a point and spreading to other geographical areas is called

The Leydig's cells as found in the human body are the secretory source of

The part of Fallopian tube closest to the ovary is

As secondary growth proceeds, in a dicot stem, the thickness of

Which one of the following statements is false in respect of viability of mammalian sperm?