List of practice Questions

Solve for $ x,\,\,{{\tan }^{-1}}(1/x)=\pi +{{\tan }^{-1}}x,\,\,0 < x < 1 $

Given two vectors are $ \hat{i}-\hat{j} $ and $ \hat{i}+2\hat{j}, $ the unit vector is coplanar with the two vectors and perpendicular to the first. Find the vector?

Integrate $ \frac{{{\sec }^{2}}\,({{\sin }^{-1}}x)}{\sqrt{1-{{x}^{2}}}} $

For what values of $x$, the numbers $ -1,\,x,-3/4 $ are in $GP$ ?

Differentiate $ \sin \,\,(\sin \,\,2x). $

Let $ A=\{1,\,\,2\,\{a,\,\,b\},\,\,3,\,\,4\}, $ which among the following statements is incorrect?

Find the range of the function $ f:[0,\,1]\to R,\,\,f(x)={{x}^{3}}-{{x}^{2}}+4x+2{{\sin }^{-1}}x $ ?

There are $7$ horses in a race, Mr. X selected $2$ horses at random and bet on them. The probability that Mr. X selected the winning horse, is

The conjugate base of hydrazoic acid is :

The appearance of colour in solid alkali metal halides is generally due to :

The ratio mass of oxygen and nitrogen of a particular gaseous mixture is $1 : 4$ The ratio of number of their molecule is

$CsCl$ crystallises in body centred cubic lattice. If 'a' is its edge length, then which of the following expressions is correct?

The binding energy per nucleon of \(Li\) and \(He\) nuclei are \(5.60\, MeV\) and \(7.06\, MeV\) respectively. In the nuclear reaction \(^7_3Li+_1^1H \rightarrow  _2^4He + _2^4He+Q\) the value of energy Q released is

Assisted reproductive technology, IVF involves transfer of

Artificial sweetener which is stable under cold conditions only is

For hydrogen - oxygen fuel cell at one $atm$ and $298\, K$ $H_2(g)+\frac {1}{2} O_2(g) \to H_2O_{(l)} ; \Delta G^\circ=-240\, kJ$ $E^\circ$ for the cell is approximately, (Given $F \,= \,96,500 \,C$)

For an ideal binary liquid mixture

Archaebacteria differ from eubacteria in

Commonly used vectors for human genome sequencing are

An infinite line charge produces a field of $ 18\times 10^{5}\,N/C $ at a distance of $ 4\,cm $ . What is the linear charge density?

Calculate the energy in joule corresponding to light of wavelength 45 nm (Planck's constant, $h=6.63\times10^{-34}$ Js; speed of light, $c=3\times 10^{8}$.

A radioisotope X with a half life $1.4 \times 10^9$ years decays to Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is

In the Young's double slit experiment, the intensity of light at a point on the screen where the path difference $\lambda$ is K,( $\lambda$ being the wavelength of light used). The intensity at a point where the path difference is ${\lambda}/4 $ will be

What is the dimensional formula for universal gravitational constant $G$ ?

The dimensions of mobility of charge carriers are