List of practice Questions

The tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at

$\int \frac{dx}{\sin x - \cos x + \sqrt{2}} $ equals to

The value of integral $\int\limits_0^1 \, \sqrt{\frac{1-x}{1+x}}dx$ is

The value of $\displaystyle\lim_{x\to\infty}\left(\frac{\pi}{2} - \tan^{-1} x\right)^{1/x} $ is

There are $5$ letters and $5$ different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

The coefficient of $x^n$ in the expansion of $\log_a (1 + x)$ is

Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n $ is 4 $\bar{x}$ .

Bond enthalpies of $H_2, X_2$ and $HX$ are in the ratio $2 : 1 : 2$. If enthalpy of formation of $HX$ is $-50 \,kJ \,mol^{-1}$, the bond enthalpy of $H_2$ is

What is the value of n so that the angle between the lines having direction ratios $(1, 1, 1)$ and $(1, -1, n)$ is $60^{\circ}$ ?

The foot of the perpendicular from the point $(7, 14, 5)$ to the plane $2x + 4y - z = 2$ are

For the function $f\left(x\right)= \frac{x^{100}}{100} + \frac{x^{99}}{99} + ... \frac{x^{2}}{2} + x + 1 , $ f ' (1) = mf' (0), where m is equal to

Formation of ozone in the upper atmosphere from oxygen takes place by the action of

If $\sin^2 \theta + \sin^2 \phi = 1/2, \cos^2 + \cos^2 \phi = 3/2$, then $\cos^2 (\theta - \phi)$ is equal to

In how many ways can $5$ prizes be distributed among $4$ boys when every boy can take one or more prizes ?

In which case the $NO_2$ will attack at the meta position

The coefficient of $x^{20}$ in the expansion of $(1 + x^2)^{40} . (x^2 + 2 + \frac{1}{x^2})^{-5}$ is

The number of positive integral solution of $abc = 30$ is

The preparation of ethyl acetoacetate involves:

The value of the determinant $\begin{vmatrix}265&240&219\\ 240&225&198\\ 219&198&181\end{vmatrix}$ is

When chlorine water is exposed to sunlight, $O_2$ is liberated. Hence,

Which alkene on ozonolysis gives \(CH_3CH_2CHO\) and

Let $x$ and $y$ be two natural numbers such that $xy = 12(x + y)$ and $x \le y$. Then the total number of pairs $(x, y)$ is

Let $T(k)$ be the statement $1 + 3 + 5 + ... + (2k - 1)= k^2 +10$ Which of the following is correct?

A sentence has been divided into four parts. Choose the part that has an error.

A sentence has been divided into four parts. Choose the part that has an error.