List of practice Questions

Find out the work done in the following process.

If the function $f(x)=x^3+e^{x/2}$ and $g(x)=f^{-1}$, then the value of $g^{\text{'}}(1)$ is

Let 4^1+x + 4^1-x, \(\frac{k}{2}\), 16^x + 16^-x are in A. P. then least value of k is____

The roots of the equation $\begin{vmatrix}x-1&1&1\\ 1&x-1&1\\ 1&1&x-1\end{vmatrix} = 0 $ are

The coefficient of $x^2$ in the expansion of the determinant $\begin{vmatrix}x^{2}&x^{3}+1&x^{5}+2\\ x^{2}+3&x^{3}+x&x^{3}+x^{4}\\ x+4&x^{3}+x^{5}&2^{3}\end{vmatrix}$ is

The term independent of $x$ in the expansion of $\left(x+\frac{1}{x^{2}}\right)^{6}$ is

The boolean expression corresponding to the combinational circuit is

$\displaystyle \lim_{x \to 2} $ $\frac{x^{100}-2^{100}}{x^{77}-2^{77}}$ is equal to

If $\left|z-\frac{3}{2}\right|=2$ , then the greatest value of $\left|z\right|$ is

Let $S_n$ denote the sum of first n terms of an $A.P.$ If $S_4 = -3 4 , S_5 = -60$ and $S_6 = -93$, then the common difference and the first term of the $A.P.$ are respectively

If $\int \frac{f\left(x\right)}{log\,cos\,x}dx=-log\left(log\,cos\,x\right)+C$, then $f\left(x\right)$ is equal to

If the vectors $ \overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k} $ and $ \overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k} $ are coplanar, then the value of $\lambda$ is equal to

$ \int{({{\sin }^{6}}x+{{\cos }^{6}}x+3{{\sin }^{2}}x \,{{\cos }^{2}}x)}dx $ is equal to

Let $a, a + r$ and $a + 2r$ be positive real numbers such that their product is $64$. Then the minimum value of $a + 2r$ is equal to

The derivative of $ {{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}}) $ with respect to $ {{\sin }^{-1}}(3x-4{{x}^{3}}) $ is

$ \int{\frac{{{x}^{3}}\sin [{{\tan }^{-1}}{{(x)}^{4}}]}{1+{{x}^{8}}}}dx $ is equal to:

If $x_1$ and $x_2$ are the roots of $3x^2 - 2x - 6 = 0$, then $x_1^2 + x_2^2$ is equal to

Amitosis usually occurs in

The magnetic field of earth at the equator is approximately $4 \times 10^{-5} \, T$. The radius of earth is $6.4 \times 10^6 \, m$. Then the dipole moment of the earth will be nearly of the order of:

The vapour pressure of a solvent at 293 K is 100 mm Hg. Then the vapour pressure of a solution containing 1 mole of a strong electrolyte $(AB_2)$ in 99 moles of the solvent at 293 K is (assume complete dissociation of solute)

For a particle, acceleration-time graph gives the velocity. Rate of change of velocity is acceleration.

If $x=exp\left\{tan^{-1}\left(\frac{y-x^{2}}{x^{2}}\right)\right\}$, then $\frac{dy}{dx}$ equals

If A and B are square matrices of the same order such that \(AB=BA\),then prove by induction that \(AB^n=B^nA\).Further, prove that \((AB)^n=A^nB^n\) for all \(n∈N\)

Water is flowing through a horizontal pipe in stream line flow at the narrowest part of the pipe?