List of practice Questions

$ \frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}\cdot 6{{-}^{8}}{{C}_{3}}{{.6}^{2}}+....{{+}^{8}}{{C}_{8}}{{\cdot 6}^{7}} $ is equal to

The number of solutions of the equation $ \sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x $ in $ \left[ 0,\frac{\pi }{2} \right] $ is

The point on the x-axis equidistant from the points $ (4,3,1) $ and $ (-2,\,-6,\,-2) $ is

In $ \Delta \,\,ABC $ if $ si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C=2, $ then the triangle is

The value of $ {{\cos }^{-1}}\,\left( \sin \,\frac{7\pi }{6} \right) $ is equal to

Find the function $ f(x_1, x_2, x_3) $ satisfying $ f(x_1, x_2, x_3) = 1 $ at $ x_1 = 1, x_2 = x_3 = 0 $ .

Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is

If $\alpha$ and $\beta$ are roots of the quadratic equation $ {{x}^{2}}+4x+3=0, $ then the equation whose roots are $ 2\alpha \,\text{+}\,\beta $ and $ \alpha \,\text{+2}\,\beta $ is

If the third term of a $G.P.$ is $3$, then the product of its first $5$ terms is

The number of diagonals of a polygon of $20$ sides is

If $X$ and $Y$ are $ 2\times 2 $ matrices such that $ 2X+3Y=O $ and $ X+2Y=I, $ where $ O $ and $ I $ denote the $ 2\times 2 $ zero matrix and the $ 2\times 2 $ identity matrix, then $X$ is equal to

If $ f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}}, $ then $ \int{4x\,\,f(x)\,\,dx} $ =

The value of $\begin{vmatrix} \log_5\,729 & \log_3\,5 \\[0.3em] \log_5\,27 & \log_9\,25 \end{vmatrix}.\begin{vmatrix} \log_3\,5 & \log_{27}\,5 \\[0.3em] \log_5\,9 & \log_5\,9 \end{vmatrix}=$

Which of the following is a soap?

Which of the following gives $RNC$ when treated with $CHCl_{3}$ and $KOH$?

$x \in R : \frac{2x -1}{x^3 + 4x^2 + 3x} \in R$ Equals

Hinsberg reagent, $C_{6}H_{5}SO_{2}Cl$ does not react with

Correct order of freezing point of $ 1\,M $ solution of sucrose, $ KCl,\,BaCl_{2}$ and $ AlCl_{3}$ is

The condensation polymer among the following is

$5$ moles of $SO_2$ and $5$ moles of $O_2$ are allowed to react. At equilibrium, it was found that $60\% $ of $SO_2$ is used up. If the partial pressure of the equilibrium mixture is one atmosphere, the partial pressure of $O_2$, is

Which of the following is properly matched ?

The greatest threat to genetic diversity in agricultural crops is

Compare the statements A and B Statement A : Ranikhet disease is the disease of poultry. Statement B : It is caused by a virus. Select the correct description.

Alzheimer disease in humans is associated with the deficiency of

The given figure shows a diagrammatic sketch of a portion of human male reproductive system. Identify the parts labelled as $A$, $B$, $C$ and $D$ and select the correct option.