List of practice Questions

If ${^{n + 2}C_8} : {^{n - 2}P_4} = 57 : 16,$ then the value of n is:

If $n (A) = 3$ and $n (B) = 5$, then the number of one-one functions that can be defined from A to B is

If $N_a = \{an, n \in N\}$, then $N_3 \cap N_5$ is equal to

If Meselson and Stahl's experiment is continued for four generations in bacteria, the ratio of $^{15}N/^{15}N : ^{15}N/^{14}N :^{ 14}N/^{14}N$ containing $DNA$ in the fourth generation would be

If momentum is increased by 20%, then kinetic energy increases by

If mean of the n observations $ {x_1, x_2, x_3,... x_n}$ be $\bar{x}$ , then the mean of n observations $ {2x_1 + 3, 2x_2 + 3, 2x_3 + 3, ...., 2x_{n} + 3}$ is

If $m = \tan \, \theta + \sin \, \theta$ and $n = \tan \, \theta - \sin \, \theta$, then $(m^2 - n^2)^2$ is equal to

If $m$ is a root of the equation $(1 - ab) x^2 - (a^2 + b^2) x - (1 + ab) = 0$, and $m$ harmonic means are inserted between $a$ and $b$, then the difference between the last and the first of the means equals

If $\lambda_1 , \lambda_2 \, and \, \lambda_3$ are the wavelengths of the waves giving resonance with the fundamental, first and second overtones respectively of a closed organ pipe. Then the ratio of wavelengths $\lambda_1 : \lambda_2 : \lambda_3$ is

If $\int\limits^{\infty}_{{0}}e^{-ax}dx=\frac{1}{a},$ then $\int\limits^{\infty}_{{0}}x^n\,e^{-ax}dx$ is

If k$\notin$ [0, 8], find the value of x for which the inequality $ {\frac{x^2 + k^2}{k(6 + x)} \geq 1}$ is satisfied.

If $k \le \sin^{-1} x + \cos^{-1} x + \tan^{-1 } x \le K$, then

if $\int\limits_{a}^{b} \frac{x^{n}}{x^{n} + \left(16 - x\right)^{n}} dx = 6$, then

If $\int^{2}_{-3} f\left(x\right)dx = \frac{7}{3} $ and $\int^{9}_{-3} f\left(x\right)dx = - \frac{5}{6} , $ then what is the value of $\int^{9}_{2} f\left(x\right)dx $ ?

If $ \int\frac{dx}{\left(x+2\right)\left(x^{2} +1\right)} = a log\left|1+x^{2}\right| +b tan^{-1} x +\frac{1}{5}log\left|x+2\right|+C$, then

If in a moderately asymmetrical distribution, mode and mean of the data are 6 $\lambda$. and 9 $\lambda$. respectively, then median is

If in a plano-convex lens radius of curvature of convex surface is 10 cm and the focal length of the lens is 30 cm, the refractive index of the lens will be:

If in a triangle ABC, tanA + tanB + tanC = 6 and tan A tan B = 2, then the triangle is

If $I_1=\int\limits_{e} ^{_e2}\frac{dx}{\log\,x}$ and $I_2=\int\limits_{1} ^{2}\frac{e^x}{x}dx$ , then

If $I_1,I_2,I_3$ be the ionising powers of $\alpha,\beta$ and $\gamma$ particles, the correct relation is

If g on the surface of the earth is $9.8m/s^2,$ its value at a height of 6400 km is (Radius of the earth = 6400km).

If H be the Harmonic mean between a and b, then the value of $\frac{1}{H-a}+ \frac{1}{H-b}$ is

If $h\left(x\right)=\frac{2+x^{2}}{2-x^{2}}$, $h'\left(1\right)=$

If half cell reaction $A + e^- \rightarrow A^-$ has a large negative reduction potential, it follows that

If $g(x) = 1 + \sqrt{x}$ and $f [g (x)] = 3 + \sqrt{2} x + x $ , then f(x) =