List of practice Questions

If one mole of a monatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/3)$, the value of g for the mixture is

If one person handshakes with the other only once and number of handshakes is $66$, then number of persons will be

If $\omega$ and $\omega^2$ are complex cube roots of unity, then $(1-\omega+\omega^2)^5+(1-\omega^2+\omega)^5$ is equal to

If $\omega$ is a complex cube root of unity, then the matrix $A = \begin{bmatrix}1&\omega^{2}&\omega\\ \omega ^{2}&\omega&1\\ \omega&1&\omega ^{2}\end{bmatrix}$ is

If number of elements in sets $A$ and $B$ are m and $n$ respectively, then the number of relations from $A$ to $B$ is

If O = (0, 0, 0), P = (4, 3, -5), Q = (-2, 1, -8), $\cos\angle POQ = \frac{a}{\sqrt{b}\sqrt{c}} $ and b > c then b - c =

If $n(\mu) = 48 , n(A) = 28, n(B) = 33$ and $n(B - A) = 12$, then $n(A \cap B)^C$ is

If $N =$ population density at time $t$, then population density at time $t + 1$ can be written as $N_{t+1}=N_{t}+\left[\left(A+B\right)-\left(C+D\right)\right]$ Select the correct option for $A$, $B$, $C$ and $D$ in the above equation.

If $^nC_{r-1}=28,\,^nC_r =56$ and $^nC_{r+1}=70$, then $r =$

If $NH_4OH$ is added to the $[PtCl_4]^{2-}$ ion, the complex formed represents

If n is an integer between 0 and 21, then the minimum value of $n ! (21 - n) !$ is

If $N$ be the set of all natural numbers, consider $f$ : $N \to N$ such that $f(x) = 2x$, $\forall\, x \in N$, then $f$ is

If n is a positive integer, then the number of terms in the expansion of $[x + a]^n$ is

If n = 1 , 2, 3, ..... , then $\cos \, \alpha \, \cos \, 2\alpha \, \cos \, 2^2 \alpha \, \cos \, 2^3 \, \alpha . ..... \cos \, 2^{n-1} \alpha $ is equal to

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.