List of practice Questions

If $S_m$ denotes the sum of first $m$ terms of a $G.P. $ of $n$ terms with common ratio $r$, then the sum of their products taken two by two is

If $PSQ$ is the focal chord of the parabola $y^2 = 8x$ such that $ SP = 6$ then the length $SQ $ is

If $R$ and $H$ represent horizontal range and maximum height of the projectile, then the angle of projection with the horizontal is

If R is the relation less than' from A={1, 2, 3, 4, 5} to B={1, 4}, the set of ordered pairs corresponding to R, then the inverse of R is

If pressure of $CO_2$ (real gas) in a container is given by $p = \frac{RT}{2V - b} - \frac{9}{4b^2},$ then mass of the gas in container ts

If p and q are true statement and r, s are false statements then the truth value of $\sim[(p \wedge \sim r) \vee (\sim q \vee s)]$ is

If p be the length of the perpendicular from the origin on the straight line x + 2by = 2p ,then what is the value of b?

if P =$\begin{bmatrix}i&0&-i\\ 0&-i&i\\ -i&i&0\end{bmatrix}$ and $Q=\begin{bmatrix}-i&i\\ 0&0\\ i&-i\end{bmatrix}$ then $PQ$ is equal to

If $P(A \cup B) = 0.8, P(A \cap B) = 0.3 $ then $P (\bar{A} ) + P(\bar{B})$ =

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