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List of top Mathematics Questions

Let $ z = 1 + i $ and $ z_1 = \frac{1 + \bar{z}}{z(1 - z) + 1} $, where $ \bar{z} $ denotes the conjugate of $ z $. Then$\frac{12}{\pi} \arg(z_1)$ is equal to:

The $4^{\text {th }}$ term of $G P$ is $500$ and its common ratio is $\frac{1}{m}, m \in N$ Let $S_n$ denote the sum of the first $n$ terms of this GP If $S_6>S_5+1$ and $S_7< S_6+\frac{1}{2}$, then the number of possible values of $m$ is

$ \lim_{x \to 0} \frac{48 x^4}{x} \int_0^x \frac{t^3}{t^6 + 1} \, dt $ is equal to:

The line $l_1$ passes through the point $(2,6,2)$ and is perpendicular to the plane $2 x+y-2 z=10$. Then the shortest distance between the line $l_1$ and the line $\frac{x+1}{2}=\frac{y+4}{-3}=\frac{z}{2}$ is :

The value of $\frac{8}{\pi} \int\limits_0^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}} d x$ is

Let a tangent to the curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $AB$ is

Let $\alpha>0$ If $\int\limits_0^\alpha \frac{x}{\sqrt{x+\alpha}-\sqrt{x}} d x=\frac{16+20 \sqrt{2}}{15}$, then $\alpha$ is equal to :

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses If he can choose at most two language courses, then the number of ways he can choose five courses is

The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is

Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is

Let $C$ be the largest circle centred at $(2,0)$ and inscribed in the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$If $(1, a)$ lies on $C$, then $10 \alpha^2$ is equal to

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial number. For example, the number 77777 has serial number 1. Then the serial number of 35337 is _________

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event .
Given below are two statements :
(S1): If $P ( A )=0$, then $A =\emptyset$
(S2): If $P(A)=1$, then $A=\Omega$
Then

Let the coefficients of three consecutive terms in the binomial expansion of (1 + 2x)n be the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of these three terms, is _______.

The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has :

If the co-efficient of x⁹ in $(αx^3+\frac{1}{βx})^{11}$ and the co-efficient of x^-9 in $(αx-\frac{1}{βx^3})^{11}$ are equal, then $(αβ)^2$ is equal to ________.

Let $f : R → R$ be a differentiable function that satisfies the relation $f(x + y) = f(x) + f(y) – 1, ∀x, y ∈R$. If $f'(0) = 2$, then $|f(–2)|$ is equal to ___________.

If all the six digit numbers x₁ x₂ x₃ x₄ x₅ x₆ with $0<x_1<x_2<x_3<x_4<x_5<x_6$ are arranged in the increasing order, then the sum of the digits in the 72^th number is _____________.

Let a b, and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be $a-b+c$, $λa-3b+4c$, $-a+2b-3c$ and $2a-4b+6c$ respectively. If AB AC , and AD are coplanar, then λ is equal to ____.

Let $p , q \in R$ and $(1-\sqrt{3})^{200}=2^{199}(p+i q), t=\sqrt{-1}$ Then $p + q + q ^2$ and $p - q + q ^2$ are roots of the equation

For three positive integers $p , q , r , x^{p q^2}=y^{y r}=z^{p^2 r }$ and $r = pq +1$ such that $3,3 \log _y x, 3 \log _z y$ $7 \log _x z$ are in AP with common difference $\frac{1}{2}$ Then $r-p-q$ is equal to

Let a₁, a₂, a₃, … be a G.P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a₁a₉+a₂a₄ a₉+a₅+a₇ is equal to __________.

Suppose f is a function satisfying $f(x + y) + f(x) + f(y)$ for all $x, y ∈N$ and $f(1)=\frac{1}{5}$. If $∑_{n=1}^{m} \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{2}$, then m is equal to _______.

The distance of the point $(-1,9,-16)$ from the plane $2 x+3 y-z=5$ measured parallel to the line $\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}$ is

Let the equation of the plane P containing the line $x+10=\frac{8-y}{2}=z$ be $ax + by + 3z = 2(a + b)$ and the distance of the plane P from the point (1, 27, 7) be c. Then a²+b²+c² is equal to ____________.