List of top Mathematics Questions

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
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 72th 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 a1 a9+a2 a4 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 ____________.
Let the co-ordinates of one vertex of \(\Delta ABC\) be \(A(0, 2, \alpha)\) and the other two vertices lie on the line \(x+\frac{\alpha}{5}=y-\frac{1}{2}=z+\frac{4}{3}\) For \(\alpha∈Z\), if the area of \(\Delta ABC\) is 21 sq. units and the line segment BC has length \(2\sqrt{21}\) units, then α2 is equal to ___________.
Let \(y = f(x)\) be the solution of the differential equation \(y(x + 1)dx - x^2dy = 0\), \(y(1) = e\). Then \(lim_{x→0^-} f (x)\) is equal to
Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ2 represent mean and variance of X, respectively, then 10(μ2+σ2) is equal to
If p, q and r are three propositions, then which of the following combination of truth values of p, q and r makes the logical expression \({(p∨q)∧((∼p)∨r)}🡢((∼q)∨r)\) false?

If $\phi(x)=\frac{1}{\sqrt{ x }} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) dt , x>$, then $\emptyset^{\prime}\left(\frac{\pi}{4}\right)$ is equal to :