List of top Mathematics Questions

Let $N$ denote the number that turns up when a fair die is rolled If the probability that the system of equations$ x+y+z=1 $ $ 2 x + Ny +2 z=2 $ $ 3 x +3 y+ N z=3$ has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is
Let T1 and T2 be two distinct common tangents to the ellipse \(E:  \frac{x^2}{6} + \frac{y^2}{3} = 1\) and the parabola \(P: y^2 = 12x\). Suppose that the tangent T1 touches P and E at the points A1 and A2, respectively and the tangent T2 touches P and E at the points A4 and A3, respectively. Then which of the following statements is(are) true?

x=logp and y=1/p differential equation

The coefficient of x5 in the expansion of \((2x^3 - \frac{1}{3x^2})^5\) is

Let \(f:R→R\) be a function defined by \(f(x)=x^2+9\).The range of \(f \) is 

Suppose P is the point on the line joining  \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?
The portion of the tangent to the curve x\(^{\frac{2}{3}}\)+y\(^{\frac{2}{3}}\)=a\(^{\frac{2}{3}}\), a>0 at any point of it, intercepted between the axes
Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is 
The largest natural number \(n\) such that \(3^n\) divides \(66!\) is:
If I=∫\(\frac{x^2dx}{(x\,sin\,x+cos\,x)^2}\)=f(x)+tan x+c, then f(x) is
The tangent at point(a cosθ, b sinθ), 0<θ<\(\frac{\pi}{2}\), to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) meets the x-axis at T and y-axis at T1, Then the value of \(\min_{\,\,\,0<\theta<\frac{\pi}{2}}\)(OT)(OT1) is
If A= {P,O,L,Y,T,E,C,H,N, I} and B = {E, X, A, M}, then \(A∩B =\)

The sum of the absolute maximum and minimum values of the function \(f(x)=\left|x^2-5 x+6\right|-3 x+2\)in the interval \([-1,3]\) is equal to :

Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?

The value of the integral \(\int \limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x+\frac{\pi}{4}}{2-\cos 2 x} d x\)is :

The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$ The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :
Two circles having radius \(r_1\) and \(r_2\) touch both the coordinate axes. Line \(x+y=2\) makes intercept 2 on both the circles. The value of \(r_{1}^{2} + r_{2}^{2} - r_{1}r_{2}\) is:
If \(sin^{-1}x=2\,tan^{-1}x\) , then the number of integral values of x is equal to:

If (21)18 + 20·(21)17 + (20)2 · (21)16 + ……….. (20)18 = k (2119 – 2019) then k =

If \(A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)\) are co-planer then \(\sum (\lambda_i + 2)^2\) is equal to

Shortest distance between lines \(\frac{(x-5)}{4}\)=\(\frac{(y-3)}{6}\)=\(\frac{(z-2)}{4}\) and \(\frac{(x-3)}{7}=\frac{(y-2)}{5}=\frac{(z-9)}{6}\) is ?

Let $y (x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)$ Then $y^{\prime}-y^{\prime \prime}$ at $x=-1$ is equal to :

Consider the lines $L_1$ and $L_2$ given by 

$L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} $ 

$ L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}$

A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively Then the length of line segment $P Q$ is

Let $H$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is _____

Let \(P(x_0, y_0)\) be the point on the hyperbola \(3x^2 - 4y^2 = 36\), which is nearest to the line \(3x + 2y = 1\). Then \(\sqrt{2}(y_0 - x_0)\) is equal to: