List of top Mathematics Questions

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

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

If a point $P (\alpha, \beta, \gamma)$ satisfying $(\alpha\,\, \beta\,\, \gamma) \begin{pmatrix} 2 & 10 & 8 \\9 & 3 & 8 \\8 & 4 & 8\end{pmatrix}=(0\,\,0\,\,0) $ lies on the plane $2 x+4 y+3 z=5$, then $6 \alpha+9 \beta+7 \gamma$ 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 ?

The absolute difference of the coefficients of \(x^{10}\) and \(x^7\) in the expansion of \(\left(2x^2 + \frac{1}{2x}\right)^{11}\) is equal to:

If the four points, whose position vectors are \(3 \hat{i}-4 j+2 \hat{k}, l+2 j-\hat{k}_4-2 \hat{k}-j+3 \hat{k}\) and \(5 \hat{i}-2 \alpha \hat{j}+4 \hat{k}\) are coplanar, then a is equal to
Let $S$ denote the set of all real values of $\lambda$ such that the system of equations
$ \lambda x+y+z=1 $
$x+\lambda y+z=1 $
$x+y+\lambda z=1$
is inconsistent, then $\displaystyle \sum_{\lambda \in S}\left(|\lambda|^2+|\lambda|\right)$ is equal to

The number of points on the curve \(y=54 x^5-135 x^4-70 x^3+180 x^2+210 x\) at which the normal lines are parallel \(to x+90 y+2=0\) is 

Let \(y = y(x), y > 0,\) be a solution curve of the differential equation \((1 +x^2)dy = y(x−y)dx.\) If \(y(0) = 1\) and \(y(2√2) = β\), then
If the n terms a1,a2........an are in A.P. with increment r, then the difference between the mean of their squares and square of their mean is 

Suppose a line parallel to \(ax+by=0\) (where \(b≠0\))intersects\( 5x-y+4=0\) and \(3x+4y-4=0\) ,respectively at P and Q. If the midpoint of PQ is \((1,5)\),then the value of \(\dfrac{a}{b}\) is

A biased die is rolled such that the probability of getting k dots,1≤k≤6, on the upper face of the die is proportional to k. Then the probability that five dots appear on the upper face of the die is 
Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and Ek={(a,b)∈S:ab=k}. If Pk=P(Ek), then the correct among the following is 
The value of 'a' for which the scaler triple product formed by the vectors \(\vec\alpha=\hat{i}+a\hat{j}+\hat{k}\),  \(\vec{\beta}=\hat{j}+a\hat{k}\)  and  \(\vec{\gamma}=a\hat{i}+\hat{k}\)  is maximum, is
The locus of points(x,y) in the plane satisfying sin2x + sin2y =1 consists of

If $ i = \sqrt{-1} $ then  $\text{Arg}\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right]=$

The surface area of the sphere x2 + y2 + z2 = 9 lying inside the cylinder x2 + y2 = 3y is
The area of the region in the first quadrant which is above the parabola \(y = x^2\) and enclosed by the circle \(x^2 +y^2 = 2 \) and the y-axis is
The area of the region in the first quadrant enclosed by the curves\( y=√x,y=-x+6 \)and the x-axis is 
Which of the following statements are true?

For \(i=1,2,3,4\), suppose the points\((\cosθi,\secθi)\) lie on the boundary of a circle,where \(θi∈[0,\frac{π}{6})\) are distinct. Then \(\cosθ_1\ \cosθ_2\ \cosθ_3\ \cosθ_4\)  equals

Let A be a set containing n elements, A subset P of A is chosen and set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is

Let α,β be the roots of the equation, ax2+bx+c=0.a,b,c are real and sn=αn+βn and \(\begin{vmatrix}3 &1+s_1  &1+s_2\\1+s_1&1+s_2  &1+s_3\\1+s_2&1+s_3  &1+s_4\end{vmatrix}=\frac{k(a+b+c)^2}{a^4}\) then k=

The mean and variance of a random variable \( X \) having binomial distribution are 4 and 2, respectively. Find \( P(X = 1) \).