List of top Mathematics Questions

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 :

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 $\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}$ be a vector such that $\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}$ and $\vec{a} \cdot \vec{b}=3$ Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :-
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
Let $\alpha$ be a root of the equation $(a-c) x^2+(b-a) x+(c-b)=0$where $a , b , c$ are distinct real numbers such that the matrix $\begin{bmatrix}\alpha^2 & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c\end{bmatrix}$is singular Then, the value of $\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}$ is
Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$, be in AP and $a_1+a_3=10$ If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to :
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 
What is the percentage drop in the production of Ludo from 1992 to 1994?

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 
What is the approximate percentage increase in the production of Monopoly from 1993 to 1995?
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
For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?
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