List of top Mathematics Questions asked in JEE Main

Let $P$ be a square matrix such that $P^2 = I - P$. For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $P^\alpha + P^\beta = \gamma I - 29P$ and $P^\alpha - P^\beta = \delta I - 13P$, then $\alpha + \beta + \gamma - \delta$ is equal to:

If the coefficient of x⁷ in (\(ax^2 +\frac{ 1}{2bx}^{11}\)) and x^-7 in (\(ax - \frac{1}{3bx^2}^{11}\)), are euual then

\(lim _{n→∞}{(2^½-2^½)(2^½-2^½)….(2^½-^2{\frac{1}{2n+1}})}\) is equal to

If the solution curve f(x, y) = 0 of the differential equation (1+log_e x) \(\frac{dx}{dy} \)- x log_e x = e^y , x > 0, passes through the points (1,0) and (α, 2) then α^a is equal to

If the tangents at the points P and Q on the circle x² + y² – 2x + y = 5 meet at the point R  \(( \frac{9}{4},2 ) \)then the area of the triangle PQR is 

A plane P contains the line of intersection of the plane  \(\overrightarrow{r} .( \^i+\^j+\^k )=6\) and \(\overrightarrow{r }.( 2\^i+3\^j+4\^k) = − 5\).  If P passes through the point (0, 2, –2), then the square of distance of the point (12, 12, 18) from the plane P is 

Let the line L pass through the point (0, 1, 2), intersect the line  \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and be parallel to the plane 2x + y – 3z = 4. Then the distance of the point P(l, –9, 2) from the line L is 

For differentiable function f: R-{0}⟶ R, let 3f(x)+2f(\(\frac{1}{x}\))-\(\frac{1}{x}\)-10, then |f(3)+f(\(\frac{1}{4}\))| is equal to

The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is

Let B =\(\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}\) , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B\(\begin{bmatrix} α \\ -2α  \\ α \end{bmatrix}\)is equal to

For the system of linear equations  
2x+4y+2az=b
x+2y+3z=4 
2x-5y+2z=8 
which of the following is NOT correct ?  

Let s₁, s₂, s₃,…..,s₁₀ respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is

Let a =\(\^i+4\^j​+2\^k,b=3\^i−2\^j​+7\^k \,\,\,\,and\,\,\.\ c=2\^i−\^j​+4\^k\). Find a vector d satisfies \(\overrightarrow{d}\times{\overrightarrow{b}}=\overrightarrow{c}\times{\overrightarrow{b}}\) and \(\overrightarrow{d}.\overrightarrow{a}=24\), then \(|\overrightarrow{d}|^2\) is equal to

\(max\\{0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)

Let the tangent and normal at the point \((3\sqrt{3},1)\) on the ellipse \(\frac{ x^2}{36}+\frac{y^2}{4} =1\) meet the y-axis at the points A and B respectively. Let the circle C be drawn taking AB as a diameter and the line x = \(2\sqrt{5}\) intersect C at the points P and Q. If the tangents at the points P and Q on the circle intersect at the point (α,β) , then α² - β² is equal to 

The distance of the point ( -1,2,3) from the plane \(\overrightarrow{r}( \^i−2 \^j+3 \^k )=10\) parallel to the line of the shortest distance between the lines \(\overrightarrow{r}=(\^i=\^j)+λ(2\^i+\^k)\) and  \(\overrightarrow{r}=(2\^i=\^j)+μ(\^i+\^j+\^k)\)  is 

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of X is

The negation of the statement \(((A\land(B\lor C)) ⇒ (A\lor B)) ⇒ A\) is

If the system of equations  
x + y + az = b  
2x + 5y + 2z = 6  
x + 2y + 3z = 3  
Has infinitely many solutions, then 2a + 3b is equal to

The straight lines l₁ and l₂ pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m₁ and m₂ are the slopes of the lines l₁ and l_2, then the point of intersection of the line y = (m₁ + m₂)x with L lies on

If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x– 3y +5z + 9 = 0 and parallel to the line  \(\frac{x+1}{−2} =\frac{ y+3}{4}= \frac{z−2}{5}\) is ax by+cz+6=0. then a + b + c is equal to 

\(5\^{i}+5\hat{j}+2λ\hat{k},\hat{i}+2\hat{j}+3\hat{k},-2\hat{i}+λ\hat{j}+4\hat{k}\) and \(-\hat{i}+5\hat{j}+6\hat{k}.\) Let the set S = {λ∈ \(\mathbb{R}\) : The points A, B, C and D are coplanar}. Then \(\displaystyle\sum_{λ∈S}^{}(λ+2)^2\) is equal to

Let D be the domain of the function f(x)=sin⁻¹(\( log_{3 x} (\frac{6+2log_3x}{−5x}\))) If the range of the function g : D → R defined by g ( x ) = x − [ x ] is the greatest integer function), is ( α , β ) , then α ² +\(\frac{ 5}{ β}\) is equal to