List of top Mathematics Questions asked in JEE Main

Match List I with List II

	List I		List II
A	Spring constant	I	[T^-1]
B	Angular speed	II	[MT^-2]
C	Angular momentum	III	[ML²]
D	Moment of Inertia	IV	[ML²T^-1]

Choose the correct answer from the options given below:

Let a, b, c be three distinct real numbers, none equal to one. If the vectors $a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c\hat{k}$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is equal to

The area of the region enclosed by the curve y = x³ and its tangent at the point (-1, -1) is

Let P $(\frac{2√3}{√7},\frac{6}{√7} )$, Q,R and S be four points on the ellipse 9x² + 4y² = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If $\frac{1}{ ( P Q )^2} +\frac{ 1}{ ( R S ) ^2} =\frac{ P }{q}$, where p and q are coprime, then p + q is equal to

If the point $(α ,\frac{7√3}{3} )$ lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ=7,θ∈( $0,\frac{π}{2}$ ) between the coordinates axes, then α is equal to

If the local maximum value of the function f( x )=$(\frac{√3e}{2 sin x} )^{ sin^2x}$ ,$ x ∈ ( 0,\frac{π}{2} )$, is $\frac{k}{e}$, then $(\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 $ is equal to

Let A=$\begin{bmatrix} 1 & \frac{1}{51} \\ 0 & 1\end{bmatrix}$. If B=$\begin{bmatrix} 1 & 2 \\ -1 & -1\end{bmatrix}$A $\begin{bmatrix} -1 & -2 \\ 1 & 1\end{bmatrix}$, then the sum of all the elements of the matrix $\sum^{50}_{n=1}B^n$ is equal to

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P \left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :

Let $\alpha$ be the area of the larger region bounded by the curve $y^2=8 x$ and the lines $y=x$ and $x=2$, which lies in the first quadrant Then the value of $3 \alpha$ is equal to _____

The number of rational terms in the expansion of (3^3/4+ 5^3/2)60?

Consider two sets A and B. Set A has 5 elements whose mean & variance are 5 and 8 respectively. Set B has also 5 elements whose mean & variance are 12 & 20 respectively. A new set C is formed by subtracting 3 from each element of set A and by adding 2 to each element of set B. The sum of mean & variance of the set C is

If the equation of the normal to the curve $𝑦= 𝑥−𝑎 (𝑥+𝑏)(𝑥−2)$ at the point $(1,−3)$ is $𝑥−4𝑦=13$, then the value of $𝑎+𝑏$ is equal to ___ .

The shortest distance between the lines $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}$ and $\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}$ is equal to

Area bounded by larger part in I quadrant by x = 4y² , x = 2 and y = x is A then 3A equals

Let S = {1, 2, 3, 4, 5}
if f : S → P(S), where P(S) is power set of S. Then number of one-one functions f can be made is

If coefficient of x¹⁵ in expansion of $(ax^3+\frac{1}{bx^{1/3}})^{15}$ is equal to coefficient of x^–15 in expansion of $(ax^{1/3}+\frac{1}{bx^3})^{15}$ then |ab – 5| is equal to

The mean and variance of 7 observations are 8 and 16 respectively If one observation 14 is omitted and $a$ and $b$ are respectively mean and variance of remaining 6 observation, then $a+3 b-5$ is equal to ______

The mean of coefficients of $x, x^2, ....., x^7$ in the binomial expansion of $(2 + x)^9$ is?

Let $S=\{1,2,3,4,5,6\}$ Then the number of one-one functions $f: S \rightarrow P ( S )$, where $P ( S )$ denote the power set of $S$, such that $f(m) \subset f(m)$ where $n < m$ is _______

Let $α_1,α_2,….,α_7$ be the roots of the equation $𝑥^7+3𝑥^5−13𝑥^3−15𝑥=0$ and $|α_1|≥|α_2|≥⋯≥ |α_7|$. Then $α_1α_2−α_3α_4+α_5α_6$ is equal to ____.

Area bounded by the curve 2y² = 3x and the line x+y = 3 outside the circle (x-3)² + y² = 2 and above the x-axis is A. The value of 4(π +4A) is?

$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$is equal to

5 boys with allotted roll numbers and seat numbers are seated in such a way that no one sits on the allotted seat. The number of such seating arrangements is?