JEE Main Mathematics PYQ

Mathematics Topics

JEE Main Mathematics questions

A cross-section of Mathematics questions asked in JEE Main, spread across topics and years. Open any one for the full solution.

• The number of elements in the set S = (r, k) : k ∈ mathbbZ and ^36C_r+1 = 6 (^35C_r ) (k^2 - 3), is :2026
• Let A,B be points on the two half-lines x-√3|y|=α, α>0 at a distance of α from their point of intersection P.…2026
• If ∫ ( 1-5 cos ^2 x sin ^5 x cos ^2 x ) d x=f(x)+ C, where C is the constant of integration, then f ( π 6 )-f…2026
• If the mean deviation about the median of the numbers k, 2 k, 3 k, …. ., 1000 k is 500, then k^2 is equal to :2026
• If A = sin 3°cos 9° + sin 9°cos 27° + sin 27°cos 81° and B = tan 81°- tan 3°, then B A is equal to .2026
• Let P Q R be a triangle such that overrightarrowP Q=-2 i- j+2 k and overrightarrow PR=a i+b j-4 k, a, b ∈…2026
• Suppose a, b, are in A.P. and a^2, 2 ~b^2, ^2 are in G.P. If a< b< and a+ b+ =1, then 9 ( a^2+ b^2+ ^2 ) is…2026
• If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0, meets the…2026
• If the solution curve y=f(x) of the differential equation (x^2-4 ) y^prime-2 x y+2 x (4-x^2 )^2=0, x>2,…2026
• From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in…2026
• The least value of (cos ^2 θ-6 sin θ cos θ+3 sin ^2 θ+2 ) is2026
• Let the line L pass through the point (-3,5,2) and make equal angles with the positive coordinate axes. If…2026
• Let S= z ∈ mathbbC: 4 z^2+ z=0. Then Σ_z ∈ S|z|^2 is equal to:2026
• Let C be a circle having centre in the first quadrant and touching the x-axis at a distance of 3 units from…2026
• Let [·] be the greatest integer function. If α=∫_0^64 (x^1 / 3- [x^1 / 3 ] ) d x, then 1 π ∫_0^α π ( sin ^2 θ…2026
• A variable X takes values 0, 0, 2, 6, 12, 20, …, n(n-1) with frequencies ^nC_0, ^nC_1, ^nC_2, ^nC_3, ^nC_4,…2026
• Considering the principal values of inverse trigonometric functions, the value of the expression tan (2 sin…2026
• If (2α+1, α^2-3α, α-1 2 ) is the image of (α, 2α, 1) in the line x-2 3= y-1 2= z 1, then the possible…2026
• Let S=z: 3 leqslant|2 z-3(1+i)| leqslant 7 be a set of complex numbers. Then min _z ∈ S | (z+ 1 2(5+3 i) ) |…2026
• Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such that the mid point…2026
• Let P_1: y=4 x^2 and P_2: y=x^2+27 be two parabolas. If the area of the bounded region enclosed between P_1…2026
• Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14, α < β, be 8 and 16 respectively.…2026
• If π 4 + Σ_p=1^11 tan^-1 ( 2^p-1 1 + 2^2p-1 ) = α, then tanα is equal to .2026
• If a and b are two vectors such that | a| = 2 and | b| = 3, then the maximum value of 3 | (3 a + 2 b ) | + 4…2026
• Let A = … and B = [b_ij], 1 ≤ i, j ≤ 3. If B = A^99 - I, then the value of b_31 - b_21 b_32 is :2026
• Let the vertex A of a triangle ABC be (1, 2), and the mid-point of the side AB be (5, -1). If the centroid of…2026
• If y=y(x) satisfies the differential equation 16(√x+9 √x)(4+√9+√x) cos y ~d y=(1+2 sin y) d x, x>0 and…2026
• If a random variable x has the probability distribution … then P(3 < x ≤ 6) is equal to2026
• If cot x= 5 12 for some x ∈ (π, 3 π 2 ), then sin 7 x (cos 13 x 2+sin 13 x 2 )+cos 7 x (cos 13 x 2-sin 13 x 2…2026
• For a triangle ABC, let overrightarrow =overrightarrow BC, overrightarrow q=overrightarrow CA and…2026
• A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can…2026
• Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0 are bisected by the…2026
• Let f: mathbbR → mathbbR be a twice differentiable function such that f''(x) > 0 for all x ∈ mathbbR and…2026
• A data consists of 20 observations x_1, x_2, …, x_20. If Σ_i=1^20(x_i + 5)^2 = 2500 and Σ_i=1^20(x_i - 5)^2 =…2026
• Let S = x ∈ [-π, π] : sin x (sin x + cos x) = a, a ∈ mathbbZ. Then n(S) is equal to :2026
• Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j. If the side PS is rotated…2026