List of top Mathematics Questions asked in JEE Main

Let a∈ Z and [t] be the greatest integer t. Then the number of points, where the function f(x)=[a+13 sin x], x ∈ (0, π) is not differentiable, is ____

If the area of the region \( S={(x,y) : 2y-y^2 ≤ x^2 ≤ 2y, x ≥ y}\) is equal to \(\frac{ n+2}{n+1}−\frac{π}{n−1}\), then the natural number n is equal to _____.

Let the tangent to the curve x² + 2x – 4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and parallel to the line x – 3y = 6 meet the parabola y² = 4x at B. If B lies on the line 2x – 3y = 8. then (AB)² is equal to___

Let y = y(x) be a solution of the differential equation (x cos x)dy +(xy sin x + y cos x – l)dx = 0, 0 < x < \(\frac{π}{2}\). If\(\frac{π}{3}y(\frac{π}{3})=\sqrt3\), then \(| \frac{π}{6 }y“( \frac{π}{6})+2 y'( \frac{π}{6})| \) is equal to______.

The number of relations, on the set {1,2,3} containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is______

Let D_k=\(\begin{vmatrix} 1 & 2k & 2k-1\\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix} \) If \(∑^n_{k=1} D_k=96,\) The n is equal to

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.

Let I(x) = \(∫√\frac{x+7}{x} dx\) and I (9) = 12 + 7 loge 7. If I (1) = α + 7 loge (1 + 2√2), then α4 is equal to_____.

Let the plane x+3y–2z+6=0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is\( (α,β,\frac{6 }{7} ), \) then 98(α + β)² is equal to___.

A fair n (n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is \(\frac{n}{9}\), then n is equal to_____.

Let S be the set of values of λ, for which the system of equations  
6λx – 3y + 3z = 4λ2 ,  
2x + 6ly + 4z = 1, 
3x + 2y + 3λz = l has no solution. Then  12\( ∑ _{λ ∈ S}\) | λ | 12 ∑ λ ∈ | λ |  is equal to ________ .

Suppose a₁, a₂, 2, a₃, a4 be in an arithmeticogeometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is \(\frac{49}{2}\) , then a4 is equal to ________ .

Let the tangent at any point P on a curve passing through the points (1, 1) and (\(\frac{1}{10}\),100), intersect positive x-axis and y-axis at the points A and B respectively. If PA : PB = 1 : k and y = y(x) is the solution of the differential equation  \(\frac{dy}{e^{dx}}Kx+\frac{K}{2}\) , y(0) = k, then 4y(1) – 5log_e3 is equal to ______ .

Let the equations of two adjacent sides of a parallelogram ABCD be 2x – 3y = –23 and 5x + 4y = 23. If the equation of its one diagonal AC is 3x + 7y = 23 and the distance of A from the other diagonal is d, then 50 d2 is equal to____.

Let the foot of perpendicular from the point A(4, 3, 1) on the plane P : x - y + 2z + 3 = 0 be N. If B(5,α,β) ∈ Z   is a point on plane P such that the area of the triangle ABN in 3√2 . then α² + β² + αβ is equal to ____ .

In the figure, θ₁ + θ₂ = \(\frac{π}{2}\) and √3 (BE) = 4 (AB). If the area of ΔCAB is 2√3 - 3 unit2 , when \(\frac{θ_2}{θ_1}\) is the largest, then the perimeter (in unit) of ΔCED is equal to ________.

let D_k=\(\begin{vmatrix} 1 & 2k& 2k-1\\ n & n^2+n+2 & n^2\\ n & n^2+n & n^2+n+2 \end{vmatrix}\) if \(∑^n_{ k=1}\) D_k=96, Then n is equal to

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x) = |[x] |+\(\sqrt{x -[x] }\)is discontinuous is _____.

If \(∫^{0.15}_{-0.15 }|100x^2-1|dx=\frac{k}{3000,}\)  then k is equal to____.

Two circles in the first quadrant of radii r₁ and r₂ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x + y = 2. Then \(r^2_1+r_2^2– r_1r_2\) is equal to_____.

Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is \((α,β,\frac{6}{7}),\) then 98(α + β)² is equal to___.

If the coefficient of $x^{15}$ in the expansion of $\left(a x^3+\frac{1}{b x^{1 / 3}}\right)^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $\left(a x^{1 / 3}-\frac{1}{b x^3}\right)^{15}$, where a and $b$ are positive real numbers, then for each such ordered pair $(a, b)$ :