List of top Mathematics Questions

Let the function f: [0,2] \(\rightarrow\) R be defined as \(f(x) =   \begin{cases}     e^{min}{x^2,x-[x]}       & \quad x \in[0,1]\\     e^{[x-log_ex]}  & \quad x\in[1,2]   \end{cases}\)
where [t] denotes the greatest integer less than or equal to t. Then the value of the integral \(\int^2_0xf(x)dx\) is 

Let P be the plane passing through the points (5, 3, 0), (13, 3, –2) and (1, 6, 2). For α ∈ N, if the distances of the points A (3, 4, α) and B (2, α, a) from the plane P are 2 and 3 respectively, then the positive value of a is

Let A = {1, 3, 4, 6, 9} and B = {2, 4, 5, 8, 10}. Let R be a relation defined on A × B such that R = {(\((a_1, b_1),(a_2, b_2)\)) : \(a_1 ≤ b_2\) and \(b_1 ≤ a_2\)}. Then the number of elements in the set R is 

Let a, b, c and d be positive real numbers such that a + b + c + d = 11. If the maximum value of \(a^5b ^3c ^2d\) is \(3750\;\beta\), then the value of \(\beta\) is

If \(\begin{vmatrix} x+1 & x & x \\ x & x+ \lambda & x \\ x & x & x+ \lambda^2 \end{vmatrix}\)= \(\frac{9}{8}\) \((103x + 81)\), then \(λ\) and \(\frac{λ}{3}\) are roots of the equation

If the shortest distance between the line joining the points \((1,2,3)\) and \((2,3,4)\), and the line \(\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-2}{0}\) is \(\alpha\), then \(28 \alpha^2\) is equal to

Two dice are rolled and sum of numbers of two dice is N then probability that 2N < N! is m/n , where m and n are co-prime, then 11m – 3n is?

\(96\cos\frac{π}{33}\cos \frac{2π}{33}\cos\frac{4π}{33}\cos\frac{8π}{33}\cos\frac{16π}{33}\) is equal to

The negation of the statement
(p v q) ∧ (q v(∼r)) is

Let a, b, c be three distinct positive real numbers such that (2a)^log_ea = (bc)^log_eb and b^log_e2 = a^log_ec. Then 6a + 5bc is equal to _____.

If the number of ways in which a mixed double badminton can be played such that no couples played into a same game is 840. Then find the number of players?

Let y = p(x) be the parabola passing through the points (–1, 0), (0, 1) and (1, 0). If the area of the region \(\{x,y):(x+1)^2+(y-1)^2≤1,y≤p(x)\}\) is A, then 12(π-4A) is equal to__.

The mean of the data

is 26 , then variance of the data is?

An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If OP = μ, OR=v and OQ=αv+βv, then α, β² are the roots of the equation

The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is

Let P be the point of intersection of the line \(\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}\) and the plane x + y + z = 2. If the distance of the point P from the plane 3x – 4y + 12z = 32 is q, then q and 2q are the roots of the equation 

Let two vertices of triangle ABC be (2, 4, 6) and (0, –2, –5), and its centroid be (2, 1, –1). If the image of third vertex in the plane x + 2y + 4z = 11 is (α, β, γ), then αβ + βγ + γα is equal to

Let the ellipse \(E : x^2 + 9y^2 = 9\) intersect the positive x- and y-axes at the points A and B respectively Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If the area of the triangle which vertices A, P and the origin O is m/n , where m and n are coprime, then m – n is equal to 

The slope of tangent at any point (x, y) on a curve y = y(x) is \(\frac{x^2+y^2}{2xy},x>0\) If y(2) = 0, then a value of y(8) is
 

Let f be a differentiable function such that x² f(x) - x = \(4 \int^x_0tf(t)dt,f(1)=\frac{2}{3}. \;\text{Then 18f(3)is equal to}\)
 

If I(x) = \(\int e^{sin^2x}\)\((cos \;x \;sin \;2x - sin \;x)dx\) and I (0) = 1, then \(I(π/3)\) is equal to

From a square of side 30 cm the squares of side x cm is cut off to make a cuboid of maximum volume. The surface area of cuboid with open top is?

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

If the coefficient of x⁷ in expansion of \((ax- \frac{1}{bx^2})^{13}\) is equal to the coefficient of x^-5 in expansion of \((ax + \frac{1}{bx^2})13\), then a⁴b⁴ is ______