List of top Mathematics Questions

Let the line passing through the points P (2, –1, 2) and Q (5, 3, 4) meet the plane x – y + z = 4 at the point R. Then the distance of the point R from the plane x + 2y + 3z + 2 = 0 measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal to

For \(a∈ C, let A = {z∈C : Re (a + z ) > Im ( a + z)}\) and \(B = {z∈C : Re (a + z ) < Im ( a + z)}.\) Then among the two statements: 
(S₁) : If \(Re (a), Im (a) > 0\), then the set A contains all the real numbers 
(S₂): If \(Re (a), Im (a) < 0,\) then the set B contains all the real numbers

The sum of the coefficients of three consecutive terms in the binomial expansion of (1 + x)ⁿ⁺², which are in the ratio 1 : 3 : 5, is equal to

Using all the letters of the word MATHS, then rank of the word THAMS is:

Let f and g be two function defined by \(f(x) =   \begin{cases}     x+1       & \quad x<0\\    |x-1|,   & \quad x \geq0   \end{cases}\) and g(x) = \(f(n) =   \begin{cases}     x+1,       & \quad x<0 \\     1,  & \quad x\geq0   \end{cases}\) Then (gof)(x) is 

If f : R \(\rightarrow\) R be a continuous function satisfying \(\int^{\frac{\pi}{2}}_0f(sin2x)sinxdx+\alpha\int^{\frac{\pi}{4}}_0f(cos2x)cosxdx=0\), then the value of \(\alpha\) is

The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45° and from the feet of another person standing due west of the tower is 30°. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

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 

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse \(x^2 + 4y^2 = 36\) is r, then \(12r^2\) is equal to

The converse of ((~ p) ∧ q) ⇒ r 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__.

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

The mean of the data

is 26 , then variance of the data is?