List of top Mathematics Questions

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 _____.

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______

Among the two statements
(S1) : (p ⇒ q)∧(q ∧(~q)) is a contradiction and  
(S2) : (p∧q) v ((~p)∧q) v (p ∧ (~q)) v ((~p) ∧ (~q)) is a tautology 

Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is \(\frac{p}{q}\), where p and q are coprime, then the sum of the positive divisors of p is equal to

Let  \(λ∈Z ,→a=λ\^i+\^j =/^ k λ ∈\)  and \(\overrightarrow{ b} = 3 \^i− \^j + 2 \^k\) . be a vector such that  ( \(\overrightarrow{ a}+\overrightarrow{ b}+\overrightarrow{ c}\) ) × \(\overrightarrow{ c}=\overrightarrow{ 0},\overrightarrow{ a}.\overrightarrow{ c}\) and  \(\overrightarrow{ b}.\overrightarrow{ C}=-20\)  Then \( | \overrightarrow{c} + ( λ \^i + \^j + \^k ) |  ^2 \) is equal to

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

Let the lines l₁: \(\frac{x+5}{3} = \frac{y+4}{1}=\frac{z−α}{−2}\) and l₂: 3x + 2y + z – 2 = 0 = x – 3y + 2z - 13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(- 4, -3, 2), then |a| + |b|+|c| is equal to

Let the plane P : 4x – y + z = 10 be rotated by an angle \(\frac{π}{2}\) about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is

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 

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

The area of the region enclosed by the curve \(y=x^3\) and its tangent at the point (−1,−1) is

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

Let be a sequence such that a1+a₂+....+ a_n=\(\frac{n^2+3n}{ (n+1 ) (n+2)}\). If  \(28∑^{10}_{k=1}\frac{1}{a_k} =\) P₁P₂P₃ . . . P_m ,  where p1, p2, …..p_m are the first m prime numbers, then m is equal to

Let C be the circle in the complex plane with centre z₀ = \(\frac{1}{2}\) (1+3i) and radius r = 1. Let z₁ = 1+ i and the complex number z2 be outside the circle C such that |z₁ – z₀| |z₂ – z₀| = 1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|² is equal to

\(\frac{nC_n}{(n+1)}\) + \(\frac{nC_{n-1}}{(n)}\) + ……… + ½ \(nC_1\) + \(nC_0\) = \(\frac{255}{8}\), Then value of n is

The number of five-digit numbers, greater than 40000 and divis ible by 5, which can be formed using the digits 0, 1, 3, 5, 7, and 9 without repetition, 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 \(∑ ^{50}_{n=1}\) Bⁿ is Equal to 

Let α,β be the roots of the quadratic equation  x²+√6x+3=0. Then  \(\frac{α^23+β^23 + α ^14 + β ^14 }{α ^15 + β ^15 + α 160 + β ^{10}}\)  is equal to

Let D be the domain of the function f(x)=sin⁻¹(\( log_{3 x} (\frac{6+2log_3x}{−5x}\))) If the range of the function g : D → R defined by g ( x ) = x − [ x ] is the greatest integer function), is ( α , β ) , then α ² +\(\frac{ 5}{ β}\) is equal to 

If the line \(l_1 : 3y - 2x = 3\) is the angular bisector of the lines \(l_2 : x - y + 1 = 0\) and \(l_3\) : \(αx + βy + 17 = 0\), then \(α^2 + β^2  - α - β\) is equal to__

Let \(\overrightarrow a=\overrightarrow i+2\overrightarrow j+3 \overrightarrow k\) and \(\overrightarrow b= \overrightarrow i+ \overrightarrow j - \overrightarrow k\) . If \(\overrightarrow c\) is a vector such that \(\overrightarrow a. \overrightarrow c=11,\overrightarrow b.(\overrightarrow a.\overrightarrow c)=27\) and \(\overrightarrow b. \overrightarrow c=-\sqrt{3}|b|,\)  then \(|\overrightarrow a \times \overrightarrow c|^2\) is equal to _______ .

Let the probability of getting head for a biased coin be \(\frac{1}{4}\) . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation \(64x² + 5Nx + 1 = 0\) has no real root is \(\frac{p}{q}\) , where p and q are co-prime, then q – p is equal to _______.

Let the line / : x = \(\frac{1-y}{2}=\frac{z-3}{\lambda}, \lambda \in R\) meet the plane P : x+2y +3z = 4 at the point \((\alpha, \beta, \lambda)\). If the angle between the line I and the plane P is \(cos^{-1}\bigg(\sqrt{\frac{5}{14}}\bigg)\) then \(\alpha+2\beta+6\lambda\) is equal to______.

Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6). Then the number of functions f: A→B satisfying f(1) + f(2) = f(4)-1 is equal to _________ .

If A is the area in the first quadrant enclosed by the curve \(C: 2x^2 – y + 1 = 0\), the tangent to C at the point (1, 3) and the line x + y = 1, then the value of 60A is ________