List of top Mathematics Questions

\(\int\limits_{0}^1\frac{xe^x}{(2+x)^3}\ dx\) is equal to
Let 
\(\begin{array}{l} f\left(x\right)=3^{\left(x^2-2\right)^3+4},x\in \mathbb{R}.\end{array}\)
Then which of the following statements are true? 
P : x = 0 is a point of local minima of f
Q : x = √2 is a point of inflection of f 
R : f ′ is increasing for x > √2

Let the abscissae of the two points P and Q on a circle be the roots of x2 – 4x – 6 = 0 and the ordinates of P and Q be the roots of y2 + 2y – 7 = 0. If PQ is a diameter of the circle x2 + y2 + 2ax + 2by + c = 0, then the value of (a + b – c) is

Let \(x_1, x_2, x_3, …, x_{20}\) be in geometric progression with \(x_1 = 3\) and the common ratio 1/2. A new data is constructed replacing each \(x_i \) by \((x_i – i)^2\). If \(x̄\) is the mean of new data, then the greatest integer less than or equal to \(x̄\) is _________
The series of positive multiples of 3 is divided into sets: {3}, {6, 9, 12}, {15, 18, 21, 24, 27},…… Then the sum of the elements in the 11th set is equal to ________.
Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < \(\frac{x}{2}\) ≤ 3}. Then A∩B is equal to
Let the system of linear equations
x + y + az = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x*, y*, z*). If (α, x*), (y*, α) and (x*, –y*) are collinear points, then the sum of absolute values of all possible values of α is
A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is \(\frac1{n}\). If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 is:
Let \((a_n)^∞_{n=0}\) be a sequence such that a0=a1=0 and \(a_{n+2}=2a_{n+1}−a_n+1\) for all n⩾0. Then, \(∑^∞_{n=2} \frac{a_n}{7^n}\) is equal to
Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it The number of females qualifying the exam is twice the number of males qualifying it A candidate is randomly chosen from the qualified candidates The probability, that the chosen candidate is a female, is :

If the standard deviation of first n natural numbers is 2, then the value of n is

The odd natural number a, such that the area of the region bounded by \(y = 1, y = 3, x = 0, x = y^a\) is \(\frac {364}{3}\), is equal to
The sum 1 + 2 ⋅ 3 + 3 ⋅ 32 + …. + 10 ⋅ 39 is equal to

The principal solutions of tan 3θ = –1 are

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈  S × S is _____.
If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x – x2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is:
The value of \(cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})\) is equal to:

Let \(S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}\) .
Then\(n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)\)is equal to :

The number of elements in the set S= {x∈R : 2cos⁡\((\frac{x_2+x}{6})\)=\(4^x+4^{-x}\)}
If $M=\begin{pmatrix}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$, then which of the following matrices is equal to $M^{2022}$ ?
Let \(\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}\), where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is

Let p and p + 2 be prime numbers and let
 \(Δ=\begin{vmatrix} p! & (p+1)! & (p+2)! \\ (p+1)! & (p+2)! & (p+3)! \\ (p+2)! & (p+3)! & (p+4)! \\ \end{vmatrix}\)
Then the sum of the maximum values of α and β, such that pα and (p + 2)β divide Δ, is _______.

If 
\(f(x) = \begin{cases}     x + a, & x \leq 0 \\     |x - 4|, &  x > 0 \end{cases}\) and \(g(x) = \begin{cases}     x + 1, & x < 0 \\     (x - 4)^2 + b, &  x \geq 0 \end{cases}\)
 are continuous on R, then (gof) (2) + (fog) (–2) is equal to

If for p ≠ q ≠ 0, the function
\(f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}\)
is continuous at x = 0, then

The three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle is