List of top Mathematics Questions

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of \(A∩B\) is ___________

2sin(\(\frac{\pi}{22}\))sin(\(\frac{3\pi}{22}\))sin(\(\frac{5\pi}{22}\))sin(\(\frac{7\pi}{22}\))sin(\(\frac{9\pi}{22}\)) is equal to

The number of matrices
\(A=\begin{pmatrix}   a & b \\   c & d \\ \end{pmatrix}\), where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A-1, is ______.

If the sum of solutions of the system of equations 2sin2θ – cos2θ = 0 and 2cos2θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

Let
\(A = \{z \in \mathbb{C} : |\frac{z+1}{z-1}| < 1\}\)
and
\(B = \{z \in \mathbb{C} : \text{arg}(\frac{z-1}{z+1}) = \frac{2\pi}{3}\}\)
Then \(A∩B\) is :

The sum of all the solutions of the equation \( \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} \), for \( \theta \in [0, 6\pi] \) is:

The number of functions f, from the set
\(A = {x∈N: x^2-10x+9≤0} \)to the set \(B = {n62:n∈N}\)
such that
\(f(x)≤(x-3)^2+1\), for every \(x∈A,\)
is ______.

\(\int\limits_{0}^1\frac{xe^x}{(2+x)^3}\ dx\) is equal to

The number of distinct real roots of the equation x5(x3 – x2 – x + 1) + x (3x3 – 4x2 – 2x + 4) – 1 = 0 is ______ .

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x – y = 3, respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true?

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
If \(\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}\), where \(\alpha, \beta, \gamma \in \mathbb{R}\) then which of the following is NOT correct?

\(\begin{array}{l} I_n\left(x\right)=\int_0^x\frac{1}{\left(t^2+5\right)^n}dt, n=1, 2, 3,\cdots\end{array}\)

Then

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 \(x(t)=2\sqrt2costsin\sqrt2t \) and \(y(t)=2\sqrt2sintsin\sqrt2t\) ,\(t ∈(0,\frac{π}{2})\)
 Then \(\frac{1+(\frac{dy}{dx})^2}{\frac{d^2y}{dx^2}}\) at \(t=\frac{π}{4}\) is equal to
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 p and q be two real numbers such that p + q = 3 and p4 + q4 = 369. Then
\((\frac{1}{p} + \frac{1}{q} )^{-2}\)
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
If the function
\(f(x) =   \begin{cases}    \frac {log_e(1−x+x^2)+log_e(1+x+x_2)}{sec⁡\ x−cos⁡\ x},      & \quad x∈(−\frac \pi2,\frac \pi2)−{0}\\     k,  & \quad x=0   \end{cases}\)
is continuous at \(x = 0\), then k is equal to
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\( A(1, 1), B(-4, 3) \)and \(C(-2, -5)\) be vertices of a triangle ABC, P be a point on side BC, and \(Δ1\) and \(Δ2\) be the areas of triangles APB and ABC, respectively. If \(Δ1 : Δ2 = 4 : 7\), then the area enclosed by the lines AP, AC and the x-axis is
A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3g is equal to ______.
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