List of top Mathematics Questions

Let \(f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)\) and \(S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}\). If \(4\beta \sum_{\theta∈S}\theta\), then \(f(\beta)\) is equal to
Consider the following system of equations
\(\alpha x + 2y + z = 1\)
\(2\alpha x + 3y + z = 1\)
\(3x + \alpha y + 2z = b\)
For some \(\alpha,\beta∈R\) then which of the following is NOT correct?
Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is
If p, q and r are three propositions, then which of the following combination of truth values of p, q and r makes the logical expression \({(p∨q)∧((∼p)∨r)}🡢((∼q)∨r)\) false?
If the vectors \(\overrightarrow{a} =\lambda \hat{i}+\mu\hat{j}+4\hat{k}\), \(\overrightarrow{b}=-2\hat{i}+4\hat{j}-2\hat{k}\) and \(\overrightarrow{c}=2\hat{i}+3\hat{j}+\hat{k}\) are coplanar and the projection of \(\overrightarrow{a}\) on the vector \(\overrightarrow{b}\) is \(\sqrt{54}\) units, then the sum of all possible values of \(\lambda + \mu\) is equal to
A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is
The domain of \(f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}\), \(x∈R\) is
Let \(y = f(x)\) be the solution of the differential equation \(y(x + 1)dx - x^2dy = 0\), \(y(1) = e\). Then \(lim_{x→0^-} f (x)\) is equal to
For two non-zero complex numbers z1 and z2, if Re(z1z2) = 0 and Re(z1 + z2), then which of the following are possible?
A. Im(z1) > 0 and Im(z2) > 0 |
B. Im(z1) < 0 and Im(z2) > 0 
C. Im(z1) > 0 and Im(z2) < 0 
D. Im(z1) < 0 and Im(z2) < 0 
Choose the correct answer from the options given below
Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ2 represent mean and variance of X, respectively, then 10(μ2+σ2) is equal to
Let a1, a2, a3, … be a G.P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a1 a9+a2 a4 a9+a5+a7 is equal to __________.
Let the equation of the plane P containing the line \(x+10=\frac{8-y}{2}=z\) be \(ax + by + 3z = 2(a + b)\) and the distance of the plane P from the point (1, 27, 7) be c. Then a2+b2+c2 is equal to ____________.
Let \(f : R → R\) be a differentiable function that satisfies the relation \(f(x + y) = f(x) + f(y) – 1, ∀x, y ∈R\). If \(f'(0) = 2\), then \(|f(–2)|\) is equal to ___________.
Let the co-ordinates of one vertex of \(\Delta ABC\) be \(A(0, 2, \alpha)\) and the other two vertices lie on the line \(x+\frac{\alpha}{5}=y-\frac{1}{2}=z+\frac{4}{3}\) For \(\alpha∈Z\), if the area of \(\Delta ABC\) is 21 sq. units and the line segment BC has length \(2\sqrt{21}\) units, then α2 is equal to ___________.
Let a b, and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be \(a-b+c\), \(λa-3b+4c\), \(-a+2b-3c\) and \(2a-4b+6c\) respectively. If AB AC , and AD are coplanar, then λ is equal to ____.
Let the coefficients of three consecutive terms in the binomial expansion of (1 + 2x)n be the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of these three terms, is _______.
Suppose f is a function satisfying \(f(x + y) + f(x) + f(y)\) for all \(x, y ∈N\) and \(f(1)=\frac{1}{5}\). If \(∑_{n=1}^{m} \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{2}\), then m is equal to _______.
If all the six digit numbers x1 x2 x3 x4 x5 x6 with \(0<x_1<x_2<x_3<x_4<x_5<x_6\) are arranged in the increasing order, then the sum of the digits in the 72th number is _____________.
If the co-efficient of x9 in \((αx^3+\frac{1}{βx})^{11}\) and the co-efficient of x-9 in \((αx-\frac{1}{βx^3})^{11}\) are equal, then \((αβ)^2\) is equal to ________.

Let α, β, γ be the three roots of the equation x3+bx+c=0. If βγ =1=-α, then b3+2c3-3α3-6β3-8γ3 is equal to

Let SK = \(\frac{1+2+...+ K}{K}\) and \(\displaystyle\sum_{j=1}^{n}S_j^2=\frac{n}{A}(Bn^2+Cn+D)\), where A,B,C,D∈N and A has least value. Then

Let \(I(x)=\int\frac{x+1}{x(1+xe^x)^2} dx\), x>0. If \(\lim\limits_{x\rightarrow\infin}I(x)=0\), then I(1) is equal to

The area of the region {(x,y): x2 ≤ y ≤8-x2, y≤7} is

Let C(α, β) be the circumcenter of the triangle formed by the lines
4x+3y=69,
4y-3x=17, and
x+7y=61.
Then (α-β)2+α+β is equal to

Let R be the focus of the parabola y2 = 20x and the line y=mx+c intersect the parabola at two points Pand Q. Let the point G(10,10) be the centroid of the triangle PQR. If c-m=6, then (PQ)2 is