List of top Mathematics Questions

If the coefficient of x10 in the binomial expansion of 
\(\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}} + \frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}\)
is 5k.l, where l, k∈N and l is co-prime to 5, then k is equal to ___________.

If two straight lines whose direction cosines are given by the relations \(l + m – n = 0\), \(3l^2 + m^2 + cnl = 0\) are parallel, then the positive value of \(c\) is :
Five numbers, \(x_1, x_2, x_3, x_4, x_5\) are randomly selected from the numbers \(1, 2, 3\),….., \(18\) and are arranged in the increasing order \((x_1<x_2<x_3<x_4<x_5)\). The probability that \(x_2 = 7\) and \(x_4 = 11\) is:
Let \(\vec a=\hat i+\hat j−\hat k\) and \(\vec c=2\hat i−3\hat j+2\hat k\). Then the number of vectors \(\vec b\) such that \(\vec b×\vec c=\vec a\) and \(|\vec b|∈{1,2,…,10}\) is :

Let a triangle ABC be inscribed in the circle
\(x² - \sqrt2(x+y)+y² = 0\)
such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

Let S = {1, 2, 3, …, 2022}. Then the probability that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, is
Let A be a matrix of order 3×3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to ______.

Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to

The statement (p∧q) ⇒ (p∧r) is equivalent to :

The equation of a common tangent to the parabolas y = x2 and y = –(x – 2)2 is

The area enclosed by y2 = 8x and y = √2x that lies outside the triangle formed by \(y=√2x,x=1,y=2√2\), is equal to 

Let 
\(\vec{a}=α\hat{i}+\hat{j}−\hat{k}\ and\ \vec{b}=2\hat{i}+\hat{j}−α\hat{k},α>0\). 
If the projection of \(\vec{a}×\vec{b}\) on the vector \(−\hat{i}+2\hat{j}−2\hat{k}\) 
is 30, then α is equal to

The sum 1 + 2 ⋅ 3 + 3 ⋅ 32 + …. + 10 ⋅ 39 is equal to
If m and n respectively are the number of local maximum and local minimum points of the function
\(f(x)=∫_0 ^{x^2} \frac{t^2–5t+4}{2+et}dt\), then the ordered pair (m, n) is equal to
A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with

Let f be a real valued continuous function on [0, 1] and
\(f(x) = x + \int_{0}^{1} (x - t) f(t) \,dt\)
Then, which of the following points (x, y) lies on the curve y = f(x)?

Let the solution curve y = f(x) of the differential equation
\(\frac{dy}{dx} + \frac{xy}{x^2 - 1} = + \frac{ x^4+2x}{\sqrt{1 - x^2}}, \quad x \in (-1, 1)\) pass through the origin. Then
\(\int_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) \,dx\)is

\(f(x) =   \begin{cases}     \frac{sin(x-|x|)}{x-|x|}       & \quad {x \in(-2,-1) } \\     max{2x,3[|x|]},  & \quad \text{|x|<1}\\1 & \quad \text{,otherwise}  \end{cases}\) Where [t] denotes greatest integer t. If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, then the ordered pair (m, n) is
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
Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4} = 1, a>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6\sqrt3\). Then the eccentricity of the ellipse is

Let the hyperbola 
\(H:\frac{x^2}{a^2}−y^2=1\)
and the ellipse
 \(E:3x^2+4y^2=12\) 
be such that the length of latus rectum of H is equal to the length of latus rectum of E. If eH and eE are the eccentricities of H and E respectively, then the value of 
\(12 (e^{2}_H+e^{2}_E)\) is equal to _____ .

Let \(\hat a\) and \(\hat b\) be two unit vectors such that \(| (a+b)+2(a × b)|\) =\( 2\). If \(θ ∈ (0, π)\) is the angle between a and b, then among the statements: \((S1)\): \(2|a×b|=|a-b|\) \((S2)\): The projection of a on \((\hat a+\hat b)\) is \(\frac{1}{2}\)
The number of distinct real roots of the equation \(x^7 – 7x – 2 = 0\) is

The area of the smaller region enclosed by the curves y2 = 8x + 4 and
x2+y2+4√3x-4=0
is equal to

Let \(\overrightarrow a\) and \(\overrightarrow b\) be the vectors along the diagonals of a parallelogram having area \(2\sqrt2\). Let the angle between \(\overrightarrow a\) and \(\overrightarrow b\) be acute,\( |\overrightarrow a|=1\), and \(|\overrightarrow a⋅\overrightarrow b|=|\overrightarrow a×\overrightarrow b|\) If \(\overrightarrow c=2\sqrt2(\overrightarrow a×\overrightarrow b→)−2\overrightarrow b\) then an angle between\( \overrightarrow b\) and \(\overrightarrow c\) is