List of top Mathematics Questions

For $t \in(0,2 \pi)$, if $ABC$ is an equilateral triangle with vertices$A ( \sin t, -{\cos t}), B ( \cos t, \sin t )$ and $C ( a , b )$ such that its orthocentre lies on a circle with centre $\left(1, \frac{1}{3}\right)$, then $\left(a^2-b^2\right)$ is equal to :
Let \(ABC\) be a triangle such that \(\overrightarrow{ BC }=\vec{ a }\), \(\overrightarrow{ CA }=\vec{ b }, \overrightarrow{ AB }=\vec{ c },|\vec{ a }|=6 \sqrt{2},|\vec{ b }|=2 \sqrt{3}\) and \(\vec{ b } \cdot \vec{ c }=12\) Consider the statements :\((S1): |(\vec{ a } \times \vec{ b })+(\vec{ c } \times \vec{ b })|-|\vec{ c }|=6(2 \sqrt{2}-1)\)\((S2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then
Let a, b ∈ R be such that the equation ax2 – 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x2 – 2bx + 21 = 0, then α2 + β2 is equal to

Let z1 and z2 be two complex numbers such that 

\(z_1=iz_2 \,and \,arg(\frac{z_1}{z_2})=π.\)

The system of equations

–kx + 3y – 14z = 25

–15x + 4y – kz = 3

–4x + y + 3z = 4

is consistent for all k in the set

\(lim(x→\frac{x}{2}) tan^2x((2sin^2x+3sinx+4)^{\frac{1}{2}}-(sin^2x+6sinx+2)^{\frac{1}{2}}\) is equal to.
The area of the region enclosed between the parabolas y2 = 2x – 1 and y2 = 4x – 3 is
The coefficient of x101 in the expression (5 + x)500 + x(5 + x)499 + x2(5 + x)498 + ……+ x500, x > 0, is
The sum 1 + 2 ⋅ 3 + 3 ⋅ 32 + …. + 10 ⋅ 39 is equal to

Let P be the plane passing through the intersection of the planes

r→.(i+3k−k)=5 and r→ .(2i−j+k)=3,

and the point (2, 1, –2). Let the position vectors of the points X and Y be

i−2j+4k and 5i−j+2k

respectively. Then the points

Choose the correct answer:

1. Let A = {x ∈ R : | x + 1 | < 2} and B = {x ∈ R : | x – 1| ≥ 2}. Then which one of the following statements is NOT true?

A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is
Water is being filled at the rate of 1 cm3/sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2/sec) at which the wet conical surface area of the vessel increase, is
If  \(b_n= ∫_0^{\frac{π}{2}} \frac{cos^2nx}{sinx }dx, n∈N,\) Then
Let \(x * y\) = \(x^2 + y^3\) and \((x * 1) * 1\) = \(x * (1 * 1)\). Then a value of \(2 sin^{-1}\bigg(\frac{x^4+x^2-2}{x^4+x^2+2}\bigg)\) is

If y = y(x) is the solution of the differential equation

\(2x^2\frac{dy}{dx}-2xy+3y^2=0\) such that \(y(e)=\frac{e}{3},\)

then y(1) is equal to

If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), 

\(y=12(1+sint)^2,0<t<\frac{π}{2}, \)

with the positive x-axis is π/3, then y0 is equal to

The value of 2 sin(12°) – sin(72°) 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:
The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to:
The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to:
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 \( tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} )\) is equal to:
The line y = x + 1 meets the ellipse \(\frac{x^2}{4}+\frac{y^2}{2}=1\) at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)2 is equal to
The total number of functions, f : {1, 2, 3, 4} \(\rightarrow\) {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to