List of top Mathematics Questions

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 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 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
For n ∈ N let \(S_n\)={z∈C:|z−3+2i|=\(\frac{n}{4}\)} and \(T_n\)={z ∈ C:|z−2+3i|=\(\frac{1}{n}\)}.Then the number of elements in the set

The number of q∈ (0, 4π) for which the system of linear equations
3(sin 3θ) x – y + z = 2
3(cos 2θ) x + 4y + 3z = 3
6x + 7y + 7z = 9
has no solution, 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
\(f(x) =   \begin{cases}     \frac{sin(x-|x|)}{x-|x|}       & \quad {x \in(-2,-1) } \\     max{2x,3[|x|]},  & \quad \text{|x|<1}\\1 & \quad \text{,otherwise}  \end{cases}\) 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 a circle C touch the lines L1 : 4x – 3y +K1 = 0 and L2 : 4x – 3y + K2 = 0, K1, K2∈R. If a line passing through the centre of the circle C intersects L1 at (–1, 2) and L2 at (3, –6), then the equation of the circle C is :

The curve y(x) = ax3 + bx2 + cx + 5 touches the x-axis at the point P(–2, 0) and cuts the y-axis at the point Q, where y′ is equal to 3. Then the local maximum value of y(x) is

 The area of the region given by A={(x,y); \(x^2\)≤y≤min{x+2,4−3x}} is
Let \(ƒ : R→R\) be defined as \(ƒ(x) = x^3 + x – 5\) . If g(x) is a function such that \(ƒ(g(x)) = x\), ∀‘x‘∈R. Then \(g^′(63)\) is equal to_____.
The slope of the tangent to a curve C: y = y(x) at any point (x, y) on it is \(\frac{2e^{2x}-6e^{-x}+9}{2+9e^{-2x}}\).If C passes through the points (0,\(\frac{1}{2}\)+\(\frac{\pi}{2\sqrt2}\)) and (α,\(\frac{1}{2e^{2\alpha}}\)), then eα is equal to
A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is \(\frac{\sqrt{29}}{3}\) then B also lies on the line :

Let the locus of the centre (α, β), β> 0, of the circle which touches the circle x2 +(y – 1)2 = 1 externally and also touches the x-axis be L. Then the area bounded by L and the line y = 4 is :

Consider the following two propositions:
\(P_1 : ~ (p → ~ q)\)
\(P_2: (p ∧ ~q) ∧ ((-~p) ∨ q)\)
If the proposition \(p → ((~p) ∨ q)\) is evaluated as FALSE, then:
If \(\frac {1}{2⋅3^{10}}+\frac {1}{2^2⋅3^9}+⋯+\frac {1}{2^{10}⋅3} = \frac {K}{2^{10}⋅3^{10}}.\) Then the remainder when \(K\) is divided by \(6\) is:
Let \(ƒ(x)\) be a polynomial function such that \(ƒ(x) + ƒ^′(x) + ƒ^{′′}(x) = x^5 + 64\). Then, the value of \(\lim\limits_{x \to 1}\frac {f(x)}{x−1}\) is equal to :
Let ABC be a triangle such that \(\vec{BC}\)=\(\vec a\),\(\vec{CA} \)=\(\vec b\),\(\vec AB\)=\(\vec c\),|\(\vec a\)|=6\(\sqrt2\),|\(\vec b\)|=2\(\sqrt3\) and \(\vec b\)⋅\(\vec c\)=12 Consider the statements:
(S1):|(\(\vec a\)×\(\vec b\))+(\(\vec c\)×\(\vec d\))|−|\(\vec c\)|=6(2\(\sqrt2\)−1)
(S2):\(\angle\)ACB=cos−1⁡(\(\sqrt{\frac{2}{3}}\))
Then

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

 If the numbers appeared on the two throws of a fair six faced die are α and β, then the probability that x2 + αx + β> 0, for all x ∈ R, is :

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

The area of the polygon, whose vertices are the non-real roots of the equation \(\bar z = iz^2\) is