List of top Mathematics Questions

For any two nonzero real numbers $a$ and $b$, if the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ is a tangent to the circle $x^2 + y^2 = 1$, then which of the following is true?
Evaluate: $$ \int \frac{dx}{(x - 3)^{4/5} (x + 1)^{6/5}} = ? $$
For the differential equation \( \frac{d^3 y}{dx^3} = 0 \), \( y = ax^2 + bx + c \) is:
There are 10 points in a plane, out of which 6 are collinear. If $ N $ is the number of triangles that can be formed, then $ N = $ ?
The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(16, 0.25)$ and $Y \sim P(2)$. Then the sum of the variances of $X$ and $Y$ is
During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6. The probability that in a given week there will be exactly two days with severe fog is
If \( A \) and \( B \) are two independent events such that \( P(A) = 0.3 \), \( P(B) = x \), and \( P(A \cup B) = 0.44 \), then \( x = \):
Let $\vec{a} = xi + yj + zk$ and $x = 2y$. If $|\vec{a}| = 5\sqrt{2}$ and $\vec{a}$ makes an angle of $135^\circ$ with the z-axis then $\vec{a} =$
Sides passing through vertex $ (\alpha, \beta) $ of a triangle are bisected at right angles by the lines: $$ y^2 - 8xy - ax^2 = 0 $$ Find the coordinates of the centroid of the triangle.
If $ a, b>0 $, then the minimum value of: $$ y = \frac{b^2}{a - x} + \frac{a^2}{x},\quad \text{for } 0<x<a $$
If variance of a Poisson distribution is 3, find: \[ P(1<X<4) \]
Find the distance between the directrices of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{20} = 1 \]
The pairs of straight lines \( 2x^2 + axy + 3y^2 = 0 \) and \( 2x^2 + bxy - 3y^2 = 0 \) share a common line, and the other lines are perpendicular. Then values of \( a \) and \( b \) are?
If $$ ^{10}C_2 = ^{3^{n+1}}C_3 $$ then the value of $ n $ is:
In any triangle $ ABC $, evaluate: $$ \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} $$
The maximum value of the variance of a Binomial distribution with parameters \( n \) and \( p \) is:
The sum of the real roots of the equation: $$ x^4 - 2x^3 + x - 380 = 0 $$ is:

\(\lim_{{x \to \frac{1}{\sqrt{2}}}} \frac{\sin(\cos^{-1}(x)) - x}{1 - \tan(\cos^{-1}(x))}\)
is equal to : 

Let 
\(S=\left\{x∈[-6,3]-\left\{-2,2 \right\} :\frac{|x+3|-1}{|x|-2}>=0 \right\} \space and \space \left\{T={x∈Z:x^2-7|x|+9<=0}\right\}\)
Then the number of elements in S ⋂ T is

g :R→R be two real valued functions defined as
\(f(x) = \begin{cases}        -|x + 3| &  x < 0 \\       e^x, & x \geq 0  \end{cases}\)
and
\(g(x) = \begin{cases}        x^2 + k_1x ,&  x < 0 \\       4x + k_2 ,&  x \geq 0  \end{cases}\)
where k1 and k2 are real constants. If (goƒ) is differentiable at x = 0, then (goƒ) (–4) + (goƒ) (4) is
equal to:

If a point \(A(x, y)\) lies in the region bounded by the \(y\)-axis, straight lines  \(2y + x = 6\) and \(5x – 6y = 30\), then the probability that \(y < 1\) is

Let S be the set of all the natural numbers, for which the line 
\(\frac{x}{a}+\frac{y}{b}=2 \)
is a tangent to the curve
\((\frac{x}{a})^n+(\frac{y}{b})^n=2 \)
at the point (a, b), ab ≠ 0. Then :

The mean and variance of the data \(4, 5, 6, 6, 7, 8, x, y\), where \(x<y\), are \(6\) and \(\frac{9}{4}\), respectively. Then \(x^4+y^2\) 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
Let \(α, β\) be the roots of the equation \(x^2-\sqrt{2}x+\sqrt{6}=0\) and\( \frac{1}{α^2}+1\),\(\frac {1}{β^2}+1\) be the roots of the equation \(x^2 + ax + b = 0\) . Then the roots of the equation \(x^2 – (a + b – 2)x + (a + b + 2) = 0\) are