List of top Mathematics Questions

If \( \frac{a}{a_1} = \frac{b}{b_1} \), then the substitution used to solve the differential equation \(\frac{dy}{dx} = \frac{ax + by + c}{a_1x + b_1y + c_1} \) using separation of variables is:
If $f(f(0)) = 0$, where $f(x) = x^2 + ax + b$, $b \neq 0$, then $a + b =$
If \( b \) and \( c \) are non-zero real numbers, and \[ A = \begin{bmatrix} 1 & b & c \\ b & 2 & 3 \\ c & 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0 \end{bmatrix}, \] then \( \det(A + B) = \) ?
Suppose $P$ and $Q$ are the midpoints of the sides $AB$ and $BC$ of a triangle where $A(1, 3)$, $B(3, 7)$ and $C(7, 15)$ are vertices. Then the locus of $R$ satisfying $AC^2 + QR^2 = PR^2$ is
If f is a relation from set of positive real numbers to the set of positive real numbers defined by \(f(x) = 3x^2-2\) then f is
Suppose ABOC is a rhombus in the first quadrant with O being the origin. If the vertices B and C of \(\triangle ABC\) lie respectively on \(y=\frac{x}{\sqrt{3}}\) and \(y=0\), and the side BC passes through \((\frac{2}{3}, \frac{2}{3})\), then the midpoint of BC is
On the locus of the point \( P(x, y) \) equidistant from \( (3, 0) \) and \( (0, 4) \), if \( A \) and \( B \) are two points that satisfy \( 4x = 3y \) and \( x = y \) respectively, then the distance between A and B is:
If \( \cosh(x - \log 3) = \sinh x \), then \( x = \):
The equation of the line which is a normal to the curve \(3x^2-xy+y^2=3\) at \((1,1)\) is
If \( \frac{d}{dx} \left( \frac{x^2+1}{(x^2+5)(x^2+9)} \right) = \frac{2x(x^2+1)}{(x^2+5)(x^2+9)} \left[ \frac{1}{f(x)} - \frac{1}{g(x)} - \frac{1}{h(x)} \right] \), then \( 2h(x)-f(x)-g(x) = \)
If $ \sin \theta = -\frac{3}{4} $, then compute $ \sin 2\theta $
For two events $A$ and $B$, a true statement among the following is
For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), the locus of the point of intersection of the tangents at the endpoints of normal chords is:
\( \int \frac{dx}{(1+\sqrt{x})^{2022}} = \)
There are 4 hotels in a town. If 3 men check into the hotels in a day, what is the probability that each checks into a different hotel?
If \( \sin\left(x + \frac{\pi}{3}\right) + \sin\left(x - \frac{\pi}{3}\right) = 1 \), then the value of \( x \) in the interval \( [0, \pi] \) is:
If \( y = \tan(3\tan^{-1} x) \), then: \[ (1 - 3x^2)\frac{d^2y}{dx^2} - 12x \frac{dy}{dx} = \]
The standard deviation of first 10 multiples of 4 is
Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$
If $\cosech\,x = \dfrac{4}{5}$, then $\sinh x = $ ?
In an exam:
- Three subjects have maximum marks = $ n $ each
- Fourth subject has max marks = $ 2n $
- Find the number of ways to score total $ 3n $ marks.
\(\tanh(\log x) = \) (Assuming \(\log x\) is natural logarithm \(\ln x\))
If $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
If the lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the x-axis, which of the following is in general incorrect
Find the locus of the point of intersection of tangents drawn at the ends of a **normal chord** of the hyperbola: $$ x^2 - y^2 = a^2 $$