List of top Mathematics Questions

Let \( f(x) = |x| \) and \( g(x) = |x| + a \), \( (a>0) \). For \( 0 \le x \le b \), \( \{(x, y) / g(x) \le y \le f(x)\} \) represents all the points in the interior of
If a real valued function \( f \) is defined by \( f(x) = \frac{ax + \sqrt{a^2 - x^2}}{bx} \), then \( f \) is:
If \( f(n) = n!(31-n)! \), where \( n \in \{ 0, 1, 2, \dots, 31 \} \), then the minimum value of \( f(n) \) is:
The range of the real valued function \( f(x) = \sqrt{9 - x^2} \) is:
The domain of the function $ y = f(x) $, where $ x $ and $ y $ are related by $ 2^x + 2^y = 2 $, is:
The range of the function $ f(x) = \begin{cases} 4x - 1, & x>3 \\ x^2 - 2, & -2 \leq x \leq 3 \\ 3x + 4, & x<-2 \end{cases} $ is:
Let \( x \) be a real number and \( -2<x<2 \). When \( \frac{x+1}{(x+3)(x-2)} \) is expanded in powers of \( x \), then the coefficient of \( x^3 \) is:
If $f(g(x+y)) = f(g(x)) + f(g(y))$, $g(1)=2$, $f(2)=1$, then $g(f(x))$ is discontinuous on:
If \( f(x) = \sqrt{x} + \sin x \), then all the points of the set \( \left( x, f(x) \right)/f'(x) = 0 \) lie on:
If \( f(x) \) is the signum function, then in terms of \( f(x) \), the constant function \( g(x)=1, \ \forall x \in \mathbb{R} \) is:
Match the ranges of the functions given in List - A with those of the items given in List - B.
Match the ranges of the functions given
If $ \sin x \cosh y = \cos \theta $ and $ \cos x \sinh y = \sin \theta $, then find $ \sin^2 x + \cosh^2 y $.
If \( \frac{dy}{dx} = f(x,y) \) is a homogeneous differential equation, then the general form of \( f(x,y) \) is:
If \( I = \int_{-a}^{a} \left( x^4 - 2x^2 \right) \, dx \), then \( I \) is minimum at \( a = \):
Which one of the following is a linear differential equation?
The degree of the differential equation $\log \left( \frac{dy}{dx} \right) = \left( 2x + 3 \frac{dy}{dx} \right)^2$ is
The order and degree of the differential equation \[ \frac{d^3 y}{dx^3} + 2 \left( \frac{d^2 y}{dx^2} \right) + xy = 0 \] are respectively:
If \( c \) and \( d \) are arbitrary constants, then \[ y = e^{2x} \left( \cosh \sqrt{2} x + d \sinh \sqrt{2} x \right) \] is the general solution of the differential equation:
The integrating factor of the linear differential equation \( \frac{dy}{dx} = \frac{1}{4x + 3y} \) is
If \( f(x) \) is a function such that \( f'(x) = \sqrt{f^2(x) - 1} \) and \( f(0) = 1 \), then \( f(1) = \):
If \( y = y(x) \) is the solution of \( \frac{dy}{dx} = \frac{x - y \cos x}{1 + \sin x} \), \( y\left(\frac{\pi}{2}\right) = \frac{\pi^2}{8} \), then \( y(\pi) = \)
The substitution \( x = vy \) converts which one of the following differential equations to an equation solvable by the variable separable method?
The order and degree of the differential equation \[ 3x^2 \frac{d^2 y}{dx^2} - \sin\left( \frac{d^3 y}{dx^3} \right) + \cos(xy) = 0 \] are:
Let $ a $ and $ b $ be arbitrary constants and $ C $ be a fixed constant. If $ y = ae^{2x} + bxe^{2x} + C $ is the general solution of a differential equation, then the order of that differential equation is:
If $\log y$ is an integrating factor of $\frac{dx}{dy}+P(y)x=Q(y)$, then $P(y)=$