List of top Mathematics Questions

The value of $ \lim_{x \to \infty} \left( \frac{x^2 - 2x + 1}{x^2 - 4x + 2} \right)^{2x} \text{ is} $

If $$f(x) = \begin{cases} 2 \sin x & \text{for} \ -\pi \leq x \leq -\frac{\pi}{2}, a \sin x + b & \text{for} \ -\frac{\pi}{2}<x<\frac{\pi}{2}, \cos x & \text{for} \ \frac{\pi}{2} \leq x \leq \pi,\end{cases}$$and it is continuous on $[- \pi, \pi]$, then the values of $ a $ and $ b $ are:

The approximate value of $ f(5.001) $, $\text{where} $ $f(x) = x^3 - 7x^2 + 10 $

Let $ f(x) = a + \left( (x - 4) \right)^4 / 9 $, $\text{ then minima of } $ f(x) $\text{ is} $

The circle $x^2 + y^2 + 3x - y + 2 = 0$ cuts an intercept on X-axis of length
The points of intersection of circles $ (x + 1)^2 + y^2 = 4 \quad \text{and} \quad (x - 1)^2 + y^2 = 9 \quad \text{are} \quad (a, \pm b), \quad \text{then} \quad (a, b) \quad \text{equals to} $
The value of $ \lim_{x \to 0} \frac{e^{ax} - e^{bx}}{2x} \text{ is equal to} $
The slope of the tangent to the curve, $ y = x^2 - xy $ at $ (1, \frac{1}{2}) $ is
The value of $a^{\log_b c} - c^{\log_b a}$, where $a, b, c>0$ but $a, b, c \neq 1$, is

Let the number  \((22)^{2022}\) + \((2022)^{22}\)  leave the remainder \( \alpha \) when divided by 3 and \( \beta \) when divided by 7. Then \( (\alpha^2 + \beta^2) \) is equal to:}

If \( S_n = 4 + 11 + 21 + 34 + 50 + \dots \) to \( n \) terms, then \( \frac{1}{60} (S_{29} - S_9) \) is equal to:
Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=12^4$ Then $\mid A ^{-1}$ adj $A \mid$ is equal to
B is three times a old as A. After 5 years the ratio in the ages of A and B will be 1: 2. After how many years from now will the ratio in the ages of A and B become 2:3?
The number of solutions of the equation \( \dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}\) is 
Let the system of linear equations $ x+y+ kz =2$ $ 2 x+3 y-z=1 $ $ 3 x+4 y +2 z= k$ have infinitely many solutions Then the system $ ( k +1) x+(2 k -1) y=7$ $ (2 k +1) x+( k +5) y=10$ has:
If the sum and product of the roots of the quadratic equation \(kx^2+6x+4k=0\) are equal, then the value of k is
If the LCM of 12 and 42 is 10m + 4, then the value of m is
Which of the following is not a quadratic equation?
After how many decimal places, the decimal expansion of the rational number \(\frac{25}{2^2\times 5}\) will terminate?
The number of zeroes of the polynomial shown in the graph is
number of zeroes of the polynomial
If the lengths of the diagonals of a rhombus are 24 cm and 10 cm, then each side of the rhombus is

If \(\int_{0}^{3} (3x^2-4x+2) \,dx = k,\) then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is

If order and degree of the differential equation corresponding to the family of curves y2 = 4a(x+a)(a is parameter) are m and n respectively, then m+n2 =

If the solution of the differential equation \(\frac{dy}{dx}=\frac{2x+3y}{3x-2y}\) is y = xtan(f(x)) + c then f(x) =

The general solution of the differential equation (x2 + 2)dy +2xydx = ex(x2+2)dx is