List of top Mathematics Questions

The value of \( k \) for which the pair of linear equations
\( (k+1)x + 2y = 15, \quad 4y = 3x - 8 \) has no solution, is:
Let \( f(x) = 10x^2 + e^x - \sin(2x) - \cos x \), \( x \in \mathbb{R} \). The number of points at which the function \( f \) has a local minimum is:
The degree of differential equation \[ 9 \frac{d^2y}{dx^2} = \left\{ 1 + \left(\frac{dy}{dx}\right)^2 \right\}^{\tfrac{3}{2}} \] is
If \( y = x^{x^{x^{.... \text{ad inf}}}} \), then prove that \( x\frac{dy}{dx} = \frac{y^2}{1 - y \log x} \).
The value of $\cos 0^\circ$ will be:
Integrate: \( \int \left(\frac{2 + \sin 2x}{1 + \cos 2x}\right) e^x dx \)
If \( y = e^{\tan^{-1}x} \), prove that \( (1 + x^2)\frac{d^2y}{dx^2} + (2x - 1)\frac{dy}{dx} = 0 \).
The value of expression \( \hat{i} \cdot \hat{i} - \hat{j} \cdot \hat{j} + \hat{k} \times \hat{k} \) is
Find the principal value of \( \sec^{-1}(-\sqrt{2}) \).
Solve for \( a \) and \( b \) given the equations: \[ \sin x + \sin y = a, \quad \cos x + \cos y = b, \quad x + y = \frac{2\pi}{3} \]
If \( A \) is the set of odd numbers less than 6 and \( B \) is the set of prime factors of 30, then:
If \( A = \{1, 2, 3, 4, 5\} \) and \( B = \{1, 3, 5, 7\} \), then \( n(A \cap B) = \dots \):
The ratio of ages of Rahul and Neha is 3:4. After 5 years, the ratio becomes 4:5. What are their current ages?
The terms containing \( x^r y^s \) (for certain r and s) are present in both the expansions of \( (x+y^2)^{13} \) and \( (x^2+y)^{14} \). If \( \alpha \) is the number of such terms, then the sum \( \sum_{r,s} \alpha (r+s) = \) (Note: The sum is over the common terms)
Differentiate \( \tan^{-1}\left(\frac{\sin x}{1 + \cos x}\right) \) with respect to x.
If \( -5<x \leq -1 \), then \( -21 \leq 5x + 4 \leq b \). Find \( b \).
If \(a\), \(b\), and \(c\) are the roots of \( 2x^3 - 3x^2 + px - 1 = 0 \) and the sum of two roots is 1, the value of \(p\) is:
If the function f: N \(\rightarrow\) N, is defined by f(x) = x - 1 for all x > 2 and f(1) = f(2) = 1, then f is
If the roots of the equation $x^2+2(m-1)x+(m+5)=0$ are real and equal, find the value of $m$.
If \( \frac{5}{x+1} + \frac{1}{y-3} = 2 \) and \( \frac{6}{x+1} - \frac{3}{y-3} = 1 \), then \( x = \dots \):
If $A = \{x \in \mathbb{R} \mid \sin^{-1}(\sqrt{x^2+x+1}) \in [-\frac{\pi}{2}, \frac{\pi}{2}]\}$ and $B = \{y \in \mathbb{R} \mid y = \sin^{-1}(\sqrt{x^2+x+1}), x \in A\}$, then
If \( \alpha, \beta \) are the roots of \( 2x^2 - 4x + 5 = 0 \), then \( (\alpha + 1)(\beta + 1) = \):

The value of $\dfrac{1+\cot^2 \theta}{1+\tan^2 \theta}$ will be:
 

The number of positive integers less than 10000 which contain the digit 5 at least once is
Ram and Syam are friends. Probability that both will have same birthday is: