List of top Mathematics Questions

Let $ [t] $ represent the greatest integer not exceeding $ t $. The number of discontinuous points of $ [10^t] $ in $ (0, 10) $ is:
If \( f(x) \) is defined as follows:

\[ f(x) = \begin{cases} \frac{x - \lfloor x \rfloor}{x - 2} & \text{if } x = 2 \\ \frac{|x - \lfloor x \rfloor|}{a^2 + (x - \lfloor x \rfloor)^2} & \text{if } 1 < x < 2 \\ 2a - b & \text{if } x = 1 \end{cases} \]

Then the limit \( \displaystyle \lim_{x \to 0} \frac{\sin(ax) + x \tan(bx)}{x^2} \) is:
Consider the following statements (A) and (B): \[ \text{(A):} \quad \int_a^b \frac{d}{dx} \left( f(x) \right) dx = \frac{d}{dx} \int_a^b f(x) dx \] \[ \text{(B):} \quad \frac{d}{dx} \left( \int f(x) dx \right) = f(x) + C \] Which one of the following is True?
The area (in square units) bounded by the curves \( x^2 = 9y \), \( (x - 6)^2 = 9y \), and the X-axis is:
If the circles $x^2+y^2 - 4x + 2fy + 1 = 0$ and $x^2+y^2 + 2gx - 4y - 1 = 0$ cut orthogonally, then $r_1^2 + r_2^2 - 8=$
If \(x_1, x_2, \ldots, x_n\) are 'n' observations and \(\bar{x}\) is their mean. If \[ \sum_{i=1}^{n}(x_i - \bar{x})^2 \text{ is almost zero, then a true statement among the following is} \]
If two angles \( \alpha, \beta \) are such that \( 0<\alpha, \beta<\frac{\pi}{4} \), \( \sqrt{1 + \cos 2\alpha} = \frac{3}{\sqrt{5}} \) and \( \frac{\sqrt{1 - \cos 2\beta}}{\sqrt{1 + \cos 2\beta}} = \frac{1}{7} \), then \( (2\alpha + \beta) = \)
If $ z_1 = 2 + 3i $, $ z_2 = 4 - 5i $, and $ z_3 $ are three points in the Argand plane such that $ 5z_1 + xz_2 + yz_3 = 0 $ (where $ x, y \in \mathbb{R} $) and $ z_3 $ is the midpoint of the line segment joining the points $ z_1 $ and $ z_2 $, then find $ x + y $.
In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)
Let \([ \cdot ]\) denote the greatest integer function.
Assertion (A): \(\lim_{x \to \infty} \frac{[x]}{x} = 1\)
Reason (R): \(f(x) = x - 1\), \(g(x) = [x]\), \(h(x) = x\) and \(\lim_{x \to \infty} \frac{f(x)}{x} = \lim_{x \to \infty} \frac{h(x)}{x} = 1\):
If a Bernoulli trial is conducted n times, then which one of the following is not suitable to use Poisson distribution?
Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is

The period of function f(x) = \(e^{log(sinx)}+(tanx)^3 - cosec(3x - 5)\)is

If R -(α,β) is the range of  \(\frac{x+3}{(x-1)(x+2)}\) then the sum of the intercepts of the line ax + βy + 1 = 0 on the coordinate axes is:

The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is

If f(x) is a function such that f(x+y) = f(x)+ f(y) and f(1) = 7 then  \( \sum_{r=1}^{n}\) f(r) = 

If Xn = cos \(\frac{ π}{2^n}\) + i sin\(\frac{ π}{2^n}\) , then 

\[\prod_{n=1}^{\infty} x_n =\]

 

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

A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is

If ∫(log x)3 x5 dx = \(\frac{x^6}{A}\) [B(log x)3 + C(logx)2 + D(log x) - 1] + k and A,B,C,D are integers, then A - (B+C+D) = 

If $ i = \sqrt{-1} $ then  $\text{Arg}\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right]=$

The quadratic equation whose roots are 

\(l = \lim_{\theta\to0} \frac{3sin\theta - 4sin^3\theta}{\theta}\)

m = \(\lim_{\theta\to0} \frac{2tan\theta}{\theta(1-tan^2\theta)}\) is

If A is a square matrix of order 3, then |Adj(Adj A2)| =

If y = \(\frac{3}{4} + \frac{3.5}{4.8}+\frac{5.5.7}{4.8.12}+ \).... to ∞, then

Let $ X = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \middle| a, b, c, d \in \mathbb{R} \right\} $. If $ f: X \to \mathbb{R} $ is defined by $ f(A) = \det(A) $ for all $ A \in X $, then $ f $ is