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List of top Mathematics Questions

Let $ F(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix} $, where $ \alpha \in \mathbb{R} $. Then $ [F(\alpha)]^{-1} $ is equal to:

Let $ p: $ I am brave, $ q: $ I will climb the Mount Everest. The symbolic form of a statement, 'I am neither brave nor I will climb the Mount Everest' is:

If $ f(x) $ is differentiable at $ x = 1 $ and \[ \lim_{h \to 0} \frac{1}{h} f(1 + h) = 5, \] then $ f'(1) $ is equal to:

If the curve $y^2 = 6x$ and $9x^2 + by^2 = 16$ intersect each other at right angles, then the value of $b$ is:

Evaluate $ i^2 + i^3 + \dots + i^{4000} $:

Evaluate the following limit: \[ \lim_{\theta \to -\frac{\pi}{4}} \frac{\cos\theta + \sin\theta}{\theta + \frac{\pi}{4}}. \]

The value of the integral $ \int_0^2 |2x - 3| \, dx $ is:

Mohan caught 100 frogs from a garden and measured their weights. The mean weight of these frogs is a :

Which of the following are components of a time series?(A) Irregular component
(B) Cyclical component
(C) Chronological component
(D) Trend Component
Choose the correct answer from the options given below:

An equilateral triangle of side $ 4\sqrt{3} $ cm formed out of a sheet is converted into a rectangle such that there is no loss of the area of the triangle. Then the least perimeter of the rectangle (in cm) will be:

The rate of change (in cm2/s) of the total surface area of a hemisphere with respect to the radius r at r = 3.

The function f(x) = |x| + |1 − x| is:

The integral of the function $ \frac{1}{9 - 4x^2} $ is:

A firm anticipates an expenditure of ₹10,000 for a new equipment at the end of 5 years from now. How much should the firm deposit at the end of each quarter into a sinking fund earning interest 10% per year compounded quarterly to provide for the purchase?
[Use (1.025)²⁰=1.7]

If $ y = e^{{2}\log_e t} $ and $ x = \log_3(e^{t^2}) $, then $ \frac{dy}{dx} $ is equal to:

Which of the following cannot be the direction ratios of the straight line $\frac{x - 3}{2} = \frac{2 - y}{3} = \frac{z + 4}{-1}$?

Subject to constraints: 2x + 4y ≤ 8, 3x + y ≤ 6, x + y ≤ 4, x, y ≥ 0; The maximum value of Z = 3x + 15y is:

The value of $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \tan^{18}x}$ is:

If \[ y = \frac{1}{\sqrt{1 - 4 \sin^2 x \cos^2 x}}, \] then $\frac{dy}{dx}$ is:

A flower vase costs 36,000. With an annual depreciation of 2,000, its cost will be 6,000 in how many years?

Match List-I with List-II:

List-I	List-II
The derivative of $ \log_e x $ with respect to $ \frac{1}{x} $ at $ x = 5 $ is	(I) -5
If $ x^3 + x^2y + xy^2 - 21x = 0 $, then $ \frac{dy}{dx} $ at $ (1, 1) $ is	(II) -6
If $ f(x) = x^3 \log_e \frac{1}{x} $, then $ f'(1) + f''(1) $ is	(III) 5
If $ y = f(x^2) $ and $ f'(x) = e^{\sqrt{x}} $, then $ \frac{dy}{dx} $ at $ x = 0 $ is	(IV) 0

Choose the correct answer from the options given below :

The area of the region bounded by the lines $ \frac{x}{7\sqrt{3a}} + \frac{y}{b} = 4 $, $ x = 0 $, and $ y = 0 $ is:

The area (in square units) of the region bounded by curves $ y = x $ and $ y = x^3 $ is:

A random variable X has the following probability distribution:

X	-2	-1	0	1	2
P(X)	0.2	0.1	0.3	0.2	0.2

The variance of X will be:

The particular solution of the differential equation $(y - x^2) dy = (1 - x^3) dx$ with $y(0) = 1$, is:

List-I	List-II
The derivative of \( \log_e x \) with respect to \( \frac{1}{x} \) at \( x = 5 \) is	(I) -5
If \( x^3 + x^2y + xy^2 - 21x = 0 \), then \( \frac{dy}{dx} \) at \( (1, 1) \) is	(II) -6
If \( f(x) = x^3 \log_e \frac{1}{x} \), then \( f'(1) + f''(1) \) is	(III) 5
If \( y = f(x^2) \) and \( f'(x) = e^{\sqrt{x}} \), then \( \frac{dy}{dx} \) at \( x = 0 \) is	(IV) 0