List of practice Questions

In \( \triangle ABC \), \( DE \parallel BC \), if \( AD = x + 1 \), \( DB = 3x - 1 \), \( AE = x \), and \( EC = 4x - 3 \), then the value of \( x \) is:
Identify the correctly spelt words from the following:
(a) separate
(b) seperate
(c) receive
(d) inspite of
Select the correct answer from the following options:
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:
Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:
A Carnot engine operates between \( 500 \, \text{K} \) and \( 300 \, \text{K} \). If it absorbs \( 1000 \, \text{J} \) of heat from the source, the amount of work done by the engine is:
If \( z \) is a complex number such that \( |z| = 5 \) and \( \text{Re}(z) = 3 \), then the value of \( z^2 \) is:
Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?
If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:
If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:
If $a$ and $b$ are the roots of the equation $2x^2 + 5x + 30 = 0$, find the value of $a^2 + b^2$.
Find the distance between the points $ (2, 3) $ and $ (5, 7) $ in the Cartesian plane.
In which group of algae are food materials stored in pyrenoids?
Descending order of Indian States according to coal reserves is-
(a) Jharkhand (b) Odisha (c) Chhattisgarh (d) Madhya Pradesh (e) West Bengal
Consider an arithmetic progression where the sum of the first 5 terms is 85, and the sum of the next 5 terms is 235. Find the common difference of the AP.
A ball is thrown vertically upward with a speed of 20 m/s. How high will it rise before coming to rest momentarily? (Take g = 10 m/s2)
A body starts from rest and accelerates uniformly at 2 m/s\(^2\). What is the distance covered in 5 seconds?
A ball is thrown vertically upwards with a speed of 20 m/s. How high will it rise? (Take \( g = 10 \, \text{m/s}^2 \))
A force of 10 N acts on a 2 kg object initially at rest, moving it 8 m along a straight line. What is the work done by the force? Assume the force is parallel to the displacement.
The major product formed when 2-bromo-2-methylbutane is treated with alcoholic KOH is:
What is the normality of a solution containing 4.9 g of \( \text{H}_2\text{SO}_4 \) in 500 mL of solution? (Molar mass of \( \text{H}_2\text{SO}_4 \) = 98 g/mol)
If the roots of the equation \[ x^3 + p x^2 + q x + r = 0 \] are in arithmetic progression, then which of the following is always true?
A solid sphere of mass $M$ and radius $R$ is rotating about its diameter. What is its moment of inertia about the same axis?
The number of ATP and NADPH molecules required respectively to synthesize one molecule of glucose in C\(_3\) plants is: