List of practice Questions

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Let f_n = $\int\limits_0^{\pi/2}$ $\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)$ cosx dx, n ∈ N. Then f₂₁ – f₂₀ is equal to____.

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

The ratio of powers of two motors is $\frac{3\sqrt x}{\sqrt x+1}$, that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

The sum $\displaystyle\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

Choose that set of numbers from the four alternative sets, that is similar to the given set.Given set: (265, 392, 285)

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{B 1}$. Then the ratio of $\frac{C p}{C v}$ will be

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k , is equal to

When 0.01 mol of an organic compound containing 60% carbon was burnt completely, 4.4 g of $CO_2$ was produced. The molar mass of compound is _______ $gmol^{−1}$. (Nearest integer).

Which of the following body constituted under the Consumer Protection Act, 2019 is authorized to render advice on promotion and protection of consumers’ rights under the Act?

Find out the rank of MONDAY in English dictionary if all alphabets are arranged in order?

The vapour pressure vs. temperature curve for a solution solvent system is shown below.

The boiling point of the solvent is _____°C.

The faces of a solved Rubik’s Cube are shown in the figure. A 90 degree clock wise turn of a face T is denoted as ‘$T+$’ and 90 degree anticlockwise rotation is denoted as ‘$T –$‘. What is the result of the operation$T+, D+, R-, L-$? All operations are done looking directly at the face.

The remainder, when $19^{200}+23^{200}$ is divided by $49$ , is_______

For the following reaction:
N₂(g)+3H₂(g)⇌2NH₃ (g)
The free energy changes at 25°C and 35°C are-33.089 and-28.018 kJ respectively. The heat of the reaction is

Which of the following is an object on which general funds could be spent as per section 15 of the Trade Union Act, 1926?

A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5×10⁻⁴Ncm⁻¹. The radius of drop in cm will be : ( Take : g=10 m/s²)

Compound A with molecular formula (C₂H₆O) on oxidation by PCC gives compound B, which on treatment with dilute alkali forms compound C (a β-hydroxy aldehyde). B on oxidation by potassium permanganate forms C.
Identify A, B, C and D and write all the chemical equations involved.

A metallic sphere of radius 𝑅 is held at electrostatic potential 𝑉. It is enclosed in a concentric thin metallic shell of radius 2𝑅 at potential 2𝑉. If the potential at the distance $\frac{3}{2}$ 𝑅 from the centre of the sphere is 𝑓𝑉, then the value of 𝑓 is _______ (rounded off to two decimal places).

Let the area enclosed by the lines $ x + y = 2 $, $ y = 0 $, $ x = 0 $, and the curve $ f(x) = \min \left\{ x^2 + \frac{3}{4}, 1 + [x] \right\} $, where $ [x] $ denotes the greatest integer less than or equal to $ x $, be $ A $. Then the value of $ 12A $ is ____________.

Let $y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)$ Then, at $x=1$

If BAG = 10, HIT = 32, then CAT = ?

Let $ S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} $ be a sample space and $ A = \{ M \in S : M \text{ is invertible} \} $ be an event. Then $ P(A) $ is equal to: