List of practice Questions

The turning point of the function $ y = \frac{ax-b}{(x-1)(x-4)} $ at the point $ P(2, -1) $ is
Evaluate the following expression: $ \sqrt{2 + \sqrt{2} + \sqrt{2 + 2 \cos(2\theta)}} \quad \text{where} \quad \theta \in \left[ -\frac{\pi}{8}, \frac{\pi}{8} \right] $

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} \quad \text{and} \quad A \, \text{adj} \, A = A A^t, \quad \text{then} \, 5a + b \, \text{is equal to}$ 
 

Which of the following relations on the set of real numbers $ \mathbb{R} $ is an equivalence relation?
If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of 3 is:
With reference to Pauling's Electronegativity scale, which one of the following options shows the correct order of electronegativity values of elements?

The solution set for the inequality $ 13x - 5 \leq 15x + 4<7x + 12;  x \in W $

Which of the following two molecular species are Diamagnetic in nature?

Match the names of reactions given in Column I with the appropriate reactions given in Column II

What is the wave number (Units cm$^{-1}$) of the longest wavelength transition in the Balmer series of the Hydrogen spectrum? $ Z = 1 $ for $ H $

Based on Valence Bond Theory, match the complexes listed in Column I with the number of unpaired electrons on the central metal ion, given in Column II.

Identify the final product formed when Benzamide undergoes the following reactions:

Identify the correct statement regarding corrosion of iron rod left exposed to atmosphere.
Two statements, Assertion and Reason are given. Choose the correct option from the following.
Assertion: In the secondary structure of RNA, double helix structure is formed.
Reason: In the double structure of RNA, two nucleic acid chains are wound about each other and held together by hydrogen bonds between pairs of bases.

Identify the end-product $ [D] $ formed when solution salicylate undergoes the following series of reactions.

For a given reaction, $ X(g) + Y(g) \to Z(g) $, the order of reaction with respect to $ X $ and $ Y $ are $ m $ and $ n $ respectively. If the concentration of $ X $ is tripled and that of $ Y $ is decreased to one third, what is the ratio between the new rate to the original rate of the reaction?
What is the nature of the function $ f(x) = x^3 - 3x^2 + 4x $ on real numbers?
Given are 4 statements related to the chemical properties of Glucose. Identify the two incorrect statements from the following.
Evaluate: $ \cos^{-1} \left( \cos \frac{35\pi}{18} \right) - \sin^{-1} \left( \sin \frac{35\pi}{18} \right) $
The maximum value of $ P = 500x + 400y $ for the given constraints $ x + y \leq 200, \quad x \geq 20, \quad y \geq 4x, \quad y \geq 0 $
If $ y = \sin^{-1} \left( \frac{5x + 12\sqrt{1 - x^2}}{13} \right) $ then $ \frac{dy}{dx} $ equals
If $ \frac{dy}{dx} = y + 3 \quad \text{and} \quad y(0) = 2, \quad \text{then} \quad y(\log 2) \text{ is equal to:} $
What is the probability of a randomly chosen 2-digit number being divisible by 3?
The area bounded by the curve $ y = \cos x $, $ x = 0 $, and $ x = \pi $ is
If $ I_n = \int_0^\pi \tan^n x \, dx $, for $ n \geq 2 $, then $ I_n + I_{n-2} = $