List of practice Questions

A particle is projected at an angle of $ 30^\circ $ from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is $ h_0 $ and height traversed in the last second, before it reaches the maximum height, is $ h_1 $. The ratio $ \frac{h_0}{h_1} $ is __________. [Take $ g = 10 \, \text{m/s}^2 $]

A compound 'X' absorbs 2 moles of hydrogen and 'X' upon oxidation with KMnO4 - H⁺ gives the following products:

The total number of $\sigma$ bonds present in the compound 'X' is ----.

Let $ \mathbf{a} = 3\hat{i} - \hat{j} + 2\hat{k} $, $ \mathbf{b} = \mathbf{a} \times (\hat{i} - 2\hat{k}) $ and $ \mathbf{c} = \mathbf{b} \times \hat{k} $. Then the projection of $ \mathbf{c} - 2\hat{j} $ on $ \mathbf{a} $ is:

Which of the following mixing of 1M base and 1M acid leads to the largest increase in temperature?

Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is:

Total number of nucleophiles from the following is: $\text{NH}_3, PhSH, (H_3C_2S)_2, H_2C = CH_2, OH−, H_3O+, (CH_3)_2CO, NCH_3$

Match List - I with List - II:

List - I:

(A) $[ \text{MnBr}_4]^{2-}$
(B) $[ \text{FeF}_6]^{3-}$
(C) $[ \text{Co(C}_2\text{O}_4)_3]^{3-}$
(D) $[ \text{Ni(CO)}_4]$

List - II:

(I) d²sp³ diamagnetic
(II) sp²d² paramagnetic
(III) sp³ diamagnetic
(IV) sp³ paramagnetic

The remainder, when $7^{98}$ is divided by 23, is equal to:

Given below are two statements:
Statement (I): On nitration of m-xylene with $ \text{HNO}_3 $, $ \text{H}_2\text{SO}_4 $, followed by oxidation, 4-nitrobenzene-1, 3-dicarboxylic acid is obtained as the major product.
Statement (II): CH$_3$ group is o/p-directing while NO$_2$ group is m-directing group.
In the light of the above statements, choose the correct answer from the options given below:

To obtain the given truth table, the following logic gate should be placed at G:

Given below are two statements, one labeled as Assertion (A) and the other as Reason (R). Assertion (A): In Young’s double slit experiment, the fringes produced by red light are closer compared to those produced by blue light. Reason (R): The fringe width is directly proportional to the wavelength of light. In the light of the above statements, choose the correct answer from the options given below:

The moment of inertia of a ring of mass $ M $ and radius $ R $ about an axis passing through a tangential point in the plane of ring is:

Find the eccentricity of the ellipse in which the length of the minor axis is equal to one fourth of the distance between foci.

The sum of all rational numbers in $ (2 + \sqrt{3})^8 $ is:

At 715 mm pressure, 300 K, volume of N$_2$ (g) evolved was 80 mL by a 0.4 g sample of organic compound. Find the percentage of N in the organic compound. Given aqueous tension at 300 K = 15 mm.

$ x $ is a peptide which is hydrolyzed to 2 amino acids $ y $ and $ z $. $ y $ when reacted with HNO$_2$ gives lactic acid. $ z $ when heated gives a cyclic structure as below:

Let $ I_1 = \int_{\frac{1}{2}}^{1} 2x \cdot f(2x(1 - 2x)) \, dx $
and $ I_2 = \int_{-1}^{1} f(x(1 - x)) \, dx \; \text{then} \frac{I_2}{I_1} \text{ equals to:} $

From the combination of resistors with resistance values $ R_1 = R_2 = R_3 = 5 \, \Omega $ and $ R_4 = 10 \, \Omega $, which of the following combination is the best circuit to get an equivalent resistance of 6 $ \Omega $?

An object is kept at rest at a distance of 3R above the earth’s surface where $ R $ is earth’s radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume $ M $ = mass of earth, $ G $ = Universal gravitational constant)

Displacement of a wave is expressed as $$ x(t) = 5 \cos \left( 628t + \frac{\pi}{2} \right) \, \text{m}. $$ The wavelength of the wave when its velocity is 300 m/s is:

A particle of charge 1.6 $\mu$C and mass 16 $\mu$g is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is _______ s. (Take $ \pi = 3.14 $)

Let the set of all values of $ p \in \mathbb{R} $, for which both the roots of the equation $ x^2 - (p + 2)x + (2p + 9) = 0 $ are negative real numbers, be the interval $ (\alpha, \beta) $. Then $ \beta - 2\alpha $ is equal to:

The number of singular matrices of order 2, whose elements are from the set $ \{2, 3, 6, 9\} $ is:

Given below are two statements:
Statement I: D-(+)-glucose + D-(+)-fructose $\xrightarrow{H_2O}$ sucrose sucrose $\xrightarrow{\text{Hydrolysis}}$ D-(+)-glucose + D-(+)-fructose
Statement II: Invert sugar is formed during sucrose hydrolysis.
In the light of the above statements, choose the correct answer from the options given below -

Let $ f(x) = \begin{cases} (1+ax)^{1/x} & , x<0 \\1+b & , x = 0 \\\frac{(x+4)^{1/2} - 2}{(x+c)^{1/3} - 2} & , x>0 \end{cases} $ be continuous at x = 0. Then $ e^a bc $ is equal to