List of practice Questions

An object of mass $ m $ is projected from the origin in a vertical $ xy $-plane at an angle $ 45^\circ $ with the x-axis with an initial velocity $ v_0 $. The magnitude and direction of the angular momentum of the object with respect to the origin, when it reaches the maximum height, will be:

A massless spring gets elongated by amount $ x_1 $ under a tension of 5 N. Its elongation is $ x_2 $ under the tension of 7 N. For the elongation of $ 5x_1 - 2x_2 $, the tension in the spring will be:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R): The magnetic field in that region is along the direction of velocity of the electron.
In the light of the above statements, choose the correct answer from the options given below:

A bar magnet has total length $ 2l = 20 $ units and the field point $ P $ is at a distance $ d = 10 $ units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:

A rod of linear mass density $ \lambda $ and length $ L $ is bent into the form of a ring of radius $ R $. The moment of inertia of the ring about any of its diameters is:

Let the triangle PQR be the image of the triangle with vertices $ (1, 3), (3, 1) $ and $ (2, 4) $ in the line $ x + 2y = 2 $. If the centroid of $ \Delta PQR $ is the point $ (\alpha, \beta) $, then $ 15(\alpha - \beta) $ is equal to :

Arrange the below-mentioned Paramveer Chakra Awardees in the correct chronological order (from earliest to current):
(A) Capt. Vikram Batra
(B) Maj. Somnath Sharma
(C) Maj. Dhan Singh Thapa
(D) Flying Officer Nirmaljit Singh Sekhon
Choose the correct answer from the options given below:

Identify the correct chronological order of these incidents from the beginning:
(A) First TV Broadcast in India
(B) Launch of Vividh Bharati
(C) SITE Project
(D) Krishi Darshan
Choose the correct answer from the options given below:

Which of these books are not written by Munshi Premchand?
(A) Gora
(B) Gaban
(C) Chitra
(D) Mahabhoj
Choose the correct answer from the options given below:

Arrange these events in correct chronological order from the beginning:
(A) Third Battle of Panipat
(B) Coronation of Shivaji
(C) Death of Aurangzeb
(D) Birth of Mirza Ghalib
Choose the correct answer from the options given below:

Which one of the following newspaper was edited by Dr. B. R. Ambedkar?

Calculate the mass of an $\alpha$-particle in atomic mass unit (u).
Given: Mass of a normal helium atom = $ 4.002603 \ \text{u} $
Mass of carbon atom = $ 1.9926 \times 10^{-26} \ \text{kg} $

Who said "Satyameva Jayate" first?

The Rupee symbol is based on:

Match List-I with List-II:

Choose the correct answer from the options given below:

Identify the correct chronological order of Bharat Ratna recipients from the beginning.
(A) Mother Theresa
(B) C.V. Raman
(C) Dr. A. P. J. Abdul Kalam
(D) Dr. Rajendra Prasad
Choose the correct answer from the options given below:

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4 bowlers. One batsman and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is:

For the reaction A(g) $\rightleftharpoons$ 2B(g), the backward reaction rate constant is higher than the forward reaction rate constant by a factor of 2500, at 1000 K.
[Given: R = 0.0831 atm $mol^{–1} K^{–1}$]
$K_p$ for the reaction at 1000 K is:

Calculate the value of Net Value Added at Factor Cost (NVA_FC):

S. No.	Particulars	Amount (in ₹ crore)
(i)	Operating Surplus	3,740
(ii)	Increase in unsold stock	600
(iii)	Sales	10,625
(iv)	Purchase of raw materials	2,625
(v)	Consumption of fixed capital	500
(vi)	Subsidies	400
(vii)	Indirect taxes	1,200

On the basis of the following data, estimate the value of National Income (NNP_FC):

S.No.	Items	Amount (in ₹ crore)
(i)	Household Consumption Expenditure	$ 800 $
(ii)	Gross Business Fixed Capital Formation	$ 150 $
(iii)	Gross Residential Construction Investment	$ 120 $
(iv)	Government Final Consumption Expenditure	$ 270 $
(v)	Excess of Imports over Exports	$ 20 $
(vi)	Inventory Investments	$ 50 $
(vii)	Gross Public Investments	$ 130 $
(viii)	Net Indirect Taxes	$ 20 $
(ix)	Net Factor Income from Abroad	$ -25 $
(x)	Consumption of Fixed Capital	$ 40 $

Calculate Net Domestic Product at Market Price (NDP_MP) from the data given below:

S. No.	Particulars	Amount (in ₹ lakh)
(i)	Gross Domestic Product at Factor Cost	2200
(ii)	Subsidies	50
(iii)	Indirect Taxes	70
(iv)	Net Factor Income from Abroad	100
(v)	Consumption of Fixed Capital	150
(vi)	Net Exports	40

Which of the following oxides is amphoteric in nature?

How many moles of $\mathrm{CO_2}$ are produced when 4 moles of $\mathrm{C_2H_6}$ (ethane) combust completely?
Given reaction: \[ 2 \mathrm{C_2H_6} + 7 \mathrm{O_2} \rightarrow 4 \mathrm{CO_2} + 6 \mathrm{H_2O} \]

Choose the incorrect statement among the following:
I. The present era is called “Golden era of Biology”.
II. Sexual system of classification was proposed by Theophrastus.
III. Study of Amphibians of plant kingdom are called Bryology.
IV. Recycling of nutrients takes place by parasitic petrophants.

One acre of trees annually absorbs CO$_2$ equal to that produced by driving 26000 miles. How many people’s oxygen needs for a year does this cover?

S.No.	Items	Amount (in ₹ crore)
(i)	Household Consumption Expenditure	\( 800 \)
(ii)	Gross Business Fixed Capital Formation	\( 150 \)
(iii)	Gross Residential Construction Investment	\( 120 \)
(iv)	Government Final Consumption Expenditure	\( 270 \)
(v)	Excess of Imports over Exports	\( 20 \)
(vi)	Inventory Investments	\( 50 \)
(vii)	Gross Public Investments	\( 130 \)
(viii)	Net Indirect Taxes	\( 20 \)
(ix)	Net Factor Income from Abroad	\( -25 \)
(x)	Consumption of Fixed Capital	\( 40 \)