List of practice Questions

Two point charges -10 ÂµC and +5 ÂµC are situated on the X-axis at $ x = 0 $ and $ x = \sqrt{2} \, \text{m} $. The point along the X-axis where the electric field becomes zero is.

If a real valued function $ f: [a, \infty) \to [b, \infty) $ is defined by $ f(x) = 2x^2 - 3x + 5 $ and is a bijection, then find the value of $ 3a + 2b $:

'चटका' शब्द है - स्तंभ II में किस श्रेणी में आता है?

If the acceleration due to gravity on the surface of a planet is 2.5 times that on Earth and radius, 10 times that of the Earth, then the ratio of the escape velocity on the surface of a planet to that on Earth is:

The slope of the tangent to the curve $ x = \sin\theta $ and $ y = \cos 2\theta $ at $ \theta = \frac{\pi}{6} $ is ___________.

Which sport is associated with the Euro Cup?

Ram said, "Anu's mother is the only daughter of my mother." How is Anu related to Ram?

The number of factors of 1800 that are multiple of 6 is …………. .

Let $ \alpha \in \mathbb{R} $. If the line $ (a + 1)x + \alpha y + \alpha = 1 $ passes through a fixed point $ (h, k) $ for all $ a $, then $ h^2 + k^2 = $:

Evaluate the limit $$ \lim_{x \to \infty} \frac{\sin x}{x} $$

______ was nominated as member of Rajya Sabha by the President in 2024.

Two bodies A and B of masses $ 2m $ and $ m $ are projected vertically upwards from the ground with velocities $ u $ and $ 2u $ respectively. The ratio of the kinetic energy of body A and the potential energy of body B at a height equal to half of the maximum height reached by body A is:

(b) Your school recently conducted an Art Exhibition where students from all classes participated, showcasing their creativity through paintings, sculptures, and other artworks. Parents and visitors appreciated the students’ efforts and congratulated them on their artistic achievements.

As the student editor, write a **report on the exhibition** to be published in your school magazine. Use the following points along with your own insights to develop your report:

Key Details to Include:

Date, venue, and time of the exhibition
Details of student participants
Types of paintings and sculptures displayed
Theme of the exhibition, if any
Feedback from visitors and parents

The major product in the given reaction sequence is Q. The mass spectrum of Q shows
([M] = molecular ion peak)

Binding energy and rest mass energy of a two-nucleon bound state are denoted by $ B $ and $ mc^2 $, respectively, where $ c $ is the speed of light. The minimum energy of a photon required to dissociate the bound state is _______.

PS I first wavelength / reaction center is:

"Trade Deficit must exist, if a country is facing situation of Current Account Deficit (CAD)." Defend or refute the above mentioned statement with valid arguments.

How many meaningful English words can be formed by using 2nd, 4th, 7th and 9th letter of the word ‘WONDERFUL’? Use each letter only once, but in different sequence.

A lamp is rated at 240V, 60W. When in use the resistance of the filament of the lamp is 20 times that of the cold filament. The resistance of the lamp when not in use is:

The general solution of $ 2 \cos^2 x - 2 \tan x + 1 = 0 $ is:

A blank of 100 mm diameter is to be cut out of a 2 mm thick sheet through blanking operation. If the radial clearance between the punch and die is 6% of the sheet thickness then the diameter (in mm) of the punch is _____ . (Rounded off to 2 decimal places)

A 45-year-old woman is diagnosed with right vestibular neuritis. What findings are expected during the head impulse test in this patient?

Two spheres A and B having respective charges 6 C and 12 C placed at a distance $ d $ repel each other by a force $ F $. The charge given to sphere A to reverse the force as $ -F $ is:

Explain the following terms:
(a) Grafting
(b) Apomixis
(c) Polyembryony
(d) Parthenocarpy

In a group of 150 students, 52 like tea, 48 like juice, and 62 like coffee. If each student in the group likes at least one among tea, juice, and coffee, then the maximum number of students that like more than one drink is _______________.