List of practice Questions

Three identical spheres of mass m, are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2m, then they will collide after ______ seconds.

Read the following statements on sickle cell anaemia:
A. It is a monogenetic disorder due to single base pair mutation in $\beta$-globin gene.
B. It occurs due to substitution of amino acid valine from glutamic acid.
C. It is a genetic disorder where a person is born with an extra copy of chromosome 21.
D. It is an autosomal recessive genetic disorder that prevents the body from removing excess copper and accumulates copper in body.
E. The point mutation in sickle cell anaemia changes the codon from GAG to GUG.
Choose the correct answer from the options given below:

In Young's double slit experiment, the separation between the two slits is 1.0 mm and the screen is 1.0 m away from the slits. A beam of light consisting of two wavelengths, 500 nm and 600 nm, is used to obtain interference fringes. Calculate:
(a) The distance between the first maxima for the two wavelengths.
(b) The least distance from the central maximum, where the bright fringes due to both the wavelengths coincide.

Let the area of a triangle $ \triangle PQR $ with vertices $ P(5, 4) $, $ Q(-2, 4) $, and $ R(a, b) $ be 35 square units. If its orthocenter and centroid are $ O(2, \frac{14}{5}) $ and $ C(c, d) $ respectively, then $ c + 2d $ is equal to:

Let R = {(1, 2), (2, 3), (3, 3)}} be a relation defined on the set $ \{1, 2, 3, 4\} $. Then the minimum number of elements needed to be added in $ R $ so that $ R $ becomes an equivalence relation, is:

Let $ A = \{1, 2, 3, \dots, 10\} $ and $ B = \left\{ \frac{m}{n} : m, n \in A, m <n \text{ and } \gcd(m, n) = 1 \right\} $. Then $ n(B) $ is equal to :

The graph of a trigonometric function is as shown. Which of the following will represent the graph of its inverse?

On the basis of the following hypothetical data:

Year	Nominal GDP (in ₹ crores)	Real GDP (Adjusted to base year prices, in ₹ crores)
2020 – 21	$ 3{,}000 $	$ 5{,}000 $
2022 – 23	$ 4{,}000 $	$ 6{,}000 $

Calculate the percentage change in Real Gross Domestic Product (GDP) in the year 2022 – 23 using 2020 – 21 as the base year.

In a compound microscope, an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. The eyepiece has a focal length of 5 cm. The final image is formed at infinity. Calculate the distance between the objective and the eyepiece.

When the resistance measured between p and n ends of a p-n junction diode is high, it can act as a/an:

Solve the following linear programming problem graphically: Maximise $ Z = 20x + 30y $ Subject to the constraints: \[ x + y \leq 0, \quad 2x + 3y \geq 100, \quad x \geq 14, \quad y \geq 14. \]

The calculated spin-only magnetic moments of $ K_3[Fe(OH)_6] $ and $ K_4[Fe(OH)_6] $ respectively are:

Choose the odd one out from the following options regarding the sectors of economy:

Let $ \hat{a} $ be a unit vector perpendicular to the vectors \[ \mathbf{b} = \hat{i} - 2\hat{j} + 3\hat{k} \quad \text{and} \quad \mathbf{c} = 2\hat{i} + 3\hat{j} - \hat{k}, \] $\text{and makes an angle of}$ $ \cos\left( -\frac{1}{3} \right) $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $. $\text{If}$ $ \hat{a} $ $\text{makes an angle of}$ $ \frac{\pi}{3} $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $, then the value of $ \alpha $ $\text{is:}$

Arrange the major developments in Harappan Archaeology in a chronological order:
(A) Report of Alexander Cunningham on Harappan seal.
(B) S.R. Rao begins excavations at Lothal.
(C) Daya Ram Sahni begins excavations at Harappa.
(D) Vasant Shinde begins archaeogenetic research at Rakhigarhi.
Choose the correct answer from the options given below:

Statement-1: $ \text{ClF}_3 $ has 3 possible structures.
Statement-2: $ \text{III} $ is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.

Which of the following options is correct?

What is the IUPAC name of the compound CH₃-CH₂-CO-CH₃?

इनमें से कौन-सा शब्द ‘एक’ का एक अर्थ प्रकट नहीं करता है?

Let the function $f(x) = (x^2 - 1)|x^2 - ax + 2| + \cos|x| $ be not differentiable at the two points $ x = \alpha = 2 $ and $ x = \beta $. Then the distance of the point $(\alpha, \beta)$ from the line $12x + 5y + 10 = 0$ is equal to:

Study the diagram above and answer the following questions:
(a) How many alleles are involved in blood grouping?

(b) A person having 'AB' blood group has both dominant alleles. What is this inheritance type called?

(c) A man with 'A' blood group marries a woman with 'B' blood group. Can they have a child with 'O' blood group? Explain with the help of a cross.

'स्वाधीन' समस्त पद का व्याख्या करके भेद भी लिखिए।

Given below are two statements:
Statement I: Experimentally determined oxygen-oxygen bond lengths in the $ O_2 $ are found to be the same and the bond length is greater than that of a $ O=O $ (double bond) but less than that of a single $ O-O $ bond.
Statement II: The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond $ O=O $ but more than that of a single bond $ O-O $.
In light of the above statements, choose the correct answer from the options given below:

Let $ A = [a_{ij}] $ be a $3 \times 3 $ matrix such that: $$ A = \begin{bmatrix} 0 & 0 & 4 \\ 1 & 0 & 0 \\ 0 & 1 & 3 \\ \end{bmatrix}, A^{-1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 3 & 0 \\ 2 & 1 & 0 \end{bmatrix}. $$ Then $ a_{23} $ equals:

Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
Assertion (A): In a reflecting telescope, the image does not have chromatic aberration.
Reason (R): Chromatic aberration occurs only due to refraction of light through an optical medium.

Kano na kine ki nuksa harum kaba hab ha ka kyntien synrap shiteng shiliang (partial reduplication)?

Year	Nominal GDP (in ₹ crores)	Real GDP (Adjusted to base year prices, in ₹ crores)
2020 – 21	\( 3{,}000 \)	\( 5{,}000 \)
2022 – 23	\( 4{,}000 \)	\( 6{,}000 \)