List of practice Questions

Education' falls under which one of the following lists given in the Indian Constitution?
Read the arguments given in favor of power sharing and choose the correct option.
1. Reduces the likelihood of bias.
2. Barricades the decision-making process.
3. Accommodates diversities.
4. Increases the participation of people in power.
Choose the correct option for the following States’ share (in percentage) in the production of ‘manganese’ in India from the highest to the lowest order.
Match Column I with Column II and choose the correct option.
Column I (Dams) Column II (Rivers)
i. Sardar Sarovara. Sutlej
ii. Hirakud b. Krishna
iii. Bhakra Nangalc. Narmada
iv. Nagarjuna Sagard. Mahanadi
Two statements are given below. They are Assertion (A) and Reason (R). Read both the statements and choose the correct option.
Assertion (A): The famous ‘Chipko Movement’ in the Himalayas successfully resisted deforestation in several areas.
Reason (R): Through this, community afforestation campaign with indigenous species was made enormously successful.
Who among the following said – “Printing is the ultimate gift of God and the greatest one”?
Choose the correct option, related to the founders of the ‘Swaraj Party’ within the Congress.
Choose the correct option to fill in the blank.
______ from India and Southeast Asia traveled through ‘Silk Route’ to other parts of the world.
Arrange the following incidents in chronological order and choose the correct option.
1. French Revolution
2. Napoleon’s invasion of Italy
3. Unification of Italy
4. Vienna Peace Treaty
The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a rhombus, and not a square.
Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.
The interior of a building is in the form of a cylinder of base radius 12 m and height 3×5 m surmounted by a cone of equal base and slant height 14 m. Find the internal curved surface area of the building.
Solve for $x$: \[ \frac{4}{x} - \frac{5}{2x + 3} = 3. \]
The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
Calculate the mean of the following data :
Class :4 – 67 – 910 – 1213 – 15
Frequency :54910
Prove that: \[ \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta \]
From an external point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. At a point $E$ on the circle, a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$ respectively. If $PA = 10$ cm, find the perimeter of $\triangle PCD$.
A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle
The monthly incomes of A and B are in the ratio 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 2500 per month, find the monthly income of each
Find the zeroes of the polynomial $f(t) = t^2 + 4\sqrt{3}t - 15$ and verify the relationship between the zeroes and the coefficients of the polynomial.
Prove that $\sqrt{3}$ is an irrational number.
A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35 m, 40 m and 50 m. Find the total area of grass field that can be grazed by them
If $\sin A = \frac{3}{5}$ and $\cos B = \frac{12}{13}$, then find the value of $(\tan A + \tan B)$.
If $\tan \theta + \sec \theta = m$, then prove that $\sec \theta = \frac{m^2 + 1}{2m}$.
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.