List of practice Questions

If area bounded by region \({x, y)| |x^{2}-2| ≤ y ≤ x}\) is A, then 6A + 16\(\sqrt{2}\) is?

Using the number 1, 2, 3 ... 7, total numbers of 7 digit number which does not contain string 154 or 2367 is (Repetition is not allowed)

Given below are two statements: one is labeled as Statement (1) and the other is labeled as Statement (2).
Statement (1): Maximum power is dissipated in a circuit containing an inductor, a ca pacitor and a resistor connected in series with an AC source, when resonance occurs
Statement (2): Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct option:

The de Broglie wavelength of a molecule in a gas at room tem perature (300 K) is λ₁. If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes

Find the equivalent capacitance across points A and B in the given electric circuit.

An object weighs 200N at the surface of earth. Find the weight at a depth of \(\frac{R}{2}\) , where R is radius of earth

The range of the projectile projected at an angle of 15° with hor izontal is 50 m. If the projectile is projected with same velocity at an angle of 45° with horizontal, then its range will be

The height of the antenna is 98 m. The radius of Earth is 6400 km. The area up to which it will transmit signal is:

A Carnot engine working between 27°C and 127°C performs 2 kJ of work. The amount of heat rejected is equal to:

Match column I with column II and choose the correct option.

Column I	Column II
(I) Torque	(a) M°LT^-2
(II) stress	(b) ML^-1T^-1
(III) Coefficient of viscosity	(c) ML^-IT^-2
(IV) Potential gradient	(d) ML²7^-2

Select the correct graph showing the difference (d) between total energy and potential energy of a particle in linear SHM with position x of the particle (x = 0 is the mean position)

Statement —I: Electromagnets are made of soft iron.
Statement —II: Soft iron has lower permeability and high retentivity.
Choose the correct option related to statements.

A body of mass \( 5 \, \text{kg} \) is moving with a momentum of \( 10 \, \text{kg} \cdot \text{ms}^{-1} \). Now a force of \( 2 \, \text{N} \) acts on the body in the direction of its motion for \( 5 \, \text{s} \). The increase in the kinetic energy of the body is _____ J.

The ratio of magnetic field due to coil at centre and at distance of R from the centre on the axis passing through the centre and perpendicular to the plane of ring is : 1x (R is the radius of coil), find the value of x.

The ratio of the wavelength of spectral lines \( H_\alpha \) and \( H_\beta \) in the Balmer series is \( \frac{x}{20} \). The value of \( x \) is _______.

What is the ratio of σ and pi bonds in pyrophosphoric acid ?

IUPAC name of the compound C₇H₁₂O₂?

Find out the oxidation number of the central metal atom of fe(CO)₅ , VO₂⁺, and WO₃. Then calculate the sum of their oxidation state.

K_sp of BaSO₄ is 8 × 10^–11. If the solubility in presence of 0.1 M CaSO₄ is?

The largest natural number \(n\) such that \(3^n\) divides \(66!\) is:

The solubility product of BaSO₄ is \(1 \times 10^{-10}\) at 298 K. The solubility of BaSO₄ in 0.1 M K₂SO₄(aq) is \(x \times 10^{-9}\) g L⁻¹. Calculate the value of \(x\).

How many of the following have five radial nodes ?
5s, 6s, 7s, 6p and 4p

In good quality cement ratio of lime total oxides of Si(SiO\(_2\)), Aluminium(Al\(_2\)O\(_3\)) and Iron(Fe\(_2\)O\(_3\)) should be as close as possible to _____ .

The area of the quadrilateral having vertices as (1,2), (5,6), (7,6), (-1,-6) is?

Let \( m \) and \( n \) be the numbers of real roots of the quadratic equations \( x^2 - 12x + [x] + 31 = 0 \) and \( x^2 - 5|x+2| - 4 = 0 \), respectively, where \( [x] \) denotes the greatest integer less than or equal to \( x \). Then \( m^2 + mn + n^2 \) is equal to ___________.