JEE Main Mock Test - 25 (05-04-2023)

Two circles of radii r₁ and r₂ are both touching the coordinate axes and intersecting each other orthogonally. The value of r₁/r₂ (where r₁ > r₂) equals

Let X and Y be two matrices satisfying this relations

then Tr.(X) – Tr.(Y) equals
[Note : Tr.(P) denotes trace of matrix P.]

The differential equation dx/dy = 3y/2x represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity can be

Line L, perpendicular to the line with equation y = 3x – 5, contains the point (1, 4). The x-intercept of L, is

Let A = [a_ij] (1 ≤ i , j ≤ 3) be a 3 × 3 matrix and B = [b_ij] (1 ≤ i , j ≤ 3) be a 3 × 3 matrix such that

If det. A = 4, then the value of det. B is

Number of words that can be formed using all the letters of the word GARGEE if no two alike letters are together, is

If acute angle between the line  and xy plane is α and acute angle between the planes x + 2y = 0 and 2x + y = 0 is β then (cos²α + sin²β) equals

If area of pentagon PQRST be 7, where P(–1, –1), Q(2, 0), R(3, 1), S(2, 2) and T(–1, t), t > 0, then the value of t is

The sum of all value of λ for which the lines 2x + y + 1 = 0; 3x + 2λy + 4 = 0; x + y - 3λ = 0 are concurrent, is

If A and B are two independent events such that P(A' ∩ B') = 2/15, P(A ∩ B') = 1/6 then P(B) =

A hyperbola has centre at origin and one focus at (6, 8). If its two directrices are 3x + 4y + 10 = 0 and 3x + 4y –10 = 0 and eccentricity is e,then the value of 4e²/5 is equal to

Number of integral values of 'k' for which the chord of the circle x² + y² = 125 passing through P(8, k) gets bisected at P (8, k) and has integral slope is

Locus of the feet of perpendiculars drawn from points (1, 2) and (3, 4) on a variable tangent to the conic | z - (1+ 2i) | - | z - (3+ 4i) | = 2 is

Number of numbers greater than a million and divisible by 5 which can be formed by using only the digits 1, 2,1, 2, 0, 5 and 2 is :

The dual of statement (p v ~ q) ∧ (~ p) is

A normal is drawn to the parabola y² = 9x at the point P(4, 6), S being the focus, a circle is described on the focal distance of the point P as diameter. The length of the intercept made by the circle on the normal at P is

Consider ellipse  Let C is centre of the ellipse and P is a variable point lying on the ellipse. If the angle between CP and tangent at P is minimum, then P may be

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

If then the value of a⁵ + b⁴ must be

The value of x satisfying the equation

then k is

The sum of squares of all integral values of a for which the quadratic expression (x−a)(x−10)+1 can be factored as a product (x+α)(x+β) of two factors and α, β ∈ I must be equal to

If f(x) = tan^-1 (sin x + cos x)³ is an increasing function, then the value of x in (0, 2π) is x ∈  Then the value of a + 10b + 100c + 1000d must be

The sum of two digit even numbers which do not end with zero is

A non-conducting rod AB of length l has a total charge q. The rod is rotated about an axis passing through its center of mass with a constant angular velocity ω as shown in the figure. The magnetic moment of the rod is

The distance between two parallel plates of a capacitor is a. A conductor of thickness b(b < a) is inserted between the plates as shown in the figure. The variation of effective capacitance between the plates of the capacitor as a function of the distance (x) is best represented by

A solid sphere of radius R, and dielectric constant ‘k’ has spherical cavity of radius R/4. A point charge q₁ is placed in the cavity. Another charge q₂ is placed outside the sphere at a distance of r from q₁. Then Coulombic force of interaction between them is found to be ‘F₁’. When the same charges are separated by same distance in vacuum then the force of interaction between them is found to be F₂ then

Energy stored in the capacitor in it’s steady state is

A point charge of 0.1C is placed on the circumference of a non-conducting ring of radius 1m which is rotating about an axis passing from centre and perpendicular to the plane of ring with a constant angular acceleration of 1 rad/sec². If ring starts from rest at t = 0, the magnetic field at the centre of the ring at t = 10 sec, is

In an L – C circuit shown in the figure, C = 1F, L = 4H. At time t = 0, charge in the capacitor is 4C and it is decreasing at a rate of √5 C/s. Choose the correct statements.

A solid conducting sphere of radius r is having a charge Q and point charges +q and –q are kept at distances d from the center of sphere as shown in the figure. The electric potential at the centre of solid sphere

Consider the circuit in the adjacent figure. What will be potential difference between A and B in the steady state

A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density σ C/m². The flux due to the charge q through the disc is ϕ. The electric force on charge q exerted by the disc is

In the given circuit diagram, find the heat generated on closing the switch S. (Initially the capacitor of capacitance C is uncharged)

A metallic ring of radius R moves in a vertical plane in the presence of a uniform magnetic field B perpendicular to the plane of the ring. At any given instant of time its centre of mass moves with a velocity v while ring rotates in its COM frame with angular velocity ω as shown in the figure. The magnitude of induced e.m.f. between points O and P is

An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?

The relation between R and r (internal resistance of the battery) for which the power consumed in the external part of the circuit is maximum

A capacitor and resistor are connected with an A.C. source as shown in figure. Reactance of capacitor is X_C = 3W and resistance of resistor is 4Ω. Phase difference between current I and I₁ is

Find the stress at distance R/2 from centre in a uniformly charged non conducting sphere having radius R and charge density ρ.

The capacitor is initially uncharged. Find ratio of current through the 10 Ω resistance and through the 20 Ω resistance initially.

In the diagram below, light is incident on the interface between media 1 and 2 as shown and is totally reflected. The light is then also totally reflected at the interface between media 1 and 3, after which it travels in a direction opposite to its initial direction. The two interfaces are perpendicular. The refractive indices are related as

Which of the following transitions of He⁺ ion will give rise to spectral line which has same wavelength as some spectral line in hydrogen atom ?

Two imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the concentric spheres. When compared to the number of field lines N₁ going through the sphere of radius R, the number of electric field lines N₂ going through the sphere of radius 2R is

A radioactive sample contains two radioactive nucleus A and B having decay constant λ hr^–1 and 2λ hr^–1. Initially 20% of decay comes from A. How long (in hr) will it take before 50% of decay comes from A. [Take λ = ln 2]

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

A block is placed on an inclined plane moving towards right horizontally with an acceleration a₀=g. The length of the plane AC = 1m. Friction is absent everywhere. Find the time taken (in seconds) by the block to reach from C to A.

In the given figure, find the horizontal velocity u (in ms^-1) of a projectile so that it hits the inclined plane perpendicularly. Given H = 6.25 m:

A uniform cylinder rests on a cart as shown. The coefficient of static friction between the cylinder and the cart is 0.5. If the cylinder is 4 cm in diameter and 10 cm in height, then what is the minimum acceleration (in m/s²) of the cart needed to cause the cylinder to tip over?

In the circuit shown in figure, find the ratio of currents i₁/i₂

The centers of two identical small conducting spheres are 1m apart. They carry charges of opposite kind and attract each other with a force F. When they are connected by a conducting thin wire, they repel each other with a force F/3. The ratio of the magnitude of charges carried by the spheres initially is n : 1. Find the value of n.

A 0.1 M solution of which salt is most acidic?

Which is the strongest acid amongst the following compounds?

Select the correct order of metallic character :

In hydrogen atom which transition produces a photon with highest energy?

The correct basicity order of indicated atoms P, Q and R is -

Select the incorrect statement regarding N^3–, O^2–, F^-, Na⁺ and Mg²⁺.

Dioxygen difluoride (O₂F₂) is a highly oxidising and unstable liquid. At 300 K it decomposes back to oxygen and fluorine, which are both gases at this temperature. The equation for the reaction is given below. 0.1 g of O₂F₂ was left for 24 hours and the 24.9 ml of gas mixture evolved was collected at 300 K and 100 kPa. What % by mass of dioxygen difluride has decomposed by this time?
O₂F₂(l) → O₂(g) + F₂(g)

Which of the following cyclic dienes does not show geometrical isomerism?

Which of the following property is different for two different isoelectronic homonuclear diatomic species?

In an analysis of solutions containing Barium ions (Ba²⁺), 50 ml of solution gave 0.233 g of BaSO₄ upon addition of sufficient sulphuric acid to precipitate all the Ba²⁺ ions present. What is concentration (in M) of Ba²⁺ ions in the solution.

Ethers are more volatile than same no. of carbon containing alcohol due to -

Select the species which becomes Bent due to lone pair – bond pair repulsion.

Quinaldine red is a useful acid-base indicator which is red in solution of pH greater than 3.5 but colorless below pH = 1.5. Which of the following solution would turn red if a few drops of quinaldine red were added?
(i) 0.1 mol L^–1 HCl
(ii) 0.05 mol L^–1 NH₃
(iii) 0.0001 mol L^–1 CH₃COOH

Identify P and Q respectively.

Oxidising nature of H₂ is observed on reaction with

A brown-black compound of thallium was found to contain 89.5% Tl and 10.5% oxygen. What is oxidation number of thallium in this compound? [Atomic weight of Tl = 204]

Identify R in the following series of reaction.

Select the incorrect match regarding action of H₂O.

Identify the correct statement :

In the mono chlorination of 3-Ethyl pentane, how many total products will be formed?

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

From the following sets of quantum numbers, state which are not possible.
a. n = 0, l = 0, m = 0, s = +1/2
b. n = 1, l = 0, m = 0, s = –1/2
c. n = 1, l = 1, m = 0, s = +1/2
d. n = 1, l = 0, m = +1, s = +1/2
e. n = 3, l = 0, m = –1, s = –1/2
f. n = 2, l = 2, m = 0, s = –1/2
g. n = 2, l = 1, m = 0, s = –1/2

200g impure CaCO₃ on heating gives 5.6L. CO₂ gas at STP. Find the percentage of Calcium in the limestone sample.

NO → N₂O + NO₂
n this reaction equivalent weight of NO is x/y M then x + y will be

10 g impure NaOH is completely neutralised by 1000 ml of 1/10 N HCI. Calculate the percentage purity of the impure NaOH.

Then weight of MgSO₄ will be formed in this series is