JEE Main Mock Test - 17 (28-03-2023)

A balloon is moving upwards with a speed of 20 m/s. When it is at a height of 14 m from ground in front of a plane mirror in as shown in figure, a boy drops himself from the balloon. Find the time duration for which he will see the image of source S placed symmetrically before plane mirror during free fall.

Prism angle & refractive index for a prism are 60^o & 1.414. Angle of minimum deviation will be

If a gas is heated at constant pressure then what percentage of total heat supplied is used for doing work ? (Given : γ for gas = 4/3)

Four persons K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform speed  v in such a way that K always moves directly towards L, L directly towards M, M directly towards N, and N directly towards K. The four persons will meet at a time .....

Estimate the speed of sound in air at standard temperature and pressure. The mass of 1 mole of air is 29.0 × 10^-3 kg

A pendulum bob is suspended on a flat car that moves with velocity v₀. The flat car is stopped by a bumper
(i) What is the angle through which the pendulum swings.
(ii) If the swing angle is θ = 60° and l = 10m, what was the initial speed of the flat car?

Two slits, 4 mm apart, are illuminated by light of wavelength 6000Å. What will be the fringe width on a screen placed 2 m from the slits?

A car moves uniformly along a horizontal sine curve y = a sin (x/α), where a and α are certain constants. The coefficient of friction between the wheels and the road is equal to k. At what velocity will the car ride without sliding?

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from h to h/2 and from h/2 to zero is

A bullet of mass 2 g is having a charge of 2μC. The potential difference it must be accelerated through, starting from rest, to acquire a speed of 10 m/s is

A wire of length L and 3 identical cells of negligible internal resistance are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time . The value of N is

The intensity of the light coming from one of the slits in YDSE is double the intensity from the other slit. Find the ratio of maximum intensity to minimum intensity in the interference fringe pattern observed.

Consider α-particles, β-particles and γ- rays each having an energy of 0.5 MeV. In increasing order of penetrating powers, the radiations are

A battery is supplying power to a tape-recorder by cable of resistance of 0.02 Ω . If the battery is generating 50 W power at 5V, then power received by tape-recorder is :

A uniform rod of mass m and length ℓ is rotating with constant angular velocity ω about an axis which passes through its one end and perpendicular to the length of rod. The area of cross section of the rod is A and its Young's modulus is Y. Neglect gravity. The strain at the mid point of the rod is :

Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0 in the same direction along a straight line. The velocity time graph of two cars is shown in figure. The time when the car B will catch the car A, will be ;

Two masses m₁ and m₂ are connected by a string of length l. They are held in a horizontal plane at a height H above two heavy plates A and B made of different material placed on the floor. Initially distance between two masses is a < l. When the masses are released under gravity they make collision with A and B co - efficient of restitution 0.8 and 0.4 respectively. The time after the collision when the string becomes tight is

The difference between (n + 2)^th Bohr radius and n^th Bohr radius is equal to the (n – 2)^th Bohr radius. The value of n is ?

The figure shows an RC circuit with a parallel plate capacitor. Before switching on the circuit, plate A of the capacitor has a charge –Q₀ while plate B has no net charge. Now, at t = 0, the circuit is switched on. How much time (in second) will elapse before the net charge on plate A becomes zero.

(GivenC=1μF, Q₀=1mC, ε=1000V and 

A thin non conducting disc of mass M = 2kg, charge Q = 2x10^–2 C and radius R = 1/6m is placed on a frictionless horizontal plane with its centre at the origin of the coordinate system. A non uniform, radial magnetic field  exists in space, where B₀ = 10T and  is a unit vector in the radially outward direction. The disc is set in motion with an angular velocity w = x*10² rad/sec, about an axis passing through its centre and perpendicular to its plane, as shown in the figure. At what value of x, the disc will lift off from the surface.

All springs, string and pulley shown in figure are light. Initially when both the springs were in their natural state, the system was released from rest. The maximum displacement of block m is  calculate x

In Young’s Double slit experiment, a thin glass mica strip of thickness (t = 8λ) is pasted infront of slit S₁. If the same strip is now shifted in front of other slit S₂. If the number of fringes which will cross the central point on the screen is N. Find N? (d >> D, λ << d and n_mica = 1.5)

A saturated aqueous solution of sparingly soluble salt AB₃ has the vapour pressure 0.08 mm lesser than the vapour pressure 17.33 mm of solvent at 25^oC. The solubility product of AB₃ is :

Photoelectric emission is observed from a surface for frequencies v₁ and v₂ of the incident radiation (v₁ > v₂). If the maximum kinetic energies of the photoelectrons in the two cases are in the ration l : k then the threshold frequency v₀ is given by :

In the following electron dot structure calculate the formal charge from left to right nitrogen atom ?

A 50 litre vessel is equally divided into three parts with the help of two stationary semi permeable membrane (SPM). The vessel contains 60 g H₂ gas in the left chamber, 160 g O₂ in the middle and 140 g N₂ in the right one. The left SPM allows transfer of only H₂ gas while the right one allows the transfer of both H₂ and N₂. The final ratio of pressure in the three chambers.

Acetamide is treated separately with the following reagents. Which of these would give methylamine ?

 White fumes. Metal (M) can be

Copper ore is heated in a blast furnace after mixing with silica. Iron oxide slags off as iron silicate and copper is produced in the form of

The ionization isomer of [Cr(H₂O)₄Cl(NO₂ )]Cl is

What is the pH of 0.01 M glycine solution ? For glycine 

Which one of the following cannot be prepared from B₂H₆ ?

Titration of I₂ produced from 0.1045 g of primary standard KIO₃ required 30.72 mL of sodium thiosulphate as shown below :

The molarity of sodium thiosulphate ion is :

The standard reduction potentials of Cu²⁺ / Cu and Cu²⁺ / Cu⁺ are 0.337 V and 0.153 V respectively. The standard electrode potential of Cu⁺ / Cu half cell is

The electron energy in hydrogen atom is given by  Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength (in cm) of light that can be used to cause this transition?

An element has fcc structure with edge length 200 pm, calculate the density if 200g of this element contains 24 × 10²³ atoms. (N_A ⁼  6 × 10²³​)

A compound that gives a positive iodoform test is

1.44 g of Titanium (Ti) reacted with an excess of O₂ and produced x gm of a non-stoichiometric compound Ti_1.44O₁. The value of x is :

A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt (II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is

One desires to prepare a positively charged solution of silver iodide. This can be achieved by

Anhydrous AlCl₃. How will it behave in Aqueous solution?

The ionisation energy of solid NaCl is 180 kcal per mol.The dissolution of the solid in water in the form of ions is endothermic to the extent of 1 kcal per mol. If the solvation energies of Na⁺ and Cl^- ions are in the ratio 6 : 5, what is the enthalpy of hydration of sodium ion ?

In gas phase what is the maximum number of coplanar atoms in X.

A 200 ml aqueous solution of KCl was electrolysed for 16 min and 5 sec. If the pH of the final solution was 13 and volume of solution remains practically unchanged, then the average current used in ampere is.

Reaction of hydrated ferric chloride (FeCl₃. 6H₂O) with thionyl chloride gives anhydrous ferric chloride with evolution of hydrochloric acid (HCl) and sulphur dioxide (SO₂) gases. The number of sulphur dioxide (SO₂) molecules involved in the balanced chemical equation is.

A complex compound is represented as CoCl₃. xNH₃. Its 0.1 M solution in water shows depression in freezing point equal to 0.0558K. Assuming 100% ionisation of complex and coordination number of Co to be six, calculate the value of x. K_f for H₂O is 1.86 K kgmol^–1.

How many stereoisomers of Pt(gly)₂Cl₂ are possible?

ABC is an acute - angled triangle with circumcentre 'O' and orthocentre H. If AO = AH, then angle A is

The locus of the mid point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix

The eccentricity of the ellipse which meets the straight line  on the axis of x and the straight line  on the axis of y and whose axes lie along the axes of coordinates, is :

A circle is described whose centre is the vertex and whose diameter is three-quarters of the latus rectum of a parabola y² = 4ax. The common chord of the circle and parabola is

A (3, 2, 0), B (5, 3, 2) and C (-9, 6, -3) are three points forming a triangle and AD is bisector of the angle  AD meets BC at the point :

If p, q ∈{1,2,3,4} the number of equations of the form px² + qx + 1 = 0 having real roots is

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

If f(x) = a - (x - 3)^8/9, then maximum value of f(x) is:

The number of terms in the expansion of  which are integers, is given by

In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ is

There are unlimited number of identical balls of four different colours. How many arrangements of at most 8 balls in row can be made by using them?

The value of iⁱ is :

For what value of  'a' is the area bounded by the curve y = a²x² + ax + 1 and the straight line y = 0, x = 0 & x = 1 the least ?

If a₁, a₂, a₃,....a₂₀ are AMs between 13 and 67, then the maximum value of product a₁ a₂ a₃ ....a₂₀ is.

The area bounded by the curvesy = (x - 1)² ,  y = (x+1) ² and y = 1/4 is

Let z and ω be two non-zero complex numbers such that z = ω and arg z + arg ω = π, then z equals

If two distinct chords, drawn from the point (p, q) on the circle x² + y² = px + qy (where pq ≠ 0) are bisected by the x-axis, then

If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex is

The summation of series  upto infinite terms is equal to length of latus rectum of standard hyperbola with e = 2. If r is radius of director circle of its conjugate hyperbola, then r² =

Let  Find tr(A²⁰¹²)

Let P, Q be points of the ellipse 16x² + 25y² = 400 so that PQ = 96/25 and P, Q lie above major axis. Circle drawn with PQ as diameter touch major axis at positive focus. If m is slope of PQ then find the value of 1/|m|

if sin⁻¹x + sin⁻¹y + sin⁻¹z =π/2 then the value of x²+y²+z²+2xyz is equal to