MET Mock Test - 5 - JEE MCQ

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of de-Broglie wavelength associated with the electron and the wavelength of the photon is:
(c = speed of light in vacuum)

A particle is projected with a velocity v, so that its range on a horizontal plane is twice the greatest height attained. If g is acceleration due to gravity, then its range is   

If the magnetic field in a plane electromagnetic wave is given by  = 3 × 10^-8 sin (1.6 × 10³x + 48 × 10¹⁰t)  T, then what will be the expression for electric field?

In a spring gun having spring constant 100 N/m, a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground, the value of d is _______________ m. (g = 10 m/s²)

A body having specific charge 8 μC/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ______________ s.

The K_sp for bismuth sulphide (Bi₂S₃) is 1.08 × 10^-73. The solubility of Bi₂S₃ in mol L^-1 at 298 K is

In the analysis of an organic compound, it was found that it contains 7 carbon atoms, there are two C = C bonds and one C ≡ C bond. This compound is a hydrocarbon. 
Hydrocarbons have only carbon and hydrogen elements. On structural analysis it was found that it is covalent in nature and expected structure is given above. The ratio between the pure and hybrid orbitals is?

Which one of the following compounds is used as a chemical in certain type of fire extinguishers?

Given below are two statements.
Statement I: The presence of weaker π-bonds make alkenes less stable than alkanes.
Statement II: The strength of the double bond is greater than that of carbon-carbon single bond.
In the light of the above statements, choose the correct answer from the options given below.

PCl₅(g) → PCl₃(g) + Cl₂(g)
In the above first order reaction, the concentration of PCl₅ reduces from initial concentration 50 mol L^-1 to 10 mol L^-1 in 120 minutes at 300 K. The rate constant for the reaction at 300 K is X × 10^-2 min^-1. The value of x is ___________.(Nearest integer)
[Given log 5 = 0.6989]

The concentration of dissolved oxygen (DO) in cold water can go upto: (Answer up to the nearest integer)

Let A and B are two events and P(A′) = 0⋅3, P(B) = 0⋅4, P(A∩B′) = 0⋅5 then P(A∪B′) is:

Let ϕ(x) be the inverse of the function f(x) and   is equal to

What will be the sum of series  given 

If U = [2 −3 4], X = [0  2  3],  , then UV + XY

Directions: The following question has four choices, out of which ONLY ONE is correct.
Find the approximate value of  where [ ] denotes g.i.f.

If ω ≠ 1 is a cube root of unity and satisfies and  then the value of  is

In a sequence of number P, Q, R, S, T, U, V, ..., Z, the value of each subsequent number is 3 more than the product of previous and 3. If it is known that T is equal to 21, what is the value of P + Q?

If e and e′ are the respective eccentricities of hyperbolas , then

If the sum of the squares of the intercepts on the axes cut off by the tangent to the curve x^1/3 + y^1/3 = a^1/3 (a > 0) at (a/8, a/8) is 2, then the value of 'a' is

The number of solutions of the equation  is/are

Let A = {a_ii} be a 3 × 3 matrix, where

then det(3 adj(2A^-1)) is equal to ________.

Let  is a vector such that  and   + 21 = 0, then  is equal to

Find the Antonym of FLEXIBLE

Find the Syonym of AMBITION

Improve the sentence by choosing best alternative for capitalised part of the sentence.

After a few minutes the unconscious boxer began to come OUT.

find the synonym of DELECTABLE