MET Mock Test - 10 Free Online Test 2026

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer?

(Speed of light = 3 × 10⁸ ms^–1)

Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness d/2 and of area equal to the area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

The equations of two waves are given by:
y₁ = 5 sin 2π(x - vt) cm
y₂ = 3 sin 2π(x - vt + 1.5) cm
These waves simultaneously pass through a string. The amplitude of the resulting wave is:

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The coefficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is _________ m.

The total current supplied to the circuit as shown in figure by the 5 V battery is __________ A.

A polysaccharide 'X' on boiling with dil. H₂SO₄ at 393 K under 2-3 atm pressure yields 'Y'. 'Y' on treatment with bromine water gives gluconic acid. 'X' contains β-glycosidic linkages only. Compound 'X' is

The metal ion (in gaseous state) with lowest spin-only magnetic moment value is

The intermediate X in the reaction

In the following structures, which one is having staggered conformation with maximum dihedral angle?

Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is _______%. (Nearest integer)

The magnitude of work done by a gas that undergoes reversible expansion along the path ABC shown in the figure is ______. (Nearest integer)

The sum of all the real roots of the equation (e^2x - 4)(6e^2x - 5e^x + 1) = 0 is

Let A be a 3 × 3 real matrix such that . If X = (x₁, x₂, x₃)^T and I is an identity matrix of order 3, then the system (A - 2I)X =  has

Let  R be defined by f(x) =  Then the value of α for which (fof)(x) = x, for all  is:

Let y = y(x) be the solution of the differential equation (x + 1)y' - y = e^3x(x + 1)², with y(0) = 1/3. Then, the point x = -4/3 for the curve y = y(x) is:

If y = tan^-1 (sec x³ - tan x³), 

Let f(x) = (sin(tan^-1x) + sin(cot^-1x))² - 1, |x| > 1. If  (sin^-1(f(x)) and y(√3) = π/6, then y(-√3) is equal to

Let x * y = x² + y³ and (x * 1) * 1 = x * (1 * 1), then value of 2sin^-1 

Let y = y(x) be a solution of the differential equation  = 0, |x| < 1. If y(1/2) = √3/2, then  is 

Let  ai > 0, i = 1, 2, 3 be a vector which makes equal angles with the coordinates axes OX, OY and OZ. Also, let the projection of  on the vector  be 7. Let  be a vector obtained by rotating  with 90°. If  and x-axis are coplanar, then projection of a vector  on  is equal to

Let  be unit vectors. If  be a vector such that the angle between  and  is π/12, and , then |6 |² is equal to:

Where [t] denotes greatest integer ≤ t. If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, then the ordered pair (m, n) is

Let P be a variable point on the parabola y = 4x² + 1. Then the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is:

Let a circle C touch the lines L₁ : 4x - 3y + K₁ = 0 and L₂ : 4x - 3y + K₂ = 0, K₁, K₂ ∈ R. If a line passing through the centre of the circle C intersects L₁ at (-1, 2) and L₂ at (3, -6), then the equation of the circle C is

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, and the ratio of other two observations is (k : 2k+1). Find the value of k.

Let A be a 3 x 3 matrix having entries from the set {-1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ______

If Sentence (C), "Ever since the price of bitcoins skyrocketed from a little under $1,000 (around ₹63,400 now) in 2016 to touch nearly $20,000 last year, people have been posing a Hamlet kind of question: to buy or not to buy?" is the first sentence, what is the order of other sentences after rearrangement?

A. Some have explicitly warned investors to exercise caution, while those like the Indian government have begun imposing a tax on the gains from the sale of bitcoins.
B. Their dilemma is understandable.
C. Ever since the price of bitcoins skyrocketed from a little under $1,000 (around ₹63,400 now) in 2016 to touch nearly $20,000 last year, people have been posing a Hamlet kind of question: to buy or not to buy?
D. On the other hand, there is the nagging feeling that one may end up investing in a virtual currency whose price is extremely volatile and whose true value cannot be assessed.
E. Adding to the confusion, most governments remain non-committal on the legality of bitcoins since it is hotly regulated by central banks.
F. On the one hand, there is the fear of losing out on an opportunity to make money hand over fist by investing or trading in bitcoins since their price rose by around 20 fold since the start of 2017.

If U.P.S.C. stands for 21, 16, 19, 3, then C.S.I.R stands for?

Five houses lettered A, B, C, D and E are built in a row next to each other. The houses are lined up in the order A, B, C, D and E. Each of the five houses has a coloured chimney. The roof and chimney of each house must be painted as follows :
(i)    The roof must be painted green, red or yellow.
(ii)    The chimney must be painted white, black or red.
(iii)    No house may have the same colour chimney as the colour of roof.
(iv)    No house may use any of the same colours that the every next house uses.
(v)    House E has a green roof.
(vi)    House B has a red roof and a black chimney.

Which of the following is not true?

(A) At least two houses have black chimney.
(B) At least two houses have red roofs.
(C) At least two houses have white chimneys.
(D) At least two houses have green roofs.

Directions: Choose the word that is incorrectly spelled.