MET Mock Test - 10 - JEE MCQ

Two rods (one semi-circular and other straight) of the same material and of same cross-sectional area are joined as shown in the diagram. The points A and B are maintained at different temperatures. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P₂ be the pressure inside the inner bubble and P₀ be the pressure outside the outer bubble. Radius of another bubble with pressure difference P₂ - P₀ between its inside and outside would be

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

A force on an object of mass 100 g is  N. The position of that object at t = 2 s is  N. The position of that object at t = 2 s is  m after starting from rest. The value of a/b will be ____________.

A monoatomic gas performs a work of Q/4, where Q is the heat supplied to it. The molar heat capacity of the gas will be ____ R during this transformation, where R is the gas constant.(In integers)

During halogen test, sodium fusion extract is boiled with concentrated HNO₃ to

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 stoichiometry and solubility product of a salt with the solubility curve given below is respectively:

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

Which of the following ketones will NOT give enamine on treatment with secondary amines?
[where t-Bu is -C(CH₃)₃]

Which of the following is an example of conjugated diketone?

The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is x × 10^-8 m. The value of x is __________. (Nearest Integer)
(Given: Energy of the electron in the first shell of the hydrogen atom is -2.2 × 10^-18 J; h = 6.63 × 10^-34 Js and c = 3 × 10⁸ ms^-1)

At 300 K, a sample of 3.0 g of gas A occupies the same volume as 0.2 g of hydrogen at 200 K at the same pressure. The molar mass of gas A is ______ g mol^-1. (Nearest integer)
Assume that the behaviour of gases as ideal. (Given: The molar mass of hydrogen (H₂) gas is 2.0 g mol^-1)

Consider the following statements:
A: Rishi is a judge.
B: Rishi is honest.
C: Rishi is not arrogant.
The negation of the statement 'if Rishi is a judge and he is not arrogant, then he is honest' is:

If the equation x² + bx + 45 = 0 (b ∈ R) has conjugate complex roots and they satisfy |z + 1| = 2,√10 then

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

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

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:

If a tangent of slope 2 of the ellipse  is normal to the circle x² + y² + 4x + 1 = 0, then the maximum value of ab is

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: Read the passage carefully and choose the best answer to the given question out of the four alternatives.

A hybrid vehicle is a vehicle which uses two or more kinds of propulsion. Most hybrid vehicles use a conventional gasoline engine as well as an electric motor to provide power to the vehicle. These are usually called hybrid-electric-vehicles, or HEVs. Hybrids use two types of propulsion in order to use gasoline more efficiently than conventional vehicles do. Most hybrid vehicles use the gasoline engine as a generator which sends power to the electric motor. The electric motor then powers the car. In conventional vehicles, the gasoline engine powers the vehicle directly. Since the main purpose of using a hybrid system is to efficiently use resources, most hybrid vehicles also use other efficient systems. Most hybrid vehicles have regenerative braking systems. In conventional vehicles, the gasoline engine powers the brake, and the energy used in braking is a lot. In regenerative braking system, the energy lost in braking is sent back into the electrical battery for use in powering the vehicle. Some hybrid vehicles use periodic engine shutoff as a gas-saving feature. When the vehicle is in idle, the engine temporarily turns off. When the vehicle is put back in gear, the engine comes back on. Some hybrids use tires made of a stiff material which rolls easily and prevents drag on the vehicle. Since hybrid vehicles use less gasoline than conventional vehicles, they put fewer emissions into the atmosphere than conventional vehicles do. As hybrids become more popular, conventional vehicles are being used less, and the level of emissions being put into the air is decreasing. Hybrid vehicles are an example of an energy efficient technology that is good for both consumers and the environment.

Q. The difference between hybrid and conventional vehicles is that