COMEDK Mock Test - 2 - JEE MCQ

The explanation is the question itself. Inertia is a property of which it resists its change of state of rest or state of motion, so as soon as the person jumps the lower part immediately comes to rest by sharing contact with the ground the upper body due to inertia of motion resists its change in state of motion.

Value of the acceleration due to gravity at any latitude φ,
g' = g - ω²Rcos²φ; where φ is latitude.
There will be no change in gravity at poles as φ = 90°.
At all other points, as ω increases, 'g' will decrease.

Hence, if the objective lens and the eyepiece lens of a microscope are interchanged that will not meet the criterion of the telescope.

So, the reason is true. But the assertion is false.

Let time taken to ascent be t₁ and that to descent be t₂.
Height will be same, so

The argument in the trigonometric function should be a dimensionless quantity.
The dimensions of time (t)  angular velocity (ω) and amplitude (A) are [t] = [T], [ω] = [T^-1], [A] = [L]
A. The dimension of the argument in the equation:

Thus, option 'A' is not wrong on dimensional grounds.
B. In the equation: x = A / T sin (t/A), the dimension of the argument in the sine function is [t/A] = |T|/L

Thus, option 'B' is wrong on dimensional grounds.
C. The dimension of the argument in equation:

Thus, option 'C' is not wrong on dimensional grounds.
D. The dimension of the argument in equation: x = A sin (ωt) is [ωt] =  [T^-1] [T] = dimensionless quantity
Thus, option 'D' is not wrong on dimensional ground. All the equations, except x = A/T sin (t/A) i.e. option 'B' have dimensionless argument.

Explanation:Motion is a change in position of an object with time. In order to specify position, we need to use a reference point and a set of axes. It is convenient to choose a rectangular coordinate system consisting of three mutually perpenducular axes, labelled X-, Y-, and Z- axes.

The point of intersection of these three axes is called origin (O) and serves as the reference point. The coordinates (x, y. z) of an object describe the position of the object with respect to this coordinate system.

To measure time, we position a clock in this system. This coordinate system along with a clock constitutes a frame of reference.

Work done in isothermal process on the gas,

Heat and work are treated as path functions in thermodynamics.
ΔQ = ΔU + ΔW
Since work done by gas depends on the type of process, i.e. path, and ΔU depends just on the initial and final states, ΔQ, i.e. heat, also has to depend on path.

N₁ + N₂ + N₃ + N₄ + N₅  =  Total ways – {when no odd}

Total ways = ⁹C₅

Number of ways when no odd number is selected is 0 (∵ only available even are 2,4,6,8) 

|x| + |y| = 1
Area enclosed = 4 × (1/2) x 1 x 1 = 2

⇒ x = 0
∵ x² + 5 = 0. Not possible ∀ x ∈ R