PCM - Mock Test (April 30) - JEE MCQ

Explanation:Position-time graph of horizontal straight line parallel to time axis represents that the position of the body does not changes with the passage of time. So it represents the rest state of motion.It means velocity of object is zero.

Explanation:To describe motion along a straight line, we can choose an axis, say X-axis, so that it coincides with the path of the object. We then measure the position of the object with reference to a conveniently chosen origin, say O,  Positions to the right of O are taken as positive and to the left of O, as negative.

Explanation:

Acceleration is the rate of change of velocity with time.It is a vector quantity.

Average acceleration is the change in velocity per unit time over an interval of time.

Let initial velocity at time interval t​​​​​​₁ is v​​​​​​₁ and final velocity at time interval t​​​​​₂ is v​​​​​​₂ Then

Explanation:Path length is defined as the total length of the path traversed by an object.

Unlike displacement, which is the total distance an object travels from a starting point, path length is the total distance travelled, regardless of where it travelled.

Explanation:When velocity – time graph is plotted for an object moving with uniform acceleration, the slope of the graph is a straight line. 

The wavelength λ is inversely proportional to the square root of kinetic energy. So if KE is increased 4 times, the wavelength becomes half.

λ∝1/√KE

Hence Option A is the answer.

Given m_p = 1.67×10^-27kg
h = 6.63×10^-34Js
v = 1.0×10³ms-1

We know wavelength λ = h/mv
∴λ = 6.63×10^-34/(1.67×10^-27 × 1.0×10³)
= 0.40×10^-10
≈ 0.40nm

Hence, Option (B) is the Correct Answer.

Correct Answer is A.

Number of orbitals in a shell = n² = (5)² = 25

n = 6, l = 2 means 6d → will have 5 orbitals. 

∴ max 10 electrons can be accommodate as each orbital can have maximum of 2 electrons. 

• An atom consists of a positively charged sphere with electrons filled into it. The negative and positive charges present inside an atom are equal and as a whole, an atom is electrically neutral.
• Thomson’s model of the atom as compared to plum pudding and watermelon.
• He compared the red edible part of the watermelon to a positively charged sphere whereas the seeds of watermelon to negatively charged particles.

• Concept of electrons moving in a circular path of fixed energy called orbits was put forward by Bohr and not derived from Rutherford's scattering experiment.
• Out of a large number of circular orbits theoretically possible around the nucleus.
• The electron revolves only in those orbits which have a tired value of energy Hence, these orbits are called energy level or stationary states.

The charge on electrons was determined by Milliken by using an oil drop experiment.

• Tritium (³H) is the only radioactive isotope of hydrogen.
• The nucleus of a tritium atom consists of a proton and two neutrons.

= 4000/2000
= 2

A relation R on a non empty set A is said to be reflexive if fx Rx for all x ∈ R, Therefore , R is not reflexive.
A relation R on a non empty set A is said to be symmetric if fx Ry ⇔ yRx, for all x, y ∈ R Therefore, R is not symmetric.
A relation R on a non empty set A is said to be antisymmetric if fx Ry and y Rx ⇒ x = y, for all x, y ∈ R. Therefore, R is not antisymmetric.

If R is a relation from A→B and S is a relation fromB→C, then S ^∘ R is a composite function from A to C.

y is defined  If -x ≥ 0, i.e.

By definition, The Signum function =  

A relation R on a non empty set A is said to be reflexive iff xRx for all x ∈ R . A relation R on a non empty set A is said to be symmetric iff xRy ⇔ yRx, for all x , y ∈ R .
A relation R on a non empty set A is said to be transitive iff xRy and yRz ⇒ xRz, for all x ∈ R. An equivalence relation satisfies all these three properties.
None of the given relations satisfies all three properties of equivalence relation.

Here * is commutative as b*a = |b−a|−1 = |a−b|−1 = a∗b.
Because ,|−x| = |x| for all x ∈ R.

Let T be the set of all triangles in a plane with R a relation in T given by R = {(T₁, T₂): T₁ is congruent to T₂}. (T₁T₂) ∈ R iff T₁ is congruent to T₂. 
Reflexivity :T₁≅T₁ ⇒ (T₁T₁) ∈ R . Symmetry :(T₁, T₂)∈ R ⇒T₁≅T₂ ⇒ T₂≅T₁ ⇒ (T₂, T₁) ∈ R
Transitivity :(T₁,T₁) ∈ R and (T₂, T₃) ∈ R ⇒ T₁≅T₂ and T₂≅T₃ ⇒ T₁≅T₃ ⇒ (T₁, T₃) ∈ R .
Therefore, R is an equivalence relation on T.

The given function is defined as Signum function. i.e.

domain is R and Range is {-1 , 0 , 1}.

For even function : f(-x) = f(x) , therefore, f(- x) = (− x)²+ sin (− x)
= x²−sin x ≠ f(x).
For an odd function : f(-x) = - f(x) , therefore, f(-x) = (− x)²+ sin (− x)
= x²− sin x
 ≠ − f(x).
Therefore f(x) is neither even nor odd.

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation is given by x = y + 3,from{8, 10, 12} to {11, 12, 13} ⇒ relation = {(8,11),(10,13)}.

The only possible integral values of sin x are {-1 ,0, 1}.