Practice problems on JEE Mains, JEE Mains 2021 Aug 27 Shift 1

Question 1

Two ions of masses 4 amu and 16 amu have charges +2 e and +3 e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

Accepted Answer

Lighter ion will be deflected more than heavier ion

Answer

No ion will be deflected

Answer

Lighter ion will be deflected less than heavier ion

Answer

Both ions will be deflected equally.

Question 2

There are 1010 radioactive nuclei in a given radioactive element. Its half-life time is 1 minute. How many nuclei will remain after 30 seconds? (2​=1.414)

Accepted Answer

7×109

Answer

4×1010

Answer

105

Answer

2×1010

Question 3

In the following sequence of reactions of P is:

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 4

The correct statement about (A), (B), (C) and (D) is:

Accepted Answer

(B) and (C) are tranquilizers

Answer

(B), (C) and (D) are tranquillizers

Answer

(A), (B) and (C) are narcotic analgesics

Answer

(A) and (D) are tranquilizers

Question 5

A tangent and a normal are drawn at the point P(2,−4) on the parabola y2=8x, which meet the directrix of the parabola at the points A and B respectively. If Q(a,b) is a point such that AQBP is a square, then 2a+b is equal to:

Accepted Answer

-16

Answer

-18

Answer

-12

Answer

-20

Question 6

Let A be a fixed point (0,6) and B be a moving point (2t , 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y -axis at C . The locus of the mid-point P of MC is:

Accepted Answer

2x2+3y−9=0

Answer

3x2−2y−6=0

Answer

3x2+2y−6=0

Answer

2x2−3y+9=0

Question 7

In polythionic acid, H2​ Sx​O6​(x=3 to 5) the oxidation state(s) of sulphur is/are:

Accepted Answer

0 and +5 only

Answer

+3 and +5 only

Answer

+5 only

Answer

+6 only

Question 8

A balloon carries a total load of 185 kg at normal pressure and temperature of 27∘C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is −7∘C. Assuming the volume constant ?

Accepted Answer

123.54 kg

Answer

214.15 kg

Answer

219.07 kg

Answer

181.46 kg

Question 9

Calculate the amount of charge on capacitor of 4μF. The internal resistance of battery is 1Ω :

Accepted Answer

8μC

Answer

Zero

Answer

16μC

Answer

4μC

Question 10

In which one of the following molecules strongest back donation of an electron pair from halide to boron is expected?

Accepted Answer

BF3​

Answer

BI3​

Answer

BBr3​

Answer

BCl3​

Question 11

A uniformly charged disc of radius R having surface charge density σ is placed in the x y plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :

Accepted Answer

E=2ε0​σ​(1−(Z2+R2)1/2Z​)

Answer

E=2ε0​σ​(z2+R21​)+z21​

Answer

E=2σ2ε0​​((Z2+R2)1/21​+Z)

Answer

E=2ε0​σ​(1+(Z2+R2)1/2Z​)

Question 12

Moment of inertia of a square plate of side ℓ about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:

Accepted Answer

32​Mℓ2

Answer

12Mℓ2​

Answer

6Mℓ2​

Answer

Mℓ2