Practice problems on JEE Mains, JEE Mains 2021 July 22 Shift 2

Question 1

Let L be the line of intersection of planes r⋅(i^−j^​+2k^)=2 and r⋅(2i^+j^​−k^)=2. If P(α,β,γ) is the foot of perpendicular on L from the point (1,2,0) then the value of 35(α+β+γ) is equal to :

Accepted Answer

119

Answer

134

Answer

101

Answer

143

Question 2

Sulphide ion is soft base and its ores are common for metals.(a) Pb (b) Al (c) Ag (d) MgChoose the correct answer from the options given below:

Accepted Answer

(a) and (c) only

Answer

(c) and (d) only

Answer

(a) and (d) only

Answer

(a) and (b) only

Question 3

The water having more dissolved O2​ is :

Accepted Answer

Water at 4ºC

Answer

Polluted water

Answer

Boiling water

Answer

Water at 80ºC

Question 4

What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km ? The average population density around the tower is 2000/km2 and the value of R⊖​=6.5×106 m.

Accepted Answer

Height = 1731 m, Population Covered = 1413×105

Answer

Height = 1600 m, Population Covered = 2×105

Answer

Height = 1800 m, Population Covered = 1413×108

Answer

Height = 1241 m, Population Covered = 7×105

Question 5

Isotopes of hydrogen which emits low energy β – particle with half life greater than 12 year is/are :

Accepted Answer

Tritium

Answer

Deuterium

Answer

Deuterium and Tritium

Answer

Protium

Question 6

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such formed matrices have all different entries and are non-singular, is:

Accepted Answer

16243​

Answer

8122​

Answer

8123​

Answer

16245​

Question 7

Which one of the following statements for D.I. Mendeleeff, is incorrect?

Accepted Answer

At the time, he proposed Periodic Table of elements structure of atom was known

Answer

He authored the textbook-Principles of Chemistry

Answer

Element with atomic number 101 is named after him.

Answer

He invented accurate barometer

Question 8

Thiamine & pyridoxine are also known respectively as:

Accepted Answer

Vitamin B1 and Vitamin B6

Answer

Vitamin B2 and Vitamin E

Answer

Vitamin B6 and Vitamin B2

Answer

Vitamin E & Vitamin B2

Question 9

Match List-I with List-II :Choose the correct answer from the options given below:

Accepted Answer

(a) - (ii), (b) - (iii), (c) - (iv), (d) - (i)

Answer

(a) - (ii), (b) - (i), (c) - (iv), (d) - (iii)

Answer

(a) - (iii), (b) - (i), (c) - (iv), (d) - (ii)

Answer

(a) - (iii), (b) - (iv), (c) - (ii), (d) - (i)

Question 10

If the shortest distance between the straight lines 3(x−1)=6(y−2)=2(z−1) and 4(x−2)=2(y−λ) =(z−3),λ∈R is 38​1​, then the integral value of λ is equal to :

Accepted Answer

3

Answer

2

Answer

5

Answer

– 1

Question 11

Let n denote the number of solutions of the equation z2+3zˉ=0, where z is a complex number. Then value of ∑k=0∞​nk1​ is equal to:

Accepted Answer

34​

Answer

23​

Answer

2

Answer

1

Question 12

Let a vector a be coplanar with vectors b=2i^+j^​+k^ and c=i^−j^​+k^. If a is perpendicular to d=3i^+2j^​+6k^, and ∣a∣=10​. Then a possible value of [abc∣+∣abd∣+∣acd∣ is equal to :

Accepted Answer

– 42

Answer

– 38

Answer

– 40

Answer

– 29

Question 13

Let the circle S: 36x2+36y2−108x+120y+C=0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x−2y=4 $ and 2x−y=5 lies inside the circle S, then:

Accepted Answer

100 < C < 156

Answer

925​<C<313​

Answer

100 < C < 165

Answer

81 < C < 156

Question 14

Choose the correct option :

Accepted Answer

True dip is less than the apparent dip

Answer

True dip is always equal to apparent dip

Answer

True dip is always greater than the apparent dip

Answer

True dip is not mathematically related to apparent dip

Question 15

Match List-I with List-II :Choose the correct answer from the option given below:

Accepted Answer

(a)-(ii); (b)-(i); (c)-(iv); (d)-(iii)

Answer

(a)-(iv); (b)-(iii); (c)-(ii); (d)-(i)

Answer

(a)-(ii); (b)-(i); (c)-(iii); (d)-(iv)

Answer

(a)-(iii); (b)-(i); (c)-(iv); (d)-(ii)

Question 16

Let a line L:2x+y=k,k>0 be a tangent to the hyperbola x2−y2=3. If L is also a tangent to the parabola y2=αx, then α is equal to :

Accepted Answer

–24

Answer

24

Answer

12

Answer

–12