Practice problems on JEE Mains, JEE Mains 2021 Feb 24 Shift 1

Question 1

The equation of the plane passing through the point (1,2,-3) and perpendicular to the planes 3x + y - 2z = 5 and 2x - 5y - z = 7, is:

Accepted Answer

11x+y+17z+38=0

Answer

3x−10y−2z+11=0

Answer

6x−5y−2z−2=0

Answer

6x−5y+2z+10=0

Question 2

Given below are two statements:Statement-I : Colourless cupric metaborate is reduced to cuprous metaborate in a luminous flame.Statement-II : Cuprous metaborate is obtained by heating boric anhydride and copper sulphate in a non-luminous flame.In the light of the above statements, choose the most appropriate answer from the options given below.

Accepted Answer

Both statement I and statement II are false

Answer

Statement I is false but statement II is true

Answer

Both statement I and statement II are true

Answer

Statement I is true but statement II is false

Question 3

The electrode potential of M2+/M of 3 d-series elements shows positive value for:

Accepted Answer

Cu

Answer

Zn

Answer

Co

Answer

Fe

Question 4

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of Oscillations will be :

Accepted Answer

AM+mM​​

Answer

AMM−m​​

Answer

AM−mM​​

Question 5

The locus of the mid-point of the line segment joining the focus of the parabola y2=4ax to a moving point of the parabola, is another parabola whose directrix is:

Accepted Answer

x=0

Answer

x=a

Answer

x=2a​

Answer

x=−2a​

Question 6

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :

Accepted Answer

21​

Answer

163​

Answer

321​

Answer

165​

Question 7

Match List I with List II

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :

Accepted Answer

1625

Answer

560

Answer

1050

Answer

575

Question 9

Let f:R→R be defined as f(x)=2x−1 and g:R−{1}→R be defined as g(x)=x−1x−21​​ Then the composition function f(g(x)) is :

Accepted Answer

One-one but not onto

Answer

Neither one-one nor onto

Answer

Onto but not one-one

Answer

Both one-one and onto

Question 10

The system of linear equations​3x−2y−kz=102x−4y−2z=6x+2y−z=5m​ is inconsistent if :

Accepted Answer

k=3,m=54​

Answer

k=3,m=54​

Answer

k=3,m∈R

Answer

k=3,m=54​

Question 11

The major components in "Gun Metal" are:

Accepted Answer

Cu ,Sn andZn

Answer

Cu , Ni andFe

Answer

Al , Cu ,Mg and Mn

Answer

Cu , Zn and Ni