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SRMJEEE Maths Mock Test - 3 - JEE MCQ


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30 Questions MCQ Test - SRMJEEE Maths Mock Test - 3

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SRMJEEE Maths Mock Test - 3 - Question 1

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 1


SRMJEEE Maths Mock Test - 3 - Question 2

If the matrix is the adjoint of the square matrix and is the value of the determinant of , then what is equal to ?

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 2
Since, adjoint of the square matrix A is B

SRMJEEE Maths Mock Test - 3 - Question 3

If sin[(π/4)cotθ] = cos[(π/4)tanθ], then θ=

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 3

SRMJEEE Maths Mock Test - 3 - Question 4

The area enclosed between the ellipse x2 + 9y2 = 9 and the straight line x + 3y = 3, in the first quadrant is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 4

The intersection points of x2 + 9y2 = 9  and x + 3y = 3 are (0,1) and (3,0).

The area A is given by the integral of the difference between the top and bottom functions from 0 to 3:

A = ∫ from 0 to 3 of [ (1/3) * sqrt(9 - x²) - (1 - x/3) ] dx

Now simplify the expression inside the integral:

This becomes:
A = ∫ from 0 to 3 of [ (1/3) * sqrt(9 - x²) - 1 + x/3 ] dx

Now break the integral into three simpler parts:

  1. First part: (1/3) * ∫ sqrt(9 - x²) dx from 0 to 3

  2. Second part: ∫ 1 dx from 0 to 3

  3. Third part: (1/3) * ∫ x dx from 0 to 3

Now evaluate each part:

  1. ∫ sqrt(9 - x²) dx from 0 to 3 = (9π) / 4

  2. ∫ 1 dx from 0 to 3 = 3

  3. ∫ x dx from 0 to 3 = (1/2) * (3²) = 9/2

Put them all together:

  • First term: (1/3) * (9π / 4) = (3π) / 4

  • Second term: -3

  • Third term: (1/3) * (9/2) = 3/2

Now compute:

A = (3π) / 4 - 3 + 3/2

Convert everything to a common denominator:

  • (3π)/4 is already in 4ths

  • 3 = 6/2

  • 3/2 stays the same

So:
A = (3π)/4 - 6/2 + 3/2 = (3π)/4 - 3/2

SRMJEEE Maths Mock Test - 3 - Question 5

a.b = 0, then

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 5

If a.b = 0
⇒ ab(cosθ) = 0
or cosθ = 0
⇒ θ = 90°
Therefore, a⊥b

SRMJEEE Maths Mock Test - 3 - Question 6

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 6

SRMJEEE Maths Mock Test - 3 - Question 7

If 0 ≤ x ≤ π and 81 sin²(x) + 81 cos²(x) = 30, then what is the value of x?

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 7

We know that:

sin²x + cos²x = 1

So the left-hand side of the equation becomes:

81 × (sin²x + cos²x) = 81 × 1 = 81

This means the value of the left-hand side is always 81, no matter what x is.

But the right-hand side of the equation is 30, which is clearly not equal to 81.

Conclusion:

There is no real value of x in the interval [0, π] that can satisfy the equation.

No solution exists.

SRMJEEE Maths Mock Test - 3 - Question 8

9 + 16/2! + 27/3! + 42/4! + ..... ∞ is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 8

SRMJEEE Maths Mock Test - 3 - Question 9

If a line passes through points (4,3) and (2,λ) and perpendicular to y=2x+3, then λ=

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 9

Two lines are perpendicular then product of slope be -1

m1​m​= −1

(3 − λ)/2​ × 2 = −1

3 − λ = −1

3 + 1 = λ.

λ = 4.

SRMJEEE Maths Mock Test - 3 - Question 10

(secA+tanA-1)(secA-tanA+1)-2 tanA=

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SRMJEEE Maths Mock Test - 3 - Question 11

The circles x2 + y2 - 12x -12y = 0 and x2 + y2 + 6x + 6y = 0

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 11


SRMJEEE Maths Mock Test - 3 - Question 12

In an Argand plane the inequality π/4 < arg (z) < π/3 represent the region bounded by

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 12

We have π/4 ​< arg (z) < π/3​
Let z = x + iy
∴ arg (z) = tan-1(y/x​)
The given inequality can be written as
π/4 ​< tan-1(y/x​) < π/3​
⇒ tan(π/4) ​< y/x ​< tan(π/3)​
⇒ 1 < y/x ​< √3​
⇒ x < y < √3​x
This inequality represents the region between the lines
 y = x and y = √3​x

SRMJEEE Maths Mock Test - 3 - Question 13

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SRMJEEE Maths Mock Test - 3 - Question 14

Length of tangent drawn from (5,1) to the circle x+ y+ 6x - 4y - 3 = 0 is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 14

Given circle is  x+ y+ 6x - 4y - 3 = 0 .....(i)
Given point is (5, 1) Let P = (5,1)
Now length of the tangent from P(x, y) to circle (i) = √ x+ y+ 2gx + 2fy + c​.
Now length of the tangent from P(5, 1) to circle (i) = √ 52+12+ 6.5 − 4.1 − 3​ = 7

SRMJEEE Maths Mock Test - 3 - Question 15

A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 15

The total number of ways in which 5 person can be chosen out of 9 person is 9C5 = 126
The couple serves the committee in 7C3 x 2C2 = 35 ways
The couple does not serve the committee in
7C5 - 7C2 = 21 ways
Since the couple will either be together or not at all
∴ favourable number of cases = 35 + 21 = 56
∴ required porbability = 56 126 = 4/9

SRMJEEE Maths Mock Test - 3 - Question 16

(d/dx){log(secx+tanx)}=

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 16

 

SRMJEEE Maths Mock Test - 3 - Question 17

How many even numbers can be formed by using all the digits 2, 3, 4, 5, 6?

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 17

For a number to be even its last digit should be divisible by 2.
Therefore, only 2,4,6 can be used as last digits.
Number of such combinations,
⇒ 4!×3 = 24×3 = 72

SRMJEEE Maths Mock Test - 3 - Question 18

Suppose that g (x) = 1 + √x and f (g(x)) = 3 + 2 √x + x, then f (x) is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 18

Given, g(x) = 1 + √x​

And f(g(x)) = 3 + 2√x​ + x

Now, f(g(x)) = 3 + 2√x​ + x [ terms splitting]

f(g(x)) = 2 + (1 + 2√x​ + x)

Also, (1 + √x​)2 = 1 + x + 2√x​

⇒ f(g(x)) = 2 + (1 + √x​)2

⇒ f(x) = 2 + x2

f(x) = x2 + 2​

SRMJEEE Maths Mock Test - 3 - Question 19

A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 19

∵ probability for odd = p

∴ probability for even = 2p

∵ p + 2p = 1

⇒ 3p = 1

⇒ p = 1/3​

∴ probability for odd = 1/3​ , probability for even = 2/3​

Sum of two no. is even means either both are odd or both are even

∴ required probability = (1/3​ × 1/3)​ + (2/3 ​× 2/3) ​= 1/9 ​+ 4/9 ​= 5/9​

 

SRMJEEE Maths Mock Test - 3 - Question 20

If a, b are the roots of x2 + x + 1 = 0 then a2 + b2 =

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 20

Sum of the roots ⇒ a+b = −1                ...(1)
Product of the roots ⇒ ab = 1               ...(2)
We know that,
(a+b)= a+ b+ 2ab
⇒ a+ b= (a+b)− 2ab
Substituting (1) and (2) in the above equation, we get
⇒ a+ b= (−1)− 2(1)
∴ a+ b= −1 

SRMJEEE Maths Mock Test - 3 - Question 21

Let Aand B be two matrices of order n×n. Let A be non-singular and B be singular. Consider the following:
1.  AB is singular
2. AB is non-singular
3. A−1 B is singular
4. A−1 B is non singular Which of the above is/ are correct?

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 21

Since, |B| = 0
AB and A(−1)B is singular ie their det = 0

SRMJEEE Maths Mock Test - 3 - Question 22

If y =  , find dy/dx

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 22

SRMJEEE Maths Mock Test - 3 - Question 23

The differential equation of the family of lines through the origin is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 23

Let y = mx be the family of lines through origin. Therefore, dy/dx = m
Eliminating m, we get y = (dy/dx).x or x(dy/dx) – y = 0.

SRMJEEE Maths Mock Test - 3 - Question 24

The slope of the tangent of the curve at the point where x = 1 is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 24

 

SRMJEEE Maths Mock Test - 3 - Question 25

If  then what is A(adj A) equal to

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 25

Let 
We have
If A is a square matrix of order n then A(adjA) = |A|.In
Here, n = 2

SRMJEEE Maths Mock Test - 3 - Question 26

The ratio in which the line joining the points (a,b,c) and (-a,-c,-b) is divided by the xy-plane is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 26

Let λ:1 be the ratio in which the line joining the points (a,b,c) and (-a, -c, -b) is divided by xy- plane.

SRMJEEE Maths Mock Test - 3 - Question 27

The differential equation y(dy/dx) + x = c represent

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 27

ydy = (c−x)dx
Integrating both sides,
∫ydy = ∫(c−x)dx
y2​/2 = cx − x2​/2 + k
x2/2 + y2/2 ​− cx = k
x2 + y2 − 2cx = 2k
(x−c)2 + y2 = 2k + c2
This is equation of a circle with center on x-axis.

SRMJEEE Maths Mock Test - 3 - Question 28

The solution of differential equation (dy/dx) = [(x(2logx + 1)) / (siny + ycosy)] is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 28

(siny+ y.cosy)dy = [x(2logx + 1)]dx

Integrating both sides, we get

SRMJEEE Maths Mock Test - 3 - Question 29

Out of 6 boys and 4 girls a group of 7 is to be formed. In how many ways can this be done if the group is to have a majority of boys?

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 29

The boys are in majority, if groups formed are 4B 3G, 5B 2G, 6B 1G.
Total number of such combinations
6C4 x 4C3 + 6C5 x 4C2 + 6C6 x 4C1
⇒ 15 x 4 + 6 x 6 + 1 x 4
⇒ 60 + 36 + 4
⇒ 100

SRMJEEE Maths Mock Test - 3 - Question 30

The third term of a G.P. is 3. The product of its first five terms is

Detailed Solution for SRMJEEE Maths Mock Test - 3 - Question 30

Third term of G.P. = ar= 3

General term = arn−1

Product of first five terms = a5⋅r0+1+2+3+4

= a5r10=(ar2)5

= (3)5

= 243.

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