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This mock test of SRMJEEE Maths Mock Test - 8 for JEE helps you for every JEE entrance exam.
This contains 35 Multiple Choice Questions for JEE SRMJEEE Maths Mock Test - 8 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

y = {x(x - 3)}^{2} increases for all values of x lying in the interval

Solution:

Since y = {x(x - 3)}^{2}

∴ dy dx = 2x (x - 3) (2x - 3)

For increasing function dy/dx > 0

or 2x (x - 3) (2x - 3) > 0

or x(x - 3) (x - 3/2) > 0

∴ x∈(0, 3/2) ∪ (3, ∞)

QUESTION: 2

The area bounded by the x-axis and the curve y = 4x - x^{2} - 3, is

Solution:

QUESTION: 3

If the sum of the coefficients in the expansion of (x+y)^{n} is 1024, then the value of the greatest coefficient in the the expansion is

Solution:

QUESTION: 4

If the equation 3x^{2} + xy - y^{2} - 3x + 6y + K = 0 represents pair of lines, then the value of K is

Solution:

QUESTION: 5

Solution:

QUESTION: 6

The equation of a circle with centre (4, 1) and having *3x + 4y -1 = 0* as tangent is

Solution:

QUESTION: 7

Solution:

QUESTION: 8

If |(z-1)/(z-i)| = 1, then the locus of z is

Solution:

QUESTION: 9

The focus of the parabola y^{2}-x-2y+2=0 is

Solution:

QUESTION: 10

If y=a cos (log x) + b sin (log x) where a,b are parametres, then x^{2}y+xy'

Solution:

QUESTION: 11

The derivative of

Solution:

QUESTION: 12

∫[(1)/(x-x^{2})]dx=

Solution:

QUESTION: 13

Solution:

QUESTION: 14

4tan⁻^{1}(1/5)-tan⁻^{1}(1/239)=

Solution:

QUESTION: 15

What is the value of

Solution:

QUESTION: 16

If f : ℝ → ℝ is defined by

then *f* is continuous on the set

Solution:

QUESTION: 17

If A is a non-singular, then adj A is

Solution:

QUESTION: 18

Let f(x) = x^{3} + 3x^{2} + 3x + 2. Then, at x = -1

Solution:

f(x) = (x+1)^{3} + 1 ∴ f'(x) = 3(x+1)^{2}.

f'(x) = 0 ⇒ x = -1.

Now, f" (-1 - ∈) = 3(-∈)^{2} > 0, f'(-1 + ∈)^{2} = 3∈^{2} > 0.

∴ f(x) has neither a maximum nor a minimum at x = -1.

Let f'(x) = φ ′ (x) = 3(x+1)^{2} ∴ φ ′ (x) = 6(x+1).

φ ′ (x) = 0 ⇒ x = -1

φ ′ (-1-∈) = 6(-∈) < 0, φ ′ (-1-∈) = 6∈ > 0

∴ φ (x) has a minimum at x = -1

QUESTION: 19

Can a quartile, a decile and a percentile be the median?

Solution:

QUESTION: 20

The gap between the highest and the lowest score is called

Solution:

QUESTION: 21

The number of 4-digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is

Solution:

Each even number must have 0, 2, 4 or 6 in is units place

Here total number of digits = 7

When 0 occurs at units place there is no restriction on other places and when 2 or 4 occurs at units place there is restriction on thousands' place as 0 can not be put at thousands' place

Case I When 0 occurs at units place:

∴ The number of numbers formed in this case

Case II. When 0 does not occur at units place:

The units' place can be filled up by any one of the three digits 2, 4 and 6 in 3 ways

∴ The number of numbers formed in this case

∴ The required number = 120 + 300 = 420

QUESTION: 22

The base of triangle is passing through a fixed point (a,b) and its sides are bisected at right angles by lines, y^{2} - 4xy - 5x^{2} = 0, then the locus of the vertex of triangle is

Solution:

y^{2} - 4xy - 5x^{2} = 0

⇒ (y - 5x) (y + x) = 0

y - 5x, cuts AB at M at right angle

and y + x = 0 cuts AC at N at right angle

By collinearity of (x_{1}, y_{1}), (x_{2}, y_{2}), (a, b) we get h = x, k = y

2x^{2} + 2y^{2} + (3a + 2b)x + (2a - 3b)y = 0

QUESTION: 23

If two dice are rolled then the probability that their sum is a prime number is

Solution:

QUESTION: 24

The diameter of the circumcircle of the triangle whose sides 61, 60, 11 is

Solution:

QUESTION: 25

If α , β are the roots of *x ^{2} - 2x* + 4 = 0 then α

Solution:

QUESTION: 26

If the roots of the equation x^{3} - 12x^{2} + 39x - 28 = 0 are in A.P., then their common difference will be

Solution:

QUESTION: 27

Which one of the following is (A - B) ∪ (B - A)?

Solution:

QUESTION: 28

Solution:

QUESTION: 29

Lines 2x+y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent

Solution:

QUESTION: 30

The tangent to the curve x=at^{2}, y=2at is perpendicular to x-axis, then its point of contact is

Solution:

QUESTION: 31

A random variable *X* has the following distribution

The value of *c* is

Solution:

QUESTION: 32

If tan2θ tanθ=1, the general value of θ is

Solution:

QUESTION: 33

If 4 sinθ=3 cosθ, then sec^{2}θ/4[1-tan^{2}θ] is

Solution:

QUESTION: 34

If a,b,c are the position vectors of vertices of a ∆ABC, the vectorial area of ∆ABC is

Solution:

QUESTION: 35

If the modulus of a and b are equal and angle between them is 120°, and a.b=-8, then the value of |a| is

Solution:

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