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This mock test of Mathematics MCQ 1 for IIT JAM helps you for every IIT JAM entrance exam.
This contains 21 Multiple Choice Questions for IIT JAM Mathematics MCQ 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If Z is a complex number, then the minimum value of |z| + |z-l| is

Solution:

Note that

, hence minimum value is 1 and it is attained at Z = 0, 1/2

QUESTION: 2

The product of all real roots of the equation x^{2} - |x| - 6 = 0 is

Solution:

Equation is x^{2} - |x| - 6 = 0

Case I: x > 0. then we have

x^{2} - x - 6 = 0 (lx| = x)

⇒ (x-3)(x+2) = 0

⇒ x = 3 is the solution as x > 0.

(So x = -2 can’t be solution)

Case II: x < 0. then we have

x^{2} + x - 6 = 0 (|x| = -x)

⇒ (x + 3)(x - 2) = 0

⇒ x = -3 is the solution as x < 0

(So x = 2 can't be solution)

∴ product of roots = 3. - 3 = -9

QUESTION: 3

The sum of the series

Solution:

QUESTION: 4

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the top faces will be at least 10 is

Solution:

Two dice are rolled simultaneously, hence total number of elements in sample space is = 6 * 6 = 36

We have event E is the collection of those elements having sum greater or equal than 10.

i.e. E = {(4,6),(5.6).(6.6).(6.5).(6.4).(5.5)}

QUESTION: 5

are defined by f(x) = 2x + 3 and g (x) = x^{2} + 7, Then the value of x such that g (f(x)) = 8 are

Solution:

Given that f(x) = 2x + 3, g(x) = x^{2}+7

∴ g(f(x)) = g(2x + 3) = (2x + 3)^{2} + 7

= 4x^{2} + 9 + 12x+ 7 = 4x^{2} + 12x + 16

Given that g (f (x)) = 8

⇒ 4x^{2} + 12x + 16 = 8

⇒ 4x^{2} + 12x + 8 = 0

⇒ 4(x^{2} + 3x + 2) = 0

⇒ 4(x + l)(x + 2) = 0

∴ x = -1 and x = -2

QUESTION: 6

Solution:

Hence limit lies between 0 and 1/2

QUESTION: 7

The area bounded by the curves y = |x| -1 and y = - |x| +1 is

Solution:

Method-I: From the figure, it is clear that ABCD fonn a square having each side √2.

Method -II: Area ofABCD = 4 x Area of OBC

(as equation of CB is y = -x+ 1)

QUESTION: 8

If X and 7are two sets, then

Solution:

(using De'morgans law)

= φ

QUESTION: 9

Let R = {(3,3),(6.6),(9,9),(12,12),(6.12),(3,9),(3,12),(3,6)} be a relation on the se A = {3,6,9,12}. The relation is

Solution:

(d) : For (3, 9) ∈ R, (9, 3) ∉ R

Therefore,relation is not symmetric which means our choice

(a) and (b) are out of court. We need to prove reflexivity and transitivity.

For reflexivity a ∈ R, (a, a) ∈ R which is hold i.e. R is reflexive. Again,

for transitivity of (a, b) ∈ R , (b, c) ∈ R

⇒ (a, c) ∈ R

which is also true in R = {(3, 3)(6, 6), (9, 9), (12, 12), (6,12), (3, 9), (3, 12), (3, 6)}.

QUESTION: 10

The radius of the circle x^{2} + y^{2} - 2x + 4y = 8

Solution:

Given circle x^{2} + y^{2} - 2x + 4y - 8 = 0

Comparing with the general equation of circle x^{2} + y^{2} + 2gx + 2fy - c = 0, we get g = -1. f = 2, c = -8

*Multiple options can be correct

QUESTION: 11

In throwing a die, let

A be the event 'coining up of an odd number'

B be the event 'coming up of an even number'

C' be the event ‘coming up of a number __>__ 4' and D be the event ‘coming up of a number <3'

Then

Solution:

For throwing a dice, sample space S = {1,2,3,4,5,6} and

A = {1,3,5}

B = {2,4,6}

C = {4,5,6}

D = {1,2}

*Multiple options can be correct

QUESTION: 12

The function f(x) = |x|+|x - 1| is

Solution:

Given that f (x) = |x| + |x-1|, then f(1) = 1

Since absolute volue functions are continuous everywhere so f(x) = |x| + |x-1|. being the sum of two continuous function is continuous everywhere. Now we check differentiability at x = 1, we have

Hence Lf'(1) ≠ Rf'(1)

∴ Derivative do not exist at x = 1.

*Multiple options can be correct

QUESTION: 13

are consecutive forms of a series, then series is

Solution:

Note that if a. b. c are three consecutive terms

*Multiple options can be correct

QUESTION: 14

The diffemetial equation representing the family of curves. y^{2} = 2c (x + √c). where c is positive parameter is of

Solution:

......(1)

differentiating both side, we have

i.e.c =yy’ ...(2)

from (1) we have

Squaring both side we have

Hence order of differential equation is 1 and degree is 3.

*Multiple options can be correct

QUESTION: 15

The equations of lines which pass through the point (3, -2) and are inclined at 60° to the line

Solution:

Let slope of a line making 60° angle with

So. there will be two lines of such type. One is having slope and the otehr one is having slope 0.

Therefore.

Line 1: passing through (3, -2) and slope

Line 2: passing through (3.-2) and slope 0.

Option (A) and (C) are correct.

*Answer can only contain numeric values

QUESTION: 16

The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.

Solution:

In BANANA. Letter A reapets 3 times and N reapets 2 times.

Total number of arrangements of word BANANA is

Let both N s are appear together, then they are considered is single letter.

In this way total number of arrangements are

Hence total number of arrangements where N do not appear adjacently is = 60 - 20 = 40

*Answer can only contain numeric values

QUESTION: 17

On the interval [0,1], the function f(x) = x^{25} (1 - x)^{75} takes its maximum value at the point _______.

Solution:

For critical point, we have f'(x) = 0

Note that sign of f' (x) depends on the sign of (1 - 4x).

hence f (x) is increasing when and f (x) is decreasing when

∴ f (x) is maximum at x = 1/4

*Answer can only contain numeric values

QUESTION: 18

Solution:

Clearly from options, we have

b = 1. a = -1

Hence (0) is answer

*Answer can only contain numeric values

QUESTION: 19

If E = {1,2,3,4} and F = {1,2}, then the niunber of onto functions on E to F is ______.

Solution:

n(E) = 4 n(F) = 2

Then total number of onto functions from E to F are =

Note: If n(A) = n and n(B) = m then total number of onto functions from A to B are

*Answer can only contain numeric values

QUESTION: 20

Solution:

*Answer can only contain numeric values

QUESTION: 21

The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is _______.

Solution:

3x + 4y = 9 and 6x + 8y = 15

We know that the distance between the two parallel lines ax + by = c_{1} and ax + by = c_{2} is

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