Mathematics Test

Result

Mathematics Test - 5

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0.25

If A = {x : x = 4n, n ∈ Z} and B = {x : x = 6n, n ∈ Z}, then A ∩ B =

A
{x : x = 2n, n ∈ Z}

B
{x : x = 10n, n ∈ Z}

C
{x : x = 12n, n ∈ Z}

D
{x : x = 24n, n ∈ Z}

Solution

Given:

A = {x : x = 4n, n ∈ Z}

B = {x : x = 6n, n ∈ Z}

Calculation:

We have,

x ∈ A ∩ B

⇒ x = 4n and x = 6n, n ∈ Z

⇒ x is a multiple of 4 and x is a multiple of 6

⇒ x is a multiple of 4 and 6 both

⇒ x is a multiple of 12

⇒ x = 12n, n ∈ Z

Hence, A ∩ B = {x : x = 12n, n ∈ Z}

Correct answer is option 3.
Question 2
1 / -0.25

A
centre at (0, 0) and radius √2

B
centre at (0, 1) and radius 2

C
centre at (0, 1) and radius √2

D
centre at (0, -1) and radius √2

Solution
Question 3
1 / -0.25

The relation R = {(a, b): a ≤ b²} on the set of real numbers is:

A
Reflexive and symmetric

B
Neither reflexive nor symmetric

C
Transitive

D
Reflexive but not symmetric

Solution

Concept:

(i) A relation is said to be reflexive if (a, a) ∈ R for every a ∈ A.

(ii) A relation is said to be symmetric if (a, b) ∈ R then (b, a) ∈ R.

(iii) A relation is said to be transitive if (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R.

Explanation:

R = {(a, b): a ≤ b2}, a ∈ R
Question 4
1 / -0.25

A
0

B
3

C
4

D
2

Solution
Question 5
1 / -0.25

A

B

C

D
none of these

Solution
Question 6
1 / -0.25

A
523

B
524

C
525

D
520

Solution

Concept:

1. The n^th term of the A.P. is given by:

an = a + (n – 1) d

2. The sum of n terms of an AP with first term a and common difference d is given by:
Question 7
1 / -0.25

The value of

A
2⁷ - 1

B
2⁸ - 2

C
2⁸ - 1

D
28

Solution
Question 8
1 / -0.25

A
1

B
0

C
3

D
2

Solution
Question 9
1 / -0.25

If the constant term in the expansion of then 25α is equal to:

A
639

B
724

C
693

D
742

Solution
Question 10
1 / -0.25

The ratio of the coefficient of x¹⁵ to the term independent of x in

A
12:32

B
1:32

C
32:12

D
32:1

Solution