Mathematics Test 106

Result

Mathematics Test 106

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Weekly Quiz Competition

Question 1
4 / -1

In a set of real numbers a relation R is defined as x R y such that then relation R is

A
reflexive and symmetric but not transitive

B
symmetric but not transitive and reflexive

C
transitive but not symmetric and reflexive

D
none of reflexive, symmetric and transitive

Solution
Question 2
4 / -1

A
4 + 2 √2

B
4 + 2 √3

C
2 + √5

D
3 + √5

Solution
Question 3
4 / -1

Let the area enclosed by the curve y = 1 – x² and the line y = a, where

A
1 < k < 3/2

B
3/2 < k < 2

C
2 < k < 5/2

D
5/2 < k < 3

Solution
Question 4
4 / -1

If system of linear equations (a – 1) x + z = α, x + (b – 1) y = β and and y + (c – 1) z = γ where does not have a unique solution, then maximum possible value of |a + b + c| is

A
5

B
1

C
3

D
4

Solution
Question 5
4 / -1

ABCD is a rectangular field. A vertical lamp post of height 12m stands at the corner A. If the angle of elevation of its top from B is 60° and from C is 45°, then the area of the field is

A
48√2 sq. meter

B
48√3 sq. meter

C
48 sq. meter

D
12√2 sq. meter

Solution
Question 6
4 / -1

Smallest positive x satisfying the equation

A
15°

B
18°

C
22.5°

D
30°

Solution

cos³ 3x + cos³ 5x = (2 cos 4x cos x)³

= (cos 5x + cos 3x)³

cos³ 3x + cos³ 5x

= cos³ 5x + cos³ 3x + 3 cos 5x cos 3x (cos 5x + cos 3x)

⇒ (3 cos 3x · cos 5x) (2 cos 4x · cos x) = 0

⇒ cos x · cos 3x · cos 4x · cos 5x = 0
Question 7
4 / -1

The set of values of x satisfying simultaneously the inequalities

A
a singleton set

B
an empty set

C
an infinite set

D
a set consisting of exactly two elements

Solution
Question 8
4 / -1

A bag contains 2 white and 4 black balls. A ball is drawn 5 times, each being replaced before another is drawn. The probability that atleast 4 of the balls drawn are white is :

A
4/81

B
10/243

C
11/243

D
None

Solution
Question 9
4 / -1

The modulus of the complex number z such that |z + 3 – i| = 1 and arg(z) = π is equal to

A
1

B
2

C
3

D
4

Solution
Question 10
4 / -1

A
(√e)^{_e2 + 1}

B
(√e₎^{_e2 + 1}

C
0

D

Solution