Mathematics Test 232

Result

Mathematics Test 232

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

The sum of all the solutions of the equation cos x. cos ((π/3) + x). cos ((π/3) – x) = 1/4, x ∈ [0, 6π] is

A
15π

B
30π

C
100π/3

D
none of these

Solution

Concept:

Calculation:

Given, cos x. cos ((π/3) + x). cos ((π/3) – x) =1/4

⇒ 4cos x. cos ((π/3) + x). cos ((π/3) – x) = 1

⇒ 2cos x(2cos ((π/3) + x). cos ((π/3) – x)) = 1

⇒ 2cos x(cos 2π/3 + cos 2x) = 1

⇒ 2cos x(–1/2 + cos 2x) = 1

⇒ – cos x + 2cos x cos 2x = 1

⇒ – cos x + cos 3x + cos x = 1

⇒ cos 3x = 1 = cos 0

⇒ 3x = 2nπ ± 0

⇒ x = 2nπ/3; n = 0, 1, … , 9

⇒ Sum of possible values of x = 2π/3(0 + 1 + 2 + … + 9)

= 2π/3 × 45 = 30π

∴ The sum of all the solutions is 30π.

The corect answer is Option 2.
Question 2
4 / -1

The area bounded by the curves y = –(x + 1)² ; y = |x + 1| and |y| = 1 – x is

A
11/6

B
13/6

C
9/6

D
3/4

Solution
Question 3
4 / -1

The value of integral

A
π/4

B
π/2

C
π

D
none of these

Solution
Question 4
4 / -1

where {x} denotes the fractional part of x, is equal to

A
-1

B
0

C
1

D
does not exist

Solution
Question 5
4 / -1

A
7/4

B
9/4

C
13/4

D
5/2

Solution
Question 6
4 / -1

The solution of the equation

A

B

C

D
none of these

Solution
Question 7
4 / -1

The angle between the two tangents from the origin to the circle (x – 7)² + (y + 1)² = 25 equals

A
π/4

B
π/3

C
π/2

D
none of these

Solution
Question 8
4 / -1

A
37/33

B
11/5

C
1

D
5/11

Solution
Question 9
4 / -1

A company has two plants to manufacture televisions. Plant I manufacture 70% of televisions and plant II manufacture 30%. At plant I, 80% of the televisions are rated as of standard quality and at plant II, 90% of the televisions are rated as of standard quality. A television is chosen at random and is found to be of standard quality. The probability that it has come from plant II is

A
17/50

B
27/83

C
3/5

D
none of these

Solution

Concept:

Let E₁, E₂, ….., E_n be n mutually exclusive and exhaustive events associated with a random experiment, and let S be the sample space. Let A be ann event that occurs together with any one of E₁ or E₂ or … or E_n such that P(A) ≠ 0. Then

The correct answer is Option 2.
Question 10
4 / -1

The coordinates of the middle point of the chord 2x – 5y + 18 = 0 cut off by the circle x² + y² – 6x + 2y – 54 = 0 are

A
(1, 4)

B
(2, 4)

C
(4, 1)

D
(1, 1)

Solution

Calculation:

⇒ b = 4

⇒ Mid point is M(1, 4)

∴ The coordinates of the middle point of the chord 2x – 5y + 18 = 0 cut off by the circle x² + y² – 6x + 2y – 54 = 0 are (1, 4).

The correct answer is Option 1.