Mathematics Test 276

Result

Mathematics Test 276

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Weekly Quiz Competition

Question 1
4 / -1

A
-1

B
{1}

C
{– 1}

D
1

Solution
Question 2
4 / -1

Let f: R → R be a mapping such that Then f is

A
Many–one and onto

B
One–one and onto

C
Into and one one

D
Many one and into

Solution
Question 3
4 / -1

The value of cos15^º− sin15^º is

A

B

C
0

D

Solution
Question 4
4 / -1

The values of x which satisfy the trigonometric equation

A
±1/2

B
±√2

C
±2.

D

Solution
Question 5
4 / -1

If cos^–1 x + cos^–1 y = π/2 and tan^–1 x – tan^–1 y = 0, then x² + xy + y² is equal to

A
0

B
1/√2

C
3/2

D
1/8

Solution
Question 6
4 / -1

The sum of the infinite series cot^–1 2 + cot^–18 + cot^–1 18 + cot^–1 32 + … is equal to

A
π/4

B
π/2

C
3π/4

D
None of these

Solution
Question 7
4 / -1

2 cos^-¹ x = cos^-¹ (2x² -1) holds true if

A
|x| ≤ 1

B
0 ≤ x ≤ 1

C
|x| < 1/2

D
None of these

Solution

2 cos^-¹ x = cos^-1 (2x² -1) ⇒ cos(2 cos^-1 x) = 2x² - 1

Since,

- 1 ≤ cos(2 cos^-1 x) ≤ 1

⇒ -1 ≤ 2x² - 1 ≤ 1

⇒ 0 ≤ 2x² ≤ 2

⇒ 0 ≤ x ≤ 1
Question 8
4 / -1

If A = (a_ij)_{3 × 3} is a matrix satisfying the equation x³ – 3x + 1 = 0, then

A
A is a unit matrix

B
A is a singular matrix

C
A is a non-singular matrix

D
None of these

Solution

A3 - 3A + l = 0 ⇒ l = A(3I - A²)

Since matrix I is an identity matrix and I is invertible, A(3I - A²) is also an invertible matrix.

So, matrix A is also invertible, hence non-singular.
Question 9
4 / -1

A
3J

B
2J

C
4J

D
1/2J

Solution
Question 10
4 / -1

The rows and columns of matrix A will be linearly dependent if

A
|A| = 0

B
|A| is not equal to zero

C
|A| > 0

D
|A| < 0

Solution

The rows and columns of the matrix A are linearly dependent if the determinant of the matrix A is equal to 0.