Mathematics Test 234

Result

Mathematics Test 234

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Weekly Quiz Competition

Question 1
4 / -1

If x is real, the expression takes all values in the interval

A

B

C

D
none of these

Solution
Question 2
4 / -1

If the coefficients of x³ and x⁴ in the expansion of (1 + ax + bx²) (1 – 2x)¹⁸ in powers of x are both zero, then (a, b) is equal to

A

B

C

D

Solution
Question 3
4 / -1

If a ∈ R and the equation –3(x – [x])²+ 2(x – [x]) + a² = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval:

A
(–1, 0) ∪ (0, 1)

B
(1, 2)

C
(–2, –1)

D
(-∞, –2) ∪ (2, ∞)

Solution

Calculation:
Question 4
4 / -1

The letters of word ‘SOCIETY’ are placed at random in a row. The probability that three vowels come together, is

A
6/7

B
1/7

C
3/7

D
none of these

Solution

Concept:

The number of ways of arranging n objects = n!

Calculation:

Given, letters of word ‘SOCIETY’ are placed at random in a row

∴ Total number of ways of arranging all the 7 letters = 7!

Now, when the three vowels are taken together, the three vowels are considered as one unit.

Hence, we get five letters 'S', 'C', 'T', 'Y', 'IEO'.

∴ The number of ways in which 5 letters (SCTY – 4, IEO – 1) can be arranged = 5!

Also, the 3 vowels can be arranged amongst themselves in 3! ways

∴ Total number of favourable cases = 5! × 3!
Question 5
4 / -1

If a, b and c are all different form zero such that then which is not true for the matrix

A
Symmetric

B
Non-singular

C
Can be written as sum of a symmetric and a skew symmetric matrix

D
None of these

Solution

= abc ≠ 0 [∵ a, b and c are all different form zero]

⇒ |A| ≠ 0

⇒ A is non-singular.

Now, every square matrix A can be represented as A = P + Q, where (which is skew symmetric).

∴ All are correct.

The correct answer is Option 4.
Question 6
4 / -1

The value of sin is equal to

A
1

B
1/16

C
1/64

D
none of these

Solution

Concept:

sin(π - θ) = sin θ

sin(π/2 − θ) = cos θ

sin(π/2 + θ) = sin θ

cos (π − θ) = cos θ
Question 7
4 / -1

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is

A
40(√2 − 1)

B
40(√3 − √2)

C
20√2

D
20(√3 − 1)

Solution
Question 8
4 / -1

A

B

C

D

Solution
Question 9
4 / -1

If α, β ≠ 0, and f(n) = αⁿ+ βⁿ and = K(1 - α)²(1 - β)²(α - β)², then K is equal to

A
αβ

B
1/αβ

C
1

D
-1

Solution
Question 10
4 / -1

The function f(x) satisfying {f(x)}² + 4f(x)f'(x) + {f'(x)}² = 0 is given by

A
ke^{(2 + √3)x}

B
ke^{(4 ± √5)x}

C
ke^{(-2 ± √3)x}

D
k log (2 + √3)x

Solution