Mathematics Test 250

Result

Mathematics Test 250

Score
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Weekly Quiz Competition

Question 1
4 / -1

A
π/36, π/12

B
π/12, 11π/36

C
12π/36, 11π/36

D
11π/36, π/36

Solution
Question 2
4 / -1

The number of solution of equation, is/are

A
1

B
2

C
3

D
None of these

Solution
Question 3
4 / -1

The domain of the function √(log_1/3log₄ ([x]² - 5)) is (where [x] denotes greatest integer function)

A
[–3, –2) ∪ [3, 4)

B
[–3, –2) ∪ (2, 3]

C
R – [–2, 3)

D
R – [–3, 3]

Solution
Question 4
4 / -1

Domain of definition of the function

A
(-1,0) ∪ (1,2) ∪ (2, ∞)

B
(1, 2)

C
(-1,0) ∪ ( 1,2)

D
(1,2) ∪ (2, ∞).

Solution
Question 5
4 / -1

A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

A
– f(x)

B
f(x)

C
f(a) + f (a – x)

D
f(– x)

Solution
Question 6
4 / -1

A
–2

B
–1

C
2

D
1

Solution
Question 7
4 / -1

then the point represented by the complex number z lies :

A
either on the real axis or on a circle passing through the origin.

B
on a circle with centre at the origin

C
either on the real axis or on a circle not passing through the origin.

D
on the imaginary axis.

Solution
Question 8
4 / -1

Calculate the least whole number, which when subtracted from both the terms of the ratio 5 : 6 gives a ratio less than 17 : 22.

A
5

B
3

C
2

D
4

Solution

Given:

Initial ratio = 5 ∶ 6

Final ratio should be less than 17 ∶ 22

Calculation:

Let the least whole number that is needed to be subtracted be a.

According to the question,

(5 - a)/(6 - a) < 17/22

⇒ 5 × 22 - 22a < 17 × 6 - 17a

⇒ 110 - 22a < 102 - 17a

⇒ 110 - 102 < - 17a + 22a

⇒ 8 < 5a

⇒ 8/5 = 1.6 < a

∴ The least whole number must be 2.
Question 9
4 / -1

Given, 6x + 2(6 - x) > 2x - 2 < 5x/2 - 3x/4, then x can take which of the following values?

A
9

B
-8

C
5

D
None of the above

Solution

⇒ 6x + 2(6 - x) > 2x - 2

⇒ 6x + 12 - 2x > 2x - 2

⇒ 2x > - 14

⇒ x > - 7 ----(1)

⇒ 2x - 2 < 5x/2 - 3x/4

⇒ 2x - 2 < 7x/4

⇒ 8x - 7x < 8

⇒ x < 8 ----(2)

From (1) and (2),

- 7 < x < 8

∴ x = 5 satisfies the given conditions from the above options.
Question 10
4 / -1

The area (in sq. units) of the region {x ∈ R : x ≥ 0, y ≥ 0, y ≥ x - 2 and y ≤ √x) is

A
13/3

B
8/3

C
10/3

D
5/3

Solution