Mathematics Test 240

Result

Mathematics Test 240

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Weekly Quiz Competition

Question 1
4 / -1

If three distinct numbers a,b,c are in G.P. and the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root, then which one of the following statements is correct?

A
d, e, f are in A.P.

B

C

D
d, e, f are in G.P.

Solution

Calculation:

The correct answer is Option 3.
Question 2
4 / -1

Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :-

A
12.8

B
13.5

C
13.9

D
13

Solution

Calculation:

From the data, we have:

∴ % of population who reads A but not B = 25 – 8 = 17%

⇒ Population reading advertisements = 30% of these = 0.3 × 17 = 5.1% of total population

Also, % of population who reads B but not A = 20 – 8 = 12%

⇒ Population reading advertisements = 40% of these = 0.4 × 12 = 4.8% of total population

ALso, % of population who reads both A and B = 8%

⇒ Population reading advertisements = 50% of these = 0.5 × 8 = 4% of total population

Total percentage of population population reading advertisements = 5.1 + 4.8 + 4 = 13.9% of total

∴ The percentage of the population who look into advertisement is 13.9.

The correct answer is Option 3.
Question 3
4 / -1

A
660

B
620

C
680

D
600

Solution
Question 4
4 / -1

The domain of the definition of the function

A
(1, 2) ∪ (2, ∞)

B
(-1, 0) ∪ (1, 2) ∪ (3, ∞)

C
(-1, 0) ∪ (1, 2) ∪ (2, ∞)

D
(-2, -1) ∪ (-1, 0) ∪ (2, ∞)

Solution
Question 5
4 / -1

Let N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d) if ad (b + c) = bc(a + d), then R is-

A
Symmetric only

B
Reflexive only

C
Transitive only

D
An equivalence relation

Solution

Calculation:

For (a, b) ∈ R, ab(b + a) = ba(a + b)

⇒ (a, b) R (b, a)

⇒ R is reflexive,

Let (a, b) R (c, d)

⇒ ad(b + c) = bc(a + d)

⇒ cb(d + a) = da(c + b)

⇒ (c, d) R (a, b)

⇒ R is symmetric

Let (a, b) R (c, d) and (c, d) R (e, f)

⇒ ad(b + c) = bc(a + d) and cf(d + e) = de(c + f)

⇒ ab/(a - d) = cd/(c - d) and cd/(c - d) = ef/(e - f)

⇒ ab/(a - d) = ef/(e - f)

⇒ af(b + e) = be(a + f)

⇒ (a, b) R (e, f)

⇒ R is transitive

∴ R is an equivalence relation.

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

The smallest integer x for which the inequality is satisfied is given by -

A
-7

B
-5

C
-4

D
-6

Solution
Question 7
4 / -1

A point ‘z’ moves on the curve | z – 4 – 3i | = 2 in an argand plane. The maximum and minimum values of |z| are -

A
2, 1

B
6, 5

C
4, 3

D
7, 3

Solution
Question 8
4 / -1

If the function f : [1, ∞) → [1, ∞) is defined by f (x) = 2^{x (x – 1)}, then f ^–1(x) is -

A

B

C

D
Not defined

Solution
Question 9
4 / -1

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then :

A
m = n = 78

B
n = m – 8

C
m + n = 68

D
m = n = 68

Solution
Question 10
4 / -1

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is :

A
288

B
306

C
360

D
310

Solution

Calculation:

Case 1 : Fixing first place as 4

4 _ _ _ _ _ _

The second place can be filled in 2 ways (4, 5), third and fourth place can be filled in 6 ways.

∴ Number of such four-digit numbers = 2 × 6 × 6 = 72

Case 2 : Fixing first place as 4 and second place as 3

4 3 _ _ _ _

The third place can be filled in 3 ways (3, 4, 5) and the fourth place can be filled in 6 ways.

∴ Number of such four-digit numbers = 3 × 6 = 18

Case 3 : Fixing first place as 4, second place as 3 and third place as 2

4 3 2 _ _

The fourth place can be filled in 4 ways (2, 3, 4, 5)

∴ Number of such four-digit numbers = 4

Case 4 : Fixing first place as 5

5 _ _ _ _ _ _

∴ Number of such four-digit numbers = 6 × 6 × 6 = 216

∴ Total number = 72 + 18 + 4 + 216

= 310

∴ Number of four digit numbers is 310.

The correct answer is Option 4.