Mathematics Test 36

Result

Mathematics Test 36

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Question 1
4 / -1

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after.

A
18 months

B
19 months

C
20 months

D
21 months

Solution

Let it happened after m months

2 × 300 + (2 × 240 + (m - 4) × 40))

= 11040

⇒ m² + 5m - 546 = 0

⇒ (m + 26) (m - 21) = 0

⇒ m = 21.

Hence, option D is correct.
Question 2
4 / -1

A person is to count 4500 currency notes. Let a_n denote the number of notes he counts in the nth minute. If a₁ = a₂ = ... = a₁₀ = 150 and a₁₀, a₁₁, ... are in an AP with the common difference –2, then the time taken by him to count all notes is

A
24 minutes

B
34 minutes

C
125 minutes

D
135 minutes

Solution

Upto the 10th minute the count is (10 X 150)=1500 notes

The 11^th minute count is 150-2=148.

The remaining count left is 4500-1500 = 3000 notes.

Thus,

a₁₁ + a₁₂ + ... up to n terms = 3000

148 + 146 + ... up to n terms = 3000

(n/2)[2 × 148 + (n–1) (–2)] = 3000

(n/2)[296-2n+2]=3000

n(149-n)=3000

n² - 149n+3000=0

∴ n = 24 & n ≠ 125 (since, for n=125 the count is not valid)

∴ Total time taken = 10 + 24 = 34 minutes.
Question 3
4 / -1

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

A
3

B
36

C
66

D
108

Solution

Required no. of ways = ³C₂ × ⁹C₂ = 3 × 36 = 108.
Question 4
4 / -1

Consider the following statements

P: Suman is brilliant

Q : Suman is rich

R: Suman is honest

The negation of the statement Suman is brilliant and dishonest if and only if Suman is rich can be expressed as

A
~P ∧ (Q ↔ ~ R)

B
~ (Q ↔ (P ∧ ~ R))

C
~ Q ↔ ~ P ∧ R

D
~ (P ∧ ~ R) ↔ Q

Solution

Suman is brilliant and dishonest if and only if Suman is rich is expressed as

Q ↔ (P ∧ ~ R)

Negation of it will be ~(Q ↔ (P ∧ ~ R))

Hence, option B is correct.
Question 5
4 / -1

Directions: Assertion–Reason type questions. Each of these questions contains two statements: statement–1 (Assertion) and Statement–2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number". and r be the statement "x is a rational number iff y is a transcendental number".

Statement–1: r is equivalent to either q or p.

Statement–2: r is equivalent to ~ (p ↔ ~q).

A
Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

B
Statement–1 is true, Statement–2 is false

C
Statement–1 is false, Statement–2 is true

D
Statement–1 is true, Statement–2 is true; Statement–2 is a correct explanation for Statement–1.

Solution

r requires q to be true for p to be true, hence it is NOT equivalent to either p or q alone. Hence statement 1 is incorrect.

(p ↔ ~q) imples that x is a rational number if y is NOT a transcendental number. negation of that is x is rational number if y is a transcendental number, which is same as r. Hence c is the right answer.