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Question (11)

QN0030063

Which of the following is the next term in the Virahāṅka–Fibonacci sequence? 1, 2, 3, 5, 8, 13, 21, 34, 55, ___

(A) 76
(B) 81
(C) 89
(D) 90

Correct Answer: C

Explanation:

Each term is the sum of the previous two terms. So, 34 + 55 = 89.

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Question (12)

QN0030064

The 9th term of the Virahāṅka–Fibonacci sequence is

(A) 21
(B) 34
(C) 55
(D) 89

Correct Answer: C

Explanation:

The sequence is 1, 2, 3, 5, 8, 13, 21, 34, 55. Hence, the 9th term is 55.

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Question (13)

QN0030065

A staircase has 6 steps. A child can climb either 1 step or 2 steps at a time. In how many different ways can the child reach the top?

(A) 8
(B) 10
(C) 13
(D) 21

Correct Answer: C

Explanation:

The number of ways follows the Virahāṅka–Fibonacci sequence. For 6 steps, the answer is 13.

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Question (14)

QN0030066

Which is the parity pattern of the first six Virahāṅka–Fibonacci numbers?

(A) Even, Odd, Even, Odd, Even, Odd
(B) Odd, Even, Odd, Odd, Even, Odd
(C) Odd, Odd, Even, Even, Odd, Odd
(D) Even, Even, Odd, Odd, Even, Even

Correct Answer: B

Explanation:

The first six terms are 1, 2, 3, 5, 8 and 13, giving the parity pattern O, E, O, O, E, O.

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Question (15)

QN0030067

A bulb is initially OFF. Its switch is toggled 100 times. What will be its final state?

(A) ON
(B) OFF
(C) Cannot be determined
(D) It keeps blinking

Correct Answer: B

Explanation:

An even number of toggles returns the bulb to its original state. Since it was OFF initially, it remains OFF.

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Question (16)

QN0030068

Which expression represents all odd numbers?

(A) 2n
(B) 2n + 2
(C) 2n − 1
(D) 4n

Correct Answer: C

Explanation:

Every odd number can be written in the form 2n − 1.

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Question (17)

QN0030069

In a cryptarithm, the same letter always represents

(A) Different digits in different places
(B) The largest digit only
(C) The same digit wherever it appears
(D) Only an even digit

Correct Answer: C

Explanation:

Each letter stands for one fixed digit throughout the cryptarithm.

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Question (18)

QN0030070

A 3 × 3 magic square has magic sum 27. What is the centre number?

(A) 7
(B) 8
(C) 9
(D) 10

Correct Answer: C

Explanation:

The centre number is one-third of the magic sum. Therefore, 27 ÷ 3 = 9.

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Question (19)

QN0030071

If every number in a magic square is multiplied by 4, the new magic sum becomes

(A) Four times the original magic sum
(B) Original magic sum + 4
(C) Original magic sum + 12
(D) Unchanged

Correct Answer: A

Explanation:

Multiplying every entry by 4 multiplies every row, column and diagonal sum by 4.

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Question (20)

QN0030072

Which statement is correct?

(A) Every expression of the form 2n + 3 is always even.
(B) Every expression of the form 6n is always odd.
(C) Every expression of the form 4n − 1 is always odd.
(D) Every expression of the form 5n is always even.

Correct Answer: C

Explanation:

Since 4n is always even, subtracting 1 always gives an odd number.

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Question (11)

Which of the following is the next term in the Virahāṅka–Fibonacci sequence? 1, 2, 3, 5, 8, 13, 21, 34, 55, ___

Explanation:

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Question (12)

The 9th term of the Virahāṅka–Fibonacci sequence is

Explanation:

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Question (13)

A staircase has 6 steps. A child can climb either 1 step or 2 steps at a time. In how many different ways can the child reach the top?

Explanation:

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Question (14)

Which is the parity pattern of the first six Virahāṅka–Fibonacci numbers?

Explanation:

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Question (15)

A bulb is initially OFF. Its switch is toggled 100 times. What will be its final state?

Explanation:

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Question (16)

Which expression represents all odd numbers?

Explanation:

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Question (17)

In a cryptarithm, the same letter always represents

Explanation:

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Question (18)

A 3 × 3 magic square has magic sum 27. What is the centre number?

Explanation:

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Question (19)

If every number in a magic square is multiplied by 4, the new magic sum becomes

Explanation:

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Question (20)

Which statement is correct?

Explanation:

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