Page 30 - Ganit Kaushal

Miscellaneous Exercise 1.4

There are four options (Q. 1 to Q. 4), out of which only one is correct. Choose the correct option.

1. The 9th Virahānka Number is
(a) 24 (b) 55 (c) 89 (d) 34
2. In the sequence 1, 3, 9, 27, _____, the next number is
(a) 12 (b) 33 (c) 89 (d) 81
3. The sum of the next two terms of the sequence 1, 3, 9, 27, _____ is

(a) 424 (b) 224 (c) 234 (d) 324
4. In the shape sequence of triangle, quadrilateral, pentagon, hexagon, _____, the next shape is a/an
(a) decagon (b) heptagon (c) octagon (d) none of these
5. Fill in the blanks.
(a) The 5th term of the sequence of hexagonal numbers is _____ .

(b) The number of edges in the sequence of complete graphs forms a sequence of _____ .
(c) When we add, we get a sequence of _____ pattern.
(d) The third term in the sequence of total line segments of shapes in the shape – sequence of Koch
snowflakes is _____.
(e) Complete the pattern: 128, _____, 32, 16, _____, _____, 2, 1.
6. State whether the following statements are True (T) or False (F).

(a) 36 is a triangular number.
(b) The number of dots representing any square number can be arranged perfectly in a square form.
(c) Adding up and down the sequence of counting numbers gives the sequence of triangular numbers.
(d) If we take up the difference of two consecutive terms of a triangular sequence, it gives us the
sequence of counting numbers starting with 2.
(e) If we multiply each term of the sequence of triangular numbers by 8 and then add 1, we get
the sequence of squares of odd numbers starting with 3.

Subjective/Competency Based Questions
7. Multiplication of two numbers with the same tens digit and with 10 as the sum of the ones digits,
follows a pattern as given: 42 × 48 = 2016.
Pattern followed: Tens digit = 4, next digit = 5; their product = 20
Ones digits = 2, 8; their product = 16
Result = 2016

Based on the above pattern answer the following:
(a) 53 × 57 = _____ (b) 62 × 68 = _____ (c) 84 × 86 = _____ (d) 71 × 79 = _____
Also, confirm your answer by actual multiplication.
8. A student has to go up to the stage to receive an award from the principal for being the topper of his
class. He has to climb 6 steps upwards to reach the stage. He climbs up by taking either 1 step each
time or a maximum of 2 steps at a time. In how many different ways can he reach the stage to receive
the award?

28 Mathematics-6