# Number System Miscellaneous Questions

Number System Miscellaneous Questions for competitive exams in Hindi and English. To excel in competitive exams, it is crucial to not only understand the concepts but also to be able to apply them effectively in solving problems.

## Number System Type 7 : Miscellaneous Questions

Question 1:
Find the value of
मान ज्ञात कीजिए $\frac{1}{5}+999 \frac{494}{495}\times 99$
(1) 90000
(2) 99000
(3) 90900
(4) 99990

(2) 99000
= $\frac{1}{5}+999 \frac{494}{495}\times 99$
= $\frac{1}{5}+999 (1-\frac{1}{495})\times 99$
= $\frac{1}{5}+999\times 99 - \frac{99}{495}$
=99000

Question 2:
Which one of the following numbers is not a square of any natural number ?
निम्नलिखित में से कौन सी संख्या किसी भी प्राकृतिक संख्या का वर्ग नहीं है
(1) 17956
(2) 18225
(3) 63592
(4) 53361

(3) 63592
In a perfect square number 2 never comes at the unit’s place.

Question 3:
The sum and product of two numbers are 12 and 35 respectively. What will be the sum of their reciprocals?
दो संख्याओं का योग और गुणनफल क्रमशः 12 और 35 है। उनके व्युत्क्रमों का योग क्या होगा?
(1) $\frac{1}{3}$
(2) $\frac{1}{5}$
(3) $\frac{12}{35}$
(4) $\frac{35}{12}$

(3) $\frac{12}{35}$
Let the two numbers be x and y.
x + y = 12 and xy = 35 $\frac{1}{y} + \frac{1}{x} = \frac{x+y}{xy} = \frac{12}{35}$

Question 4:
380 mangoes are distributed among some boys and girls who are 85 in number. Each boy gets four mangoes and each girl gets five. The number of boys is
85 की संख्या वाले कुछ लड़के और लड़कियों में 380 आम बांटे गए। प्रत्येक लड़के को चार आम मिलते हैं और प्रत्येक लड़की को पाँच। लड़कों की संख्या है
(1) 15
(2) 38
(3) 40
(4) 45

(4) 45
Let number of boys =x and number of girls = 85 –x
According to the question, x × 4 + (85 –x) × 5 = 380
4x + 425 – 5x = 380
x = 45

Question 5:
On multiplying a number by 7, all the digits in the product appear as 3’s. the smallest such number is
किसी संख्या को 7 से गुणा करने पर गुणनफल के सभी अंक 3 के रूप में प्रकट होते हैं। ऐसी सबसे छोटी संख्या है
(1) 47649
(2) 47719
(3) 47619
(4) 48619

x = $\frac{33333....}{7}$= 47619