CTET Solved Paper MCQ - UPTET December 2016

86 The sum of two numbers is 36. Their HCF and LCM are 3 and 105, respectively. The sum of reciprocals of those two numbers will be

Sum of two numbers = 36
Let the two number be x and (36 - x)
We know that,
(x)(36 - x) = HCF × LCM of two numbers
⇒ x(36 - x) = 3 × 105
⇒ 36x - x² = 315
⇒ x² - 36x + 315 = 0
⇒ x² - 21x - 15x + 315 = 0
x(x - 21)-15(x - 21) = 0
⇒(x - 15)(x - 21) = 0
⇒x = 15, 21
Two numbers are 15 and 21.
Sum of reciprocals

87 Half the perimeter of a rectangular garden, whose length is 4 m more than its width is 36 m. Length of the garden will be

Let the length of the rectangular garden be 'l' m.
Then, breadth of the rectangular garden be (l - 4)m.
Perimeter of rectangular garden = 2 (l + b)

⇒ 36 = l + l - 4 [half of perimeter given = 36 given]
⇒ 36 = 2l -4
⇒ 40 = 2l
⇒ l = 20 m

88 Rajdhani express starts from a station at 7.29 pm and reaches next destination after 17 hours and 42 minutes. The time by which it reaches the destination is

Rajdhani express starts from station at 7:29 pm.
Total time taken by train to reach the destination = 17 h 42 min.
Train reaches its destination at time 7:29 pm + 17:42 = 25 h 11 min
=l:ll pm

89 The age of the labourers working in a factory in years is as follows
31, 41, 28, 54, 34, 27, 23, 33, 35, 42.
Range of their is

Arrange the age of the labourers in ascending order
23, 27, 28, 31, 33, 34, 35, 41, 42, 54
Range of age = Highest age - Lowest age
= 54 - 23 = 31 yr

90 The smallest prime number is

∵ Prime number has exactly two factors, 1 and itself.
∴ Smallest prime number is 2. As prime number is always greater than 1.