CTET Solved Paper - UPTET December 2016
- Option : C
- Explanation : (C) 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
- Option : A
- Explanation : (A) 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
- Option : D
- Explanation : (D) 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
- Option : A
- Explanation : (A) 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
- Option : C
- Explanation : (C) ∵ Prime number has exactly two factors, 1 and itself.
∴ Smallest prime number is 2. As prime number is always greater than 1.
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