CTET Solved Paper MCQ - UPTET December 2016

61 If the speed of a bus is increased by 5 km/h from its normal speed, it takes 2 hour less for a journey of 300 km, then the normal speed of bus (in km/h) is

Let the normal speed of the bus be 'x' km/h to cover the distance of 300 km in time 't' h.
∴ Distance = speed × time
⇒ 300 = x × t

If speed increased by 5 km/h, then
speed = (x + 5) km/h
and time = (t - 2)h
Then, distance = (x + 5) (t - 2)
⇒ 300 =(x + 5)(t - 2)
⇒ 300 = xt - 2x + 5t - 10

⇒ 2x² + 10x - 1500 = 0
⇒ x² + 5x - 750 = 0
⇒ x² + 30x - 25x - 750 = 0
⇒ x(x + 30) - 25 (x + 30) = 0
⇒ (x - 25)(x + 30) = 0
⇒ x = 25, -30
Hence, normal speed of the bus is 25km/h

62 If 9^2x-1 = 2⁵ - 5, then value of x is

9^2x-1 = 2⁵ - 5
⇒ 9^2x-1 = 32 - 5
⇒ 9^2x-1 = 27
⇒ 3^2(2x-1) = 3³
Powers of same base are equal.
∴ 2(2x - 1) = 3
⇒ 4x - 2 = 3
⇒ 4x = 5
⇒ x = 5/4

63 The areas of three adjacent faces of a cuboid are in the ratio 7 : 10 : 14. If the volume of cuboid is 350cm³, then the longest side has a length of

Area of three adjacent faces of a cuboid are in the ratio of 7: 10 : 14.
Let area of three faces be 7x, 10x, and 14x.
Let the length, breadth and height of cuboid be l, b and h, respectively.

Volume of cuboid = 350 cm³
⇒ l × b × h = 350 cm³ ........(i)
According to the figure,
l × b = 14x .........(ii)
l × h = 7x ..........(iii)
b × h = 10x ............(iv)
On multiplying (ii), (iii) and (iv)
l²b²h² = (14x)(7x)(10x)
⇒ (lbh)² = (14 × 7 × 10)x³
⇒ (350)² = (980)x³

x³ = 125 ⇒ x = 5
Area of the faces are
7x = 7 × 5 = 35 = l × h
10x = 10 × 5 = 50 = b × h
14x = 14 × 5 = 70 = l × b
Put the value of l × h = 35 in Eq (i), then
l × b × h = 350
⇒ 35 × b = 350
⇒ b = 10 cm
Similarly,
l × b × h = 350
⇒ l × 50 = 350
⇒ l = 7 cm
and l × b × h = 350
⇒ 70 × h = 350
⇒ h = 5 cm
∴ Longest side has a length of 10 cm.

64 The sum of three consecutive multiples of 3 is 99. These multiples are

Let the three consecutive multiples of 3 be 3x, 3x + 3, 3x + 6
Then, according to the question,
3x + 3x + 3 + 3x + 6 = 99
⇒ 9x + 9 = 99
⇒ 9(x + 1) = 99
⇒ x + 1 = 11
⇒ x = 11 - 1 = 10
Thus, the three multiples are
3x = 3 × 10 = 30
3x + 3 = 3 × 10 + 3 = 33
3x + 6 = 3 × 10 + 6 = 36
Multiples of 3 are 30, 33, 36.

65 Seema reads

of a book per hour. If she goes to sleeping after reading the book for

hours. How much part of book is now left to be read?