1.If the perimeter of one face of a cube is 20 cm, then its surface area is
a) 120 cm2
b) 150 cm2. c) 195 cm2 d) 400 cm
2.Which of the following will have a terminating decimal expansion?
a. 77/420
b. 23/30
c. 125/441. d. 23/8
3.If xsino3 + ycos30 = sino cos 0 and xsino = ycose, than x2 + y2 is equal to
a) 0
b) 1/2
c) 1
d) 3/2
One of the two students, while solving a quadratic equation in x copied the constant term
comely and got the roots 3 and 2. The other copied the constant term and coefficient of
x2 correctly as - 6 and 1 respectively. The correct roots are
a) 3,-2
b) -3,2
c) -6, -1
d) 6,-1
A motor boat takes 2 hours to travel a distance 9 km down the current and it takes 6 hours
to travel the same distance against the current. The speed of the boat in still water and that
of the current (in km/hour) respectively are
a) 3, 1.5
b) 3,2
c) 3.5, 2.5 d) 3,1
Answers
Answer:
1). Perimeter = 4× side
4× side = 20cm
side = 5 cm.
Now surface area of cube = 6×side^2
= 6 × 5^2
= 6 × 25 = 150 cm^2
b. 150cm2 is correct answer.
2). For terminating decimal expansion, denominator must have only 2 or only 5 or 2 and 5 as factor
So,
d. 23/8 is answer coz , 23/2^3
3).
Xsin³∅ + ycos³∅ = sin∅. cos∅
x.sin³∅ + cos²∅.(ycos∅) = sin∅.cos∅
use xsin∅= ycos∅ in above
xsin³∅ + cos²∅.xsin∅ = sin∅.cos∅
xsin∅( sin²∅ + cos²∅) = sin∅.cos∅
xsin∅ = sin∅.cos∅
x = cos∅
so, y = sin∅
now we know,
sin²∅ + cos²∅ = 1
put sin∅ = y
cos∅ = x
hence, x² + y² = 1
4).
Downstream speed,
= 92
92
= 4.5 kmph
Upstream speed,
= 96
96
= 1.5 kmph
Thus, speed of boat in still water,
= 4.5+1.52
4.5+1.52
= 3 km/h
Speed of current = 4.5−1.52
4.5−1.52
= 1.5 km/h
a. 3 , 1.5 is correct answer.
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