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# Maths Questions for CTET Exam 2017

Q1. The internal angle bisectors of the ∠B and ∠C of the ∆ABC intersect at O. If ∠A = 100°, then the measure of ∠BOC is:
(a) 110°
(b) 140°
(c) 130°
(d) 120°
Q2. The ratio of each interior angle to each exterior angle of a regular polygon is 3 : 1. The number of sides of the polygon is:
(a) 6
(b) 7
(c) 8
(d) 9
Q3. Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is:
(a) 2 cm
(b) 3 cm
(c) 4 cm
(d) 5 cm
Q4. If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in the expenditure on the commodity?
(a) 4% increase
(b) 4% decrease
(c) 8% decrease
(d) 8% increase
Q5. A motorcyclist goes from Mumbai to Pune, a distance of 192 km at an average speed of 32 km/h. Another man starts from Mumbai by car, 2 (1/2) hours after the first and reaches Pune half an hour earlier. What is the rate of the speed of the motorcycle and the car?
(a) 1 : 2
(b) 1 : 3
(c) 10 : 27
(d) 5 : 4
Q6. A person sets to cover a distance of 12 km in 45 minutes. If he covers 3/4 of the distance in 2/3rd time, what should his speed to cover the remaining distance in the remaining time?
(a) 16 km/hr
(b) 8 km/hr
(c) 12 km/hr
(d) 14 km/hr

Q7. Length of a train is 287 m and it passes a bridge in 38 sec at the speed of 90 km/h. What is the length of the bridge?
(a) 665 m
(b) 663 m
(c) 680 m
(d) 580 m
Q8. A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train, which of the following information is necessary?
(a) Only the length of the train
(b) Only the length of the engine
(c) Either the length of the train or the length of the engine
(d) Both the length of the train and the length of the engine
Q9. The area of an equilateral triangle is 400√3 sq. m. Its perimeter is:
(a) 120 m
(b) 150 m
(c) 90 m
(d) 135 m
Q10. From a point in the interior of an equilateral triangle, the perpendicular distance of the sides are √3 cm, 2√3 cm and 5√3 cm. The perimeter (in cm) of the triangle is
(a) 64
(b) 32
(c) 48
(d) 24
Solutions:
S1. Ans.(b)
Sol. ∠BOC = 90° + (∠A)/2
= 90° + (100°)/2
= 90° + 50°
= 140°
S2. Ans.(c)
Sol.(x – 2)/2 = (3/1)
x – 2 = 6
x = 8
S3. Ans.(b)
Sol. Let the radius of one circle be ‘r’ & other circle be (14-r)
According to the given condition
π r^2 + π (14-r)^2 = 130 π
By solving, we get
x = 11 or 3
S4. Ans.(b)
Sol. By using formula,
% decrease = x^2/100
x = 20%
% decrease = (20 × 20)/100 = 4% decrease
S5. Ans.(a)
Sol.
Speed of the first man = 32 km/hr
Time taken = 192 ÷ 32 = 6 hr
Second man covers 192 km in 3 hr
∴ Speed of the second man
= 192 ÷ 3 = 64 km/hr
Ratio = 32 : 64 or 1 : 2
S6. Ans.(c)
Sol.
Distance already covered = (3/4) × 12 = 9 km
Time spent = (2/3) × 45 min = 30 min
Distance left = (12-9) km = 3 km
Time left = (45-30) min = 15 min
∴ Required speed =3/ (15/60) km/hr
= 12 km/hr
S7. Ans.(b)
Sol.
Total distance covered = 90 × (5/18) × 38 = 950 m
So, length of bridge = 950 – 287 = 663
S8. Ans.(d)
Sol. Since the sum of the length of the train and the engine is needed, so both the lengths must be known.
S9. Ans.(a)
Sol. √3/4 a^2 = 400√3
a^2 = 1600
a=40
Perimeter = 40 × 3
= 120 m
S10. Ans.(c)
Sol. a/h = 2/√3
a = 2/√3 (p1+p2+p3 )
a=2/√3 (√3 + 2√3 + 5√3)
a=(2/√3) × (8√3)
a = 16
Perimeter = 16 × 3
= 48 m