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Maths Quiz for KVS and CTET Exams Q1. Anil had to do a multiplication. Instead of taking 35 as one of the multiplies, he took 53. As a result the product went up by 540. What is the new product?
(a) 1150
(b) 540
(c) 1440
(d) 1590

Q2. What is the least number of soldiers in a regiment, such that they stand in rows of 18, 15 and 25 and also from a solid square?
(a) 1800
(b) 225
(c) 900
(d) None of these

Q3. The average weight of 5 apples is 100 g and the average weight of 4 oranges is 80 g. If 2 apples and 2 oranges are picked from them that average weight is found to be 85 g. What is the average weight of the remaining apples and oranges?
(a) 88 g
(b) 90 g
(c) 96 g
(d) 95 g

Q4. In an exam the average was found to be p marks. After deducting typographical error the average marks of 94 students reduced from 84 to 64. Due to this the average came down by 18.8 marks What was the number of students who took the exam?
(a) 100
(b) 90
(c) 110
(d) 120

Q5. Tanuj Johri travels from X to Y at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for the whole journey?
(a) 36 kmph
(b) 45 kmph
(c) 48 kmph
(d) 50 kmph

Q6. In the figure AB || CD, find x°:

(a) 50°
(b) 90°
(c) 30°
(d) 70°

Q7. A pole broken by the storm of wind and its top stuck the ground at an angle of 30° and at a distance of 20 m from the foot of the pole, the height of the pole before it was broken was
(a) 20√3 m
(b) (40√3)/3 m
(c) 60√3 m
(d) (100√3)/3 m

Q8. In a right-angled triangle PQR, PR is the hypotenuse of length 20 cm, PRQ = 30°, the area of the triangle is
(a) 100√3  cm^2
(b) 100/√3 cm^2
(c) 50√3  cm^2
(d) 25√3  cm^2

Q9. The value of tan 1° tan 2° tan 3° …… tan 89° is:
(a) 1
(b) 0
(c) √3
(d) 1/√3

Q10. If 5 tanθ = 4, then (5 sin⁡θ-3 cos⁡θ)/(5 sin⁡θ+2 cos⁡θ ) is equal to
(a) 2/3
(b) 1/4
(c) 1/6
(d) 1/3
Solutions

S1. Ans.(d)
Sol. Let the number be x.
Increase in product = 53x – 35x = 18x = 18x = 540 ⇒ x = 30
Hence, new product = 53 × 30 = 1590. Hence, option (d) is the answer.

S2. Ans.(c)
Sol. Number of soldiers should be a multiple of 18, 15 and 25 ⇒ Number should be a multiple of LCM (18, 15, 25)
Now lowest multiple of 450 that is a perfect square = 900. Hence option (c) is the answer.
S3. Ans.(c)
Sol. Weight of 5 apples = 500 g
Weight of 4 oranges = 320 g
Weight of 2 apples and 2 oranges picked = 340 g
So, weight of 3 apples and 2 oranges remaining = (500 + 320 – 340)g = 480 g
Average weight = 480/5 = 96 g

S4. Ans.(a)
Sol. Number of students = (84 – 64) × 94/18.8 = 100

S5. Ans.(c)
Sol. Let the distance between X and Y be x km.
Time taken from X to Y @ 40 km/h =x/40 hours
Time taken from Y to X @ 60 km/h =x/60 hours
Average speed =(2x)/(x/40  + x/60)= 48 km/h.

S6. Ans.(a)
Sol. CEF = ABF = 70°
∴ FED = 180° – 70° = 110°
EDF + DFE + FED = 180°
∴ FDE = 180° – (110° + 20°) = 50°

S7. Ans.(a)
Sol.

3 : √3 (here 3unit= height of tree =2unit +1unit)
3/√3 ∶1
20×(3/√3) ∶20
20√3

S8. Ans.(c)
Sol.

Triangle = 1/2×B×P
=1/2×10×10√3
=50√3

S9. Ans.(a)
Sol. tan 1°.tan 2°.tan 3° …… tan 45°…… tan 88°.tan 89°
= (tan 1°. tan 89°)(tan 2°. tan 88°) … tan 45°
= (tan 1°. cot 1°).(tan2°. cot 2°) …… tan 45° = 1
[∵ tan (90° – θ) = cot θ, tan θ.cot θ = 1]

S10. Ans. (c)
Sol. ∴ 5 tan θ = 4
⇒tan⁡θ=4/5  ,(5 sin⁡θ-3 cos⁡θ )/(5 sin⁡θ+2 cos⁡θ )
Divide numerator and denominator by cos θ
=(5(sin⁡θ/cos⁡θ) -3  (cos⁡θ/cos⁡θ ))/(5  (sin⁡θ/cos⁡θ) +2  (cos⁡θ/cos⁡θ))
=(5 tan⁡θ-3)/(5 tan⁡θ+2)
=(5×(4/5))-3/(5 × (4/5))  + 2)
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