**Q1. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees? **

(a) 75

(b) 90

(c) 120

(d) 150

**Q2. Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD=∠BAC. What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC? **

(a) 7/9

(b) 8/9

(c) 6/9

(d) 5/9

**Q3. What is the distance (in cm) between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm? **

(a) 1 or 7

(b) 2 or 14

(c) 3 or 21

(d) 4 or 28

**Q4. In the given diagram ABCD is a rectangle with AP = PQ = FB. What is the ratio of the area of triangle CPQ to that of ∆ACQ**

(a) 1 : 2

(b) 2 : 3

(c) 2 : 5

(d) 3 : 4

**S4. Ans.(a)**

**Sol.** Let DC = 3x unit

AP = PQ = QB = x unit (given in question)

(area of ∆CPQ)/(area of ∆ACQ)=x/2x=1/2 {height of the both triangle is equal)

**5. A train running at a speed of 120 km/h crosses a signal post in 15 seconds. What is the length of the train in metres.**

(a) 300 m

(b) 200 m

(c) 500 m

(d) Can’t be determined

**S5. Ans.(c)**

**Sol. **Speed = 120 km/h

=120×5/18=100/3 m/s

Length of train =100/3×15

= 500 m

**Q6. A car finishes a journey in 10 h at the speed of 80 km/h. If the same distance to be covered in 8 hr, then how much speed would the train gather:**

(a) 8 km/h

(b) 10 km/h

(c) 12 km/h

(d) None of these

**S6. Ans.(d)**

**Sol. **Distance travelled by the car =80×10=800 km

Speed =800/8=100 km/hr

Increase in speed = 20 km/h

**Q7. Excluding stoppages, the speed of a bus is 60 km/hr and including stoppages it is 40 km/hr. For how many minute does the bus stop per hour. **

(a) 10 minutes

(b) 20 minutes

(c) 30 minutes

(d) 25 minutes

**S7. Ans.(b)**

**Sol. **Stoppage time per hour =(Difference of speed )/(Speed without Stoppage)

=(60-40)/60=20/60= 20 minutes

**Q8. A five digit number is made using digits 2, 8, 4, 7 and 6. Is the number divisible by 9? **

(a) Yes

(b) No

(c) Can’t say

(d) None of these

**S8. Ans.(a)**

**Sol.** We know that divisibility of 9 is the sum of all the digits divisible by 9

Sum of digit = 2 + 8 + 4 + 7 + 6 = 27

Which is divisible by 9

So the digit formed by these five number always be divisible by 9.

(a) 2312/1062

(b) 2361/921

(c) 2355/999

(d) None of these

**S9. Ans.(c)**

**Sol**. Let x = 2.357357357 …(i)

multiplied both side by 1000

1000x = 2357.357357 …(ii)

(ii) – (i)

999x = 2355

x=2355/999

**Q10. The LCM of two numbers is 1680 and their HCF is 120. If one number is 504, find the other number.**

(a) 204

(b) 320

(c) 400

(d) 560

**S10. Ans.(c)**

**Sol. **Let the other number = x

LCM × HCF = first number × second number

1680 × 120 = 504×x

x=(1680 ×120)/504=400

**11. If a man runs at 3 m/s. How many km does he run in 1 hr 40 minutes?**

(a) 16 km

(b) 18 km

(c) 17.5 km

(d) 15.5 km

**S11. Ans.(b)**

**Sol.** Speed of the man = 3 x 18/5 km/h = 54/5 km/h

Distance covered in 5/3 hrs=54/5 x 5/3 = 18 km

**12. Walking at the rate of 4 kmph a man covers certain distance in 2hr 45 min. running at a speed of 16.5 km/h the man will cover the same distance in.**

(a) 45 min

(b) 42 min

(c) 40 min

(d) none of these

**S12. Ans.(c)**

**Sol.** Distance=Speed x time

4 x 11/4=11 km

New speed =16.5 km/h

Therefore, Time=D/S=11/16.5 = 40 min

**Q13. If the ****denominator**** of a fraction is increased by 350%, and **** numerator**** is increased by 150%, then the resultant fraction is 25/51, what is the original fraction:**

(a) 11/17

(b) 11/15

(c) 15/17

(d) 13/15

**Q14. An election there were only two candidates, one of the candidates secured 40% of votes and is defeated by the other candidate by 298 votes. The total number of votes polled is:**

(a) 745

(b) 1460

(c) 1490

(d) 1500

**S14. Ans.(c)**

**Sol. **Let the total number of votes polled be x%

Now, according to the question

x×((60-40)/100)=298

x=298×5=1490

**Q15. In a test consisting of 80 questions carrying one mark each, Arpita answer 65% of the first 40 question correctly, what percent of the other 40 question does she need to answer correctly to score 75% on the entire test:**

(a) 60

(b) 85

(c) 75

(d) 40

**S15. Ans.(b)**

**Sol.** ⇒(60-40 × 65/100 )/40× 100=34/40×100=85%