**Mathematics Question Papers**

**05-March-2020 (Shift-1)**

**Q1. If 5 sin Ø = 4, then the value of secØ + 4cotØ / 4tanØ – 5cosØ is:**

(a) 3/2

(b) 2

(c) 1

(d) 5/4

Correct Answer: 2

**Q2. The given table represents the exports (in `crores) of four items A, B, C and D over a period of six years. Study the table and answer the question that follows.**

What is the ratio of the total exports of item A in 2014 and 2015 to the total exports of item C in 2011 and 2015?

(a) 4 : 3

(b) 3 : 2

(c) 7 : 5

(d) 5 : 4

Correct Answer: 3 : 2

**Q3. The value of sec6Ø – tan6Ø – 3sec2 Øtan2 Ø + 1 / cos4 Ø – sin4 Ø + 2sin2 Ø + 2 is:**

(a) 2/3

(b) 1

(c) 3/4

(d) 1/2

Correct Answer : 2/3

**Q4. Two chords AB and CD of a circle with centre O intersect each other at P. If ∠APC = 95° and ∠AOD = 110°, then ∠BOC is :**

(a) 55°

(b) 70°

(c) 60°

(d) 65°

Correct Answer: 60°

**Q5. The compound interest on a certain sum at 50/3% p.a. for 3 years is 6,350. What will be the simple interest on the same some at the same rate for 17/3 years?**

(a) `11,400

(b) `7,620

(c) `9,600

(d) `10,200

Correct Answer: `10,200

**Q6. The given table represents the exports (in Rs. crores) of four items A, B, C, and D over a period of six years. Study the table and answer the question that follows.**

The total exports of item A from 2012 to 2014 is what percentage less than the total exports of all the four items in 2015? (correct to one decimal place)

(a) 15.2%

(b) 14.3%

(c) 16.7%

(d) 13.8%

Correct Answer: 14.3%

**Q7. If 12cos2 Ø – 2sin2 Ø + 3cosØ = 3 , 0° < Ø < 90° , then what is the value of cosecØ + secØ / tanØ + cotØ?**

(a) 1+√3/2

(b) 2+√3/4

(c) 4+√3/4

(d) 1+2√2/2

Correct Answer: 1+√3/2

**Q8. Ifx2 – 2√5x + 1 = 0, then what is the value of x5 + 1/x5 ?**

(a) 610√5

(b) 406√5

(c) 612√5

(d) 408√5

Correct Answer: 610√5

**Q9. The given table represents the exports (in Rs. crores) of four items A, B, C and D over a period of six years. Study the table and answer the question that follows.**

The total exports of item D in 2010, 2012 and 2014 is what percentage of the total exports of all the four items in 2011 and 2012?

(a) 44%

(b) 46.2%

(c) 44.8%

(d) 45%

Correct Answer: 44%

**Q10. A shopkeeper bought 80 kg of rice at a discount of 10%. Besides 1 kg rice was offered free to him on the purchase of every 20kg rice. If he sells the rice at the marked price, his profit percentage will be:**

(a) 50.3%

(b) 100/7%

(c) 108/7%

(d) 46/3%

Correct Answer: 50.3%

**Q11. In an examination in which the full marks were 500. Ascored 25% more marks than B, B scored 60% more marks than C and C scored 20% less marks than D. If A scored 80% marks, then the percentage of marks obtained by D is :**

(a) 54%

(b) 50%

(c) 60%

(d) 65%

Correct Answer: 50%

**Q12. The diagonal of a square A is (a + b) units. What is the area (in square units) of the square drawn on the diagonal of square B whose area is twice the area of A?**

(a) 2 (a + b)2

(b) 8 (a + b)2

(c) (a + b)2

(d) 4 (a + b)2

Correct Answer: 2 (a + b)2

**Q13. If 16a4 + 36a2 b2 + 81b4 = 91 and 4a2 + 9b2 – 6ab = 13, then what is the value of 3ab?**

(a) -3/2

(b) 5

(c) 3/2

(d) -3

Correct Answer: -3/2

**Q14. Pipes A and B can fill a tank in 10 hours and 40 hours, respectively. C is an outlet pipe attached to the tank. If all the three pipes are opened simultaneously, it takes 80 minutes more time than what A together take to fill the tank. A and B are kept opened for 7 hours and then closed and C was opened, C will now empty the tank in:**

(a) 49 hours

(b) 45.5 hours

(c) 42 hours

(d) 38.5 hours

Correct Answer: 49 hours

**Q15. The given table represents the exports (in Rs. crores) of four items A, B, C and D over a period of six years. Study the table and answer the question that follows.**

In which year, the exports of item D were 1.4 times the average exports of item B during six years?

(a) 2011

(b) 2013

(c) 2012

(d) 2014

Correct Answer: 2013

**Q16. If the nine-digit number 708x6y8z9 is divisible by 99, then what is the value of x + y + z?**

(a) 9

(b) 27

(c) 5

(d) 16

Correct Answer: 16

**Q17. ****A train takes 5/2 hours less for a journey of 300 km, if its speed is increased by 20 km/h from its usual speed. How much time will it take to cover a distance of 192 km at its usual speed?**

(a) 4.8 hours

(b) 2.4 hours

(c) 6 hours

(d) 3 hours

Correct Answer: 4.8 hours

**Q18. The ratio of the ages of A and B, 8 years ago, was 2:3. Four years ago. the ratio of their ages was 5:7. What will be the ratio of their ages 8 years from now?**

(a) 7 : 8

(b) 3 : 4

(c) 4 : 5

(d) 5 : 6

Correct Answer: 4 : 5

**Q19. In ▲ABC, ∠C = 90°, AC =5cm and BC = 12cm. The besector of ∠A meets BC at D. What is the length of AD?**

(a) 5√13 / 3cm

(b) 2√13cm

(c) 4/3 √13cm

(d) 2/3 √13cm

Correct Answer: 5√13 / 3cm

**Q20. Sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, and sides AD and BC are produced to meet at F. If ∠ADC = 75°, and ∠BEC = 52°, then the difference between ∠BAD and ∠AFB is:**

(a) 22°

(b) 31°

(c) 23°

(d) 21°

Correct Answer: 31°

**Q21. D is the midpoint of side BC of ▲ABC. Point E lies on AC such that CE = 1/3 AC. BE and AD intersect at G. What is AG/GD?**

(a) 8 : 3

(b) 4 : 1

(c) 3 : 1

(d) 5 : 2

Correct Answer: 4 : 1

**Q22. The value of 11/3 ÷ 11/30 of 2/3-1/4 of 5/2÷3/5×24/5 / 2/3 of 15/2÷3/4-3/4×3/2÷9/4 is :**

(a) 20/7

(b) 20/9

(c) 10/21

(d) 25/7

Correct Answer: 20/7

**Q23. Sudha sold an article to Renu for Rs. 576 at a loss of 20%. Renu spent a sum of Rs.224 on its transportation and sold it to Raghu at a price which would have given Sudha a profit of 24%. The percentage of gain for Renu is:**

(a) 10.5%

(b) 11.6%

(c) 13.2%

(d) 12.9%

Correct Answer: 11.6%

**Q24. If P = x2 + y2 / (x-y)2 + 3xy, Q = (x+y)2 – 3xy / x2-y2 and R = (x+y)2 + (x-y)2 / x2-y2, then what is the value of (P÷Q) x R?**

(a) 2xy

(b) x2 + y2

(c) 4xy

(d) 2 (x2 + y2)

Correct Answer: 2 (x2 + y2)

**Q25. The average of 24 numbers is 56. The average of the first 10 numbers is 71.7 and that of the next 11 numbers is 42. The next three numbers (i.e., 22nd, 23rd, and 24th) are in the ratio 1/2 : 1/3 : 5/12, What is the average of the 22nd and 24th numbers?**

(a) 55

(b) 49.5

(c) 60.5

(d) 58

Correct Answer: 60.5