### Quantitative Aptitude (Mathematics)

**Q.1:** A sum of ₹ x is divided among A, B and C such that the ratio of the shares of A and C is 8 : 7 and that of B and C is 3 : 2. If the difference between the shares of A and B is ₹ 240, then what is the value of x ?

(A) 2544

(B) 2580

(C) 2490

(D) 2448

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**Q.2:** If a pair of shoes marked at ₹350 is offered at ₹308, then what will be the discount percentage?

(A) 42%

(B) 13.6%

(C) 12%

(D) 14%

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**Q.3:** In AD is the bisector of meeting BC at D, If AB = 15 cm, BC = 10 cm and the length of BD is 2 cm less than that of DC, then the length of AC is:

(A) 18.5 cm

(B) 18 cm

(C) 16 cm

(D) 22.5 cm

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**Q.4:** Simplify the following expression.

(A)

(B)

(C)

(D)

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**Q.5:** The value of cosec + sin15^{o}sin35^{o}sec55^{o}sin30^{o}sec75^{o} is :

(A) 1

(B) 2

(C)

(D) 0

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**Q.6:** Some persons went on an outstation tour. The histogram shows their ages. How many persons are less than 20 years of age?

(A) 22

(B) 31

(C) 25

(D) 18

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**Q.7:** Study the given and answer the question that follows.

The total production of paper by company B in 2015 and 2017 to 2019 was what percentage less than 90% of the total production of paper by company A in 2014 to 2019 (correct to one decimal place)?

(A) 22.4%

(B) 19.6%

(C) 21.2%

(D) 17.5%

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**Q.8:** In and E are points on AB and BC, respectively, such that DE is parallel to AC. If DE = 3 cm. AC = 5 cm and the area of trapezium ACED = 32 cm^{2} , then what will be the area of ?

(A) cm^{2}

(B) cm^{2}

(C) 16 cm^{2}

(D) 18 cm^{2}

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**Q.9:** Study the given pie chart and answer the question that follows.

Total number of students admitted in a college = 700.

Distribution of the percentage of students in various caurses.

Percentage-wise distribution of the number of boys.

Course | Number of boys |

B. Sc. Maths | 40% |

B. Sc. Physics | 68% |

B. Sc. Chemistry | 58% |

B. Sc. Computer Science | 80% |

B. Com | 75% |

BBA | 65% |

(A) 3 : 7

(B) 4 : 7

(C) 3 : 5

(D) 2 : 5

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**Q10:** In a circle with centre O and radius 6.5 cm, a chord AB is at a distance 2.5 cm from the centre. If tangents at A and B intersect at P, then find the distance of P from the centre.

(A) 16.9 cm

(B) 18 cm

(C) 15 cm

(D) 17 cm

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**Q.11:** What is the compound interest (in ₹) on a sum of ₹46,000 for years at 15% per annum, interest being compounded annually ( nearest to a ₹) ?

(A) 18,458

(B) 18,485

(C) 19,485

(D) 19,458

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**Q.12:** If , then what will be the value of x^{4} +?

(A) 10402

(B) 9606

(C) 9602

(D) 10406

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**Q.13:** If 3x – 2y + 3 = 0 , then what will be the value of 27 x^{3} + 54xy + 30 – 8y^{3 }?

(A) -27

(B) 57

(C) -57

(D) 3

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**Q.14:** Chords AB and CD of a circle meet at point P (outside the circle), when produced, If AB = 9 cm, PB = AB and CD = 5 cm, then the length of PD (in cm ) is:

(A) 7

(B) 6

(C) 5

(D) 4

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**Q.15:** By selling an article for ₹3,150, a shopkeeper earns 5% profit. For how much money should he sell the article in order to gain 8% ?

(A) ₹3,240

(B) ₹3,180

(C) ₹3,200

(D) ₹3,250

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**Q.16:** Given that , the value of (A^{2} + B^{2} – C^{2}) is:

(A) 4

(B) 8

(C) 12

(D) 0

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**Q.17:** A solid metallic sphere of radius 12 cm is melted and recast in the form of small spheres of radius 2 cm. How many small spheres are formed ?

(A) 24

(B) 96

(C) 864

(D) 216

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**Q.18:** A tap can fill a tank in 4 hours. Another tap can fill the same tank in 6 hours. If both the taps are opened at the same time, then in how much time will the empty tank be filled completely?

(A) 2 h 30 min

(B) 2 h 24 min

(C) 3 h

(D) 2 h

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**Q.19:** If is an acute angle, then what will be the value of ?

(A)

(B)

(C)

(D) 1

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**Q.20:** A boat can go 15 km downstream and 8 km upstream in 2 h. It can go 20 km downstream and 12 km upstream in 2 h 50 min. What is the speed (in km/h ) of the boat while going downstream?

(A) 16

(B) 15

(C) 20

(D) 18

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**Q.21:** Study the given pie chart and answer the question that follows.

The pie chart shows the distribution (degree wise) of the number of computers sold by a shopkeeper during five months.

If the difference between the numbers of computers sold in May and the numbers of computers sold in February is x, then the value of x will be:

(A) 450

(B) 480

(C) 540

(D) 420

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**Q.22:** The average of 40 numbers is 48.2. The average of the first 15 numbers is 45 and that of the next 22 numbers is 50.5. The 38^{th} and 40^{th} numbers ?

(A) 48

(B) 49

(C) 47.5

(D) 48.5

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**Q.23:** If the five-digit number 457 ab is divisible by 3, 7 and 11, then what is the value of a^{2} + b^{2} – ab ?

(A) 49

(B) 36

(C) 24

(D) 33

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**Q.24:**

(A) 62.5%

(B) 37.98%

(C) 61.25%

(D) 51.6%

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**Q.25:** If , then what will be the value of ?

(A) 1

(B) 7

(C) 11

(D) -1

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