Quant(Geometry) mock(Speed test-16) for Govt. exams(10 qns)

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Q1. The ratio between the number of sides of two regular polygons is 1:2 and the ratio between their interior angles is 2:3. The number of sides of the polygons are respectively  a. 5, 10    b.6, 12    c.7, 14    d.4, 8

 Q2. The length of the diagonal BD of the parallelogram ABCD is 18cm. If P and Q are the centroids of △ABC and △ADC respectively, length of PQ  is

a.4cm     b.12cm    c.6cm   d.9cm

Q3. A, B and C are three points on the circumference of a circle. If AB=AC=52√cm and ∠BAC=90⁰. the length of radius is

a. 15cm  b.5cm  c.10cm  d.20cm

Q4.AB and CD  are two parallel chords of respective lengths 8cm and 6cm on the same side of the center of a circle. The distance between them is 1cm. Then the radius of the circle is

a.4cm    b.5cm   c.3cm    d.2cm

Q5.△ABC is an isosceles triangle with AB=AC and AD as the median to base BC. If ∠ABC=35⁰, the ∠BAD is     a.70⁰    b. 35⁰   c. 55⁰   d. 110⁰ 

Q6.  If I is the incenter of △ABC,  ∠ABC=65⁰ and ∠ACB=55⁰, the ∠BIC is, 

a.110⁰   b. 120⁰  c. 130⁰  d. 140⁰

Q7. Sides of a right-angled triangle are in the ratio 4 : 5 : 6. If the in-radius of the triangle is 3 cm, the altitude of the triangle with base as the largest side is

a.7.5 cm  b.6 cm  c.8 cm  d.10 cm

Q8.The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is  a.7 cm  b.6 cm  c.5.5 cm  d.8 cm

Q9.A, B and C are three points on a circle such that angles subtended by the chords AB and AC at the centre are non-overlapping 90⁰ and 110⁰ respectively. ∠BAC is then equal to

a.80⁰  b.  90⁰  c 100⁰  d.70⁰

Q10.If the inradius of an equilateral triangle be 5 cm, its circumradius (in cm) is

a.10  b.15  c.25  d.30

Quant mock(Speed test-14) for Govt. exams(15 qns)

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1.If the length of the rectangle is increased by 20%, by what percent should the width be reduced to maintain the same area?
a) 13.37  b) 16.67  c) 21.33  d) 33.33

2.A rectangle whose sides are in the ratio 6:5 is formed by bending a circular wire of radius 21cm. Find the difference between the length and breadth of the rectangle?
a) 6cm   b) 8cm  c) 10cm  d) 12cm

3.Three professors P, Q, R are evaluating answer script of a subject. P is 40 more efficient than Q, who is 20 more efficient than R. P takes 10 days less than Q to complete the evaluation work. P starts the evaluation work and works for 10 days and then Q takes over. Q evaluates for next 15 days and then stops. In how many days, R can complete the remaining evaluation work?
a) 6.2 days  b) 7.2 days  c) 8.2 days  d) 9.2 days

4.9 men and 12 women can complete the job in 12 days.In how many days can 3 men and 4 women finish the same job working together ?
a.36days  b.42days  c.30days  d.28days

5.Kavya’s age is 3 times more than that of Rita. Kavya will be 2 ½ times that of Rita 8 years after. How many times will Kavya’s age be that of Rita 8 more years after?
a) 2.5  b) 2  c) 3  d) 3.5  e) 1.5

6.If 10 labourers can dig a well 40 m deep in 18 days, working 9 hours a day, how many additional labourers should be engaged to dig a similar well 80 m deep in 6 days, each labourer working 9 hours a day?
a) 30  b) 40  c) 50  d) 60

7.A train covers a distance between two stations P and Q in 30 minutes. If the speed of the train is reduced by 10km/hr, then the same distance is covered in 45 minutes. The distance between P and Q
a) 10km  b) 15km  c) 20km  d) 30km 

8.Without any stoppages a person travels a certain distance at an average speed of 40 km/hr and with stoppages he covers the same distance at an average of 20 km/hr. How many minutes per hour does he stop?
a) 15 min  b) 20 min  c) 30 min  d) 45 min

9.12 persons are seated at a circular table. Find the probability that 3 particular persons always seated together.
a) 9/55   b) 7/55  c) 4/55  d) 3/55

10.A boat takes 25 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 5 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?
a) 100 km  b) 122 km  c) 146 km  d) 178 km  e) 150 km

11.The difference between compound interest earned after 3 years at 5% p.a. and simple interest earned after 4 years at 4% p.a. is Rs 76. Find the principal amount.
a) Rs 32,000  b) Rs 28,000  c) Rs 31,500  d) Rs 32,500

12.A container filled with liquid containing 4 parts of water and 6 parts of milk. How much of mixture must be drawn off and filled with water so that the mixture contains half milk and half water.
a) ¼    b) 1/3  c) 1/6  d) 1/5

13.Sum of 2 numbers is 128 and their HCF is 8. How many numbers of pairs of numbers will satisfy this condition?
a) 2  b) 5  c) 3  d) 6  e) 4

14.What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

a.2 units  b.12 units  c.6.5 units  d.6 units  e.7.5 units

15.If the ratio of an external anglre and an internal angle of a regular polygon is 1:17

, the number of sides of the regular polygon is,

a.12  b.36  c.20  d.18

Quant mock(Speed test-13) for Govt. exams(15 qns)

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1. How many diagonals does a 63-sided convex polygon have?

a.3780  b.1890  c.3843  d.3906  e.1953

2. y = x² + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?

a.-32  b.-256  c.-255  d.-257 

3.How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!

a.25  b.8  c.6  d.5  e.2

4. The MRP of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

a.31%  b.22%  c.15%  d.13%  e.11%

5.How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?

a. 5¹⁰  b.10⁵  c.10P₅  d.10C₅

6. 10²⁵ - 7 is divisible by

a.2  b.3  c.9  d.NOT

7. 'a' and 'b' are the lengths of the base and height of a right angled triangle whose hypotenuse is 'h'. If the values of 'a' and 'b' are positive integers, which of the following cannot be a value of the square of the hypotenuse?

a.13  b.23  c.37  d.41

8. A passenger train covers the distance between stations X and Y, 50 minutes faster than a goods train. Find this distance if the average speed of the passenger train is 60 kmph and that of goods train is 20 kmph.

a.20 kms  b.25 kms  c.45 kms  d.40 kms

9. I travel the first part of my journey at 40 km/h and the second part at 60 km/h and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?

a.4 h   b.2 h   c.3h   d.NOT

10. Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?

a.18 d  b.36d  c.54d  d.NOT

11.A contractor undertakes to do a job in 18 days. He employees certain number of men, but 12 of them being absent from the very first day, the rest can complete the work in 30 days. The number of men originally employed?

a. 20  b. 25  c.30  d. 40

12.A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?
a.Rs 25,600  b.Rs 20,000  c.Rs 26,040  d.Rs 40,500

13.A mixture containing milk and water in the ratio 3:2 and another mixture contains them in the ratio 4:5. How many litres of the later must be mixed with 3 litres of the former so that the resulting mixture may contain equal quantities of milk and water?
a. 3.3/4 litre  b. 4.1/2 litre  c. 5.2/3 litre  d. 5.2/5 litre

14.In a group of 8 boys, 2 men aged at 21 and 23 were replaced two new boys. Due to this the average cost of the group increased by 2 years. What is the average age of the 2 new boys?
a. 17  b.30  c.28   d.23

15.The ratio between the rate of speed of travelling of A and B is 2:3 and therefore A takes 20 minutes more than time taken by B to reach a particular destination. If A had walked at double the speed, how long would he have taken to cover the distance?
a.60 min  b.35 min  c.20 min  d.30 min

Quant mock(Speed test-12) for Govt. exams(15 qns)

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1.If a Shopkeeper offers a discount of 30% on the Marked price, then he makes a loss of 16%. What % profit or % loss will he make if he sells at a discount of 10% of the Marked  price?

a.6% loss   b. 0.8% profit    c. 6.25% loss  d.8% profit

2.A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work in

a. 1   b.3   c.5   d.4

3.’A’ completes 60% of a task in 15 days and then takes the help of  B and C. B is 50% as efficient as ‘A’ is and C is 50% as efficient as B is. In how many more days will they complete the work?

a.13(1/3)  b.8(1/3)  c.5(5/7)   d.7(5/7)

4.The average age of a family of 5 members is 20 years. If the age of the youngest member is 10 years, what was the average age of the family just a day before the birth of the youngest member?

a. 13.5  b.14  c.15  d.12.5

5.The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

a.44  b.22  c.19  d.NOT

6.A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.

a.50  b.100  c.150  d.200

7.’A’ weighs twice as much as B. B’s weight is 60% of C's weight. D's weight is 50% of E's. E weighs 190% as much as A does. Which of these 5 persons weighs the least?

a.C  b.D  c.A  d.E  e.B

8.If x units are added to the length of the radius of a circle, what is the number of units by which the circumference of the circle is increased?

a.x  b.2  c.2π  d.2πx  e.x²

9.A triangle has sides a², b² and c². Then the triangle with sides a, b, c has to be:-

a.Right-angled  b.Acute-angled  c.Obtuse-angled d.NOT

10.Circle with center O and radius 25 cms has a chord AB of length of 14 cms in it. Find the area of triangle AOB.

a.144 cm²    b.121 cm²    c.156 cm²  d.168 cm²

11: What is the distance between the orthocentre and the circumcenter of a triangle who sides measure 24 cm, 26 cm and 10 cm?

a.13 cm   b.12 cm  c.7.5 cm   d.√30 cm

12.Pipes A, B and C can fill a tank in 30, 60 and 120 min respectively. Pipes B and C are kept open for 10 min, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 min before the tank overflows. How long does it take to fill the tank?

a.40 min  b.28 min  c.30 min  d.36 min

13.The sides of a triangle are 5, 6 and 10.  Find the length of the longest side of a similar triangle whose shortest side is 15

a.10  b.15  c.18  d.4

14.For what value of 'z' will the quadratic equation x² - zx + 4 = 0 have real and equal roots?

a.16  b.8  c.2  d.-4

15.If both 11² and 3³ are factors of the number a * 4³ * 6² * 13¹¹, then what is the smallest possible value of a?

a.121  b.3267  c.363  d.33