Mock Quant Test for Trigonometry and Mensuration 1(20 Qn) 15min for all Govt. Exams

Solution

1.The Co-ordinates of the centroid of the triangle ABC are (6, 1). If two vertices A and B are (3, 2) and (11, 4) find the third vertex

(a) (4, –3) (b) (2, 1) (c) (2, 4) (d) (3, 3)

2.In a triangle ABC, the lengths of the sides AB, AC and BC are 3, 5 and 6 cm, respectively. If a point D on BC is drawn such that the line AD bisects the angle A internally, then what is the length of BD ?

(a) 2 cm (b) 2.25 cm (c) 2.5 cm (d) 3 cm

3.Arc ADC is a semicircle and DB  perpendicular to  AC. If AB = 9 and BC = 4, find DB.

(a) 6 (b) 8 (c) 10 (d) 12

4.The perimeter of the triangle whose vertices are (– 1,4),(– 4, –2), (3, –4), will be :

(a) 38 (b) 16 (c) 42 (d) None of these

5.The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is

(a) 6 cm (b) 7 cm (c) 8 cm (d) 5.5 cm

6.Two parallel chords of a circle of diameter 20 cm are 12 cm and 16 cm long. If the chords are in the same side of the centre, then the distance between them is

(a) 28 cm (b) 2 cm (c) 4 cm (d) 8 cm

7.Two circles with radii 25 cm and 9 cm touch each other externally. The length of the direct common tangent is     

(a) 34 cm (b) 30 cm (c) 36 cm (d) 32 cm

8.A and B are centres of the two circles whose radii are 5 cm and 2 cm respectively. The direct  ommon tangents to the circles meet AB extended at P. Then P divides AB.

(a) externally in the ratio 5 : 2 (b) internally in the ratio 2 : 5 (c) internally in the ratio 5 : 2 (d) externally in the ratio 7 : 2

9.When two circles touch externally, the number of common tangents are

(a) 4 (b) 3 (c) 2 (d) 1

10.If the inradius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle in sq. cm is

(a) 48 (b) 100 (c) 64 (d) 96

11.If the diagonal of a square is doubled, then its area will be

(a) three times (b) four times (c) same (d) none of these

12.A square is inscribed in a circle of radius 8 cm. The area of the square is

(a) 16 cm² (b) 64 cm² (c) 128 cm² (d) 148 cm²

13.A wire is bent into the form of a circle, whose area is 154 cm². If the same wire is bent into the form of an equilateral triangle, the approximate area of the equilateral triangle is

(a) 93.14 cm² (b) 90.14 cm² (c) 83.14 cm² (d) 39.14 cm²

14.A metal pipe of negligible thickness has radius 21 cm and length 90 cm. The outer curved surface area of the pipe in square cm is

(a) 11880 (b) 11680 (c) 11480 (d) 10080

15.A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marble tiles 20 cm × 20 cm, the number of tiles required to cover the path is

(a) 1800 (b) 200 (c) 2000 (d) 2150

16.If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm². The radius of the sphere before the increase was:

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

17.A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is

(a) 3 : 1 (b) 13 : 9 (c) 17 : 9 (d) 34 : 9

18.A cylinder is filled to 4/5th its volume. It is then filled so that the level of water coincides with one edge of its bottom and top edge of the opposite side, In the process, 30 cc of the water is spilled. What is  the volume of the cylinder?

(a) 75 cc (b) 96 cc (c) Data insufficient (d) 100 cc

19.A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of  radius 9 cm. The percentage of the wood wasted is:

(a) 25% (b) 30% (c) 50% (d) 75%

20.A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel.

(a) 18 cm (b) 22 cm (c) 24 cm (d) None of these

SSC(CGL) Quant Mock Test10(20-25 min) 40 Qn

Solution


1.A car travels 25km/h faster than a bus for a journey  of 500 km. If the bus takes 10hr more than the car, then the speed of car and bus is.. 

a.25,40  b.50,25  c.25,60  d.NOT                      

2.find the value of √(30+√(30+√(30+(.............    

a. 5    b.3√10    c.6   d.7  

3. Three persons undertake to compete a piece of work for Rs. 1,200. The first person can complete the work in 8 days, second person in 12 days and third person in 16 days. They complete the work with the help of a fourth person in 3 days. What does the fourth person get a.180 b.200    c.225     d.250
4. Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone ,A would require   a.5(1/5)days  b.6(1/4)days c.7(1/2)days    d.8(3/4)days
5.When 335 is added to 5A7, the result is 8B2. 8B2 is divisible by 3.What is the largest possible value of A   a.8      b.2        c.1      d.4
6.The greatest 4 digit number exactly divisible by 10,15,20 is  

a.. 9990    b.9960     c.9980     d.9995
7.If the students of 9th class are arranged in rows of 6,8,12 or 16, no student is left behind. Then the possible number of students in the class is           

a.60      b.72    c.80    d.96
8.The unit digit in 3 x 38 x 537 x 1256 is            

a.4         b.2     c.6      d.8
9.Ram got twice as many marks in English as in Science. His total marks in English, Science and mathematics are 180. If the ratio of his marks in English and Maths is 2:3, what are his marks in Science?                    

a.30       b.60     c.72    d.90   e.NOT
10.Three numbers are in the ratio 2:3:4. If the sum of their squares is 1856, then the numbers are ?
a.8,12 and 16      b.16, 24 and 32    c.12, 18 and 24    d.None of the above
11.If x runs are scored by A, y runs by B and z runs by C, then x:y=y:Z=3:2. If total number of runs scored by A,B and C is 342, the runs scored by each would be respectively  

 a.144,96,64      b.162,108,72     c.180,120,80     d.189,126,84
12. Rs. 900 is divided among A,B,C; The division is such that 1/2 of A,s money = 1/3 rd of B's money = 1/4 th of C's money. Find the amount (in Rs.) received by A,B,C.
a.300,400,200     b.350,450,100     c.200,300,400     d.400,150,350
13.The average of first three numbers is double of the fourth number. If the average of all the four numbers is 12, find the 4th number     a.16     b.78/7     c.20      d.18/7
14.Sunil completes a work in 4 days, whereas Dinesh completes the work in 6 days. Ramesh works 1 ( 1/2 )times as fast as Sunil. The three together can complete the work in
a.1(5/12) days     b.1(5/7) days     c.1(3/8) days      d.1( 5/19) days
15.Two successive discount of a% and b% on the marked price of an article are equivalent to the single discount of       

a.(a+b)%     b.(a+b - ab/100)%     c.(a+b)/100 %      d. (a+b)/2%
16.Gita buys a plot of land for Rs. 96,000. She sells 2/5 of it at a loss of 6%. She wants to make a profit of 10% on the whole transaction by selling the remaining land. The gain % on the remaining land is              

a.20         b.20(2/3)        c.14        d.7
17.An article is sold at a gain of 15%. Had it been sold for Rs. 27 more, the profit would have been 20% more. The cost price of the article is          

a.Rs. 500       b.Rs. 700     c.Rs. 540     d.Rs. 545
18. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price (in Rs.) of a ball is

 a.45          b.50            c.55                d.60
19. A number increased by 22 and 1/2% gives 98.The number is      

a.45      b.18      c.80      d.81
20.Two items A and B are sold at a profit of 10% and 15% respectively. If the amount of profit received is the same, then the cost of A , B may be    

a.1000,1500     b.5000, 2000    c.3000,2000    d.3000, 5000
21.If the average of 6 consecutive even numbers is 25, the difference between the largest and the smallest number is                                                

a.8     b.10    c.12    d.14
22. By selling 25 meters of cloth a trader gains the selling price of 5 meters of cloth. The gain % is               a.25     b.20     c.28    d.29
23. What sum will give Rs. 244 as the difference between simple interest and compound interest at 10% in 1 and 1/2 years compounded half yearly.   

a.40000     b.36000    c.32000     d.28000
24. A sum of Rs. 3200 invested at 10% p.a. compounded quarterly amounts to Rs. 3362. Compute the time period.                                                  

a.1/2 year           b.1 year            c.2 years           d.3/4 year
25.If sum of money compounded annually becomes 1.44 times of itself in 2 years, then the R% is         

 a.25% b.22% c.21% d.20%
26. A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. Its melted and recast into right circular cone with radius of its base as 1.2 cm. Then the height of the cone (in cm) is                             

a.3.6 b.4.8 c.6.4 d.7.2
27. The area of a rectangle is thrice that of a square. The length of the rectangle is 20 cm and the breadth of the rectangle is 3/2 times that of the side of the square. The side of the square in cm is
a.10 b.20 c.30 d.60

28.How many plants will be there in a circular bed whose outer edge measure 30 cms, allowing 4 cm². for each plant ?                                         

a.18    b.750      c.24      d.120

29. A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is  a.1:4      b.4:1     c.1:2    d.2:1

30. If the area of a circle decreases by 36%, then the radius of a circle decreases by                 

a.20%      b.18%    c.36%    d.64%

31.A cylindrical bucket of height 36 cm and radius 21 cm is  filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed, the height of the heap being  12 cm. The radius of the heap at the base is

a.63 cm  b.53 cm  c.56 cm  d.66 cm

32.The area of a square field is 576 km2. How long will it take for a horse to run around at the speed of 12 km/h ? 

a.12 h       b.10 h    c.8 h    d.6 h

33.A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper    

a.140 cm²  b.240 cm²  c.560 cm²  d.None of these

34.The water in a rectangular reservoir having a base 80 metres by 60 metres is 6.5 metres deep. In what time can the water be emptied by a pipe whose cross section is a square of  side 20 cm, if the water runs through the pipe at the rate of  15 km per hour 

a.52 hrs  b.26 hrs  c.65 hrs d. 42 hrs

35. Wheels of diameters 7 cm and 14 cm start rolling  simultaneously from X and Y, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of  revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is:

a. 22 cm / sec b. 44 cm / sec  c. 66 cm / sec d.132 cm / sec

36.A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is         a.100 m  b. 200 m  c.100 (2)^1/2 m d.10(2)^1/2  m

37.AB and CD two chords of a circle such that AB = 6 cm CD = 12 cm. And AB|| CD . The distance between AB and CD is 3 cm. Find the radius of the circle.

a. 3(5)^1/2 (b) 2(5)^1/2 (c) 3(4)^1/2 (d) 5(3)^1/2

38.65% of students in a class like cartoon movies ,70% like horror movies and 75% like war movies. What is the smallest % of students liking all the 3 types of movies.

a.30%   b.20%   c.10%   d.5%

39.Shyam has 3 notebooks x,y and z. Of these , X has 120 pages, Y has 10% more and Z has 10% less .If he tore out 5%,10% and 15% of pages in X,Y and Z , then what % of total pages did he tear out.

a.8%  b. 15%  c.7%  d.not

40. A,B and C together earn Rs 1450 and spend 60%,65%and 70% of their salaries respectively. If their savings are in ratio 14:21:15, the salary of B is

a.500  b.600  c.450  d.750

SSC(CGL) Quant Mock Test9(20-25 min) 30 Qn

Solution

1.AB and CD are 2 parallel chords of a circle in which AB=10cm and CD=24cm. If these chords are on opposite side of the centre and the distance between them is 17cm. Then the radius of the circle will be.

a.11cm  b.13cm  c.12cm  d.10cm

2.There is a pole inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each corner point is equal then the position of foot of the pole in the park ABC is

a.At centroid  b.at Circumcentre  c.at Incentre  d.at Orthocentre

3. The area of rhombus is 4800m² . and side is 40m. Find the diagonals

a.65.8,124  b.145.83,65.83  c.33.9,117  d.38.7,128

4.A manufacturer of fridges produced 600 units in the third year and 700 units in the seventh year. Assuming that the production increases uniformly by a fixed no. Every year, the total production in seventh year will be       

a.4537  b.4375  c.4753  d.4735

5.In an arithmetic sequence ,the first term is 11,the nth term is 143 and the second term is 15, find the sum of first n terms of the sequence. 

 a.2681  b.2861  c.2618  d.2816

6.65% of students in a class like cartoon movies ,70% like horror movies and 75% like war movies. What is the smallest % of students liking all the 3 types of movies. 

a.30%  b.20%  c.10%  d.5%

7. The product of first 3 composite numbers is equal to                                  a.316  b.192  c.315  d.218

8.A,B and C have 40,x and y balls respectively. If B gave 20 balls to A, he is left with half as many balls as C . If together they had 60 more balls, each of them would have 100 balls on an average. Find ratio of x to y.

a.3:2   b.2:3  c.2:1  d.3:4

9. The auto fare consist of a fixed charge together with the charge for the distance covered. For a journey of 10 km, the charge paid is Rs85/- and for a journey of 15km, the charge paid is Rs120/-.The fare for the journey of 25km will be 

a..175  b.190  c.180  d.225

10.The avg. Marks of  a student in 8 subjects is 87. Of these highest marks is 2 more than the one next in value. If these 2 subjects are eliminated the avg. Marks of the remaining subjects is 85. Find the highest score.

a.91  b.94  c.89  d.96

 11. Shyam has 3 notebooks x,y and z. Of these , X has 120 pages, Y has 10% more and Z has 10% less .If he tore out 5%,10% and 15% of pages in X,Y and Z , then what % of total pages did he tear out.

a.8%  b. 15%  c.7%  d.not

 

12. A grocer sells rice at profit of 10% and uses wt which is 20% less. Find his total % gain.

a.25%  b.20%  c.10%  d.NOT

 

13.What is the maximum percentage discount that a merchant can offer on her marked price so that she ends up selling no profit or loss, if she had initially marked her goods up by 50%.

a.16.67%  b.20%  c.50%  d.33.33%

14. The concentration of petrol in 3 different mix. of(kerosene and petrol) is  ½, 3/5, 4/5. If 2L,3L and 1 L are taken from these three different vessels and mixed ,what is the ratio of petrol  and kerosene in the new mixture.                                                                                                         a. 4:5   b.3:2  c.3:5  d.2:3

15.A and B can do a piece of work in 20 and 15 days respectively. They work together for 6 days , after which B was replaced by C . If the work was finished in next 4 days,Then the no. Of days in which C alone could do work will be. 

 a.60 Days  b.40 days  c.35 Days  d.30days

16.Ratio of earnings of A and B is 4:7. If the earning of A increase by 50% and B decrease by 25%, the new ratio of their earnings become 8:7, How much is A earning.

a.28000  b.21000  c.26000  d.Data Inadequate

17. The Rate of Interest for Ist 2 years is 3%pa, for next 3yrs is 8%pa and for period beyond 5yrs is 10% pa. If a man earns Rs1520/- as SI for 6years, How much money did he deposit.

a.3500  b.3600  c.3700  d.3800

18.A sum of money lent at CI for 2 years at 20% pa would fetch Rs 462 more, if the interest was payable half yearly than if it was payable annually. The sum is       

 a.10000  b.20000  c.40000  d.50000

19.A,B and C together earn Rs 1450 and spend 60%,65%and 70% of their salaries respectively. If their savings are in ratio 14:21:15, the salary of B is 

a.500  b.600  c.450  d.750

20.In a test consisting of 150 qns carrying 1 mark each, Saurabh answered 80% of first 75 qns correctly. What % of the other 75 qns does he need to answer correctly to score 60% overall.

a.20  b.40  c.50  d.60

21, Postcard costing 30p each and Inland letters costing Rs1.50 each were purchased for Rs 66. Total no. Of postcard and inland letters purchased were 60 . If the number of postcards and Inland letters is interchanged, Then the cost is  

 a.42  b.30  c.21  d.60  

    

22. If (x-a)(x-b)=1 and a-b+5=0, then the value of (x-a)³ - 1/(x-a)³ is
a. -125 b. 1 c. 125 d. 140
23. If √x = √3 - √5, then the value of x²-16x+6 is
a. 0     b. -2    c. 2    d. 4
24. The value of √(2 ³√(4 √(2 ³√(4...... is        a. 2  b. 2²  c. 2³  d. 2⁵
25. The value of {3√2/(√3 + √6) - 4√3/(√6 + √2) + √6/(√2 + √3)} is   a.√2    b.0   c.√3   d.√6
26. If a²+b²+c² = 2(a-b-c), then the value of 4a-3b+5c is  a.2     b.3   c.5   d.6
27. If 2x + 2/x =3, then the value of x³ + 1/x³ +2 is  a.-9/8    b.-25/8    c.7/8    d.11
28. Out of the given , one of the factors of (a²-b²)³+(b²-c²)³+(c²-a²)³ is
a.(a+b)(a-b)    b.(a+b)(a+b)    c.(a-b)(a-b)  d.(b-c)(b-c)
29. An isosceles triangle ABC is right angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of ΔABC. If AP=a cm, AQ=b cm and <BAD=15°, sin75°=
a.2b/√3a     b.a/2b   c.√3a/2b   d.2a/√3b
30. Each interior angle of a regular octagon in radians is  a.π/4   b.3π/4   c.2π/3 d.π/3