M. Prakash Academy Entrance Examination for Three Year Foun-dation Program

Maths - April 2019 to April 2012 past question papers

April 2019

1. Find x, if x− 6√x+ 1 + 10 = 0.

2. 10% of N is 25

of 33. Then 34

of N equals .

3. 32490 can be factorised as P 11 P

12 P

23 P

24 where P1, P2, P3, P4 are prime factors. Then

P1 + P2 + P3 + P4 equals .

4. If a2 − b2 = 369 and a+ b = 41 then a equals.

5. Given93 + 53

92 + 52 − x= 14. Find x.

6. L is LCM of 90, 30 and 36 and G is GCD or HCF of 90,30,36. Find value of LG.

7. Raju’s profit in first month is Rs.1600. His profit increases by Rs.50 per month.That is in second month his profit is Rs.1650. In third month it is Rs.1700 and soon. If his profit in 25th month is Rs.K then K

1000equals .

8. Given3√

7x+5 = 75. Find x.

9. Given15

8+

11

24− 3

5+

1

6= S. Find 10S.

10. How many three digited natural numbers are there which are divisible by 13? .

11. Givena

b=

4

3. Find

6a+ 4b

6a− 5b.

12. A completes a job in 45 days. B takes 30 days to complete the same job. How manydays will they require if they work together .

13. Average of Hardik in 30 cricket matches is 50. His average in first 18 matches is 30.What is his average in next 12 matches.

14. Average of first seven numbers in row is 45. Average of first four is 42. Average oflast 4 is 46. What is 4th number?

15. How many seconds will require for a train of length 385 meter running at 63 Km/Hrto cross an electric pole .

16. What is the angle between minute hand and hour hand when the clock shows time4 hrs 10 minutes .

17. Measures of interior angles of triangle are 2x+45, x+10 and 2x+20. Find measureof smallest angle .

18. In right angled triangle ABC as shown in figure AB = 12, AD = 13 & AC =√

544.Find DC.

544

D C

A

B

12 13

19. In 4MNP, m∠MPN = 45. MD is perpendicular to NP as shown. If MP =2√

106 and MN = 4√

14. Find NP.

18 22 106

45°PN D

M

20. Find the ratio of volume of a cube having side 12 units to surface area of the cube.

21. Area of circle is 49π. Find area of square inscribed in it .

22. 2ABCD is trapezium as shown in figure. Distance between two parallel sides ABand CD is h. DC = 2AB = 2h. Area of ABCD = 384. Find h.

2h

h

h

D C

BA

23. 6 kg of brass is made using 98.8% copper and remaining zinc. How many grams ofzinc is required .

24. 10% of 20% of 30% of 40% of 50% of 10000 is .

April 2017

1. Rohit secured 42% of the total marks and secured 10 marks more than the passingmarks. In the same exam, Mohit scored 29% of the total marks and failed by 16marks. What was the passing percentage?

2. A number when divided by 72 leaves remainder 65. Find the remainder when thesame number is divided by 12.

3. The number n = 26136 × k, where k is a natural number. What is the least valueof k such that n is a perfect cube?

4. If(52)x.(25)x

10x= 6400. Find the value of x.

5. 555, 55555, 5555555, · · · In this arrangement of numbers, how many 5’s are there inthe 25th number?

6. If n =[16.34 + 3.66]2[(16.34)2 + (3.66)2 − (3.66)(32.68)]

[(16.34)2 − (3.66)2](16.34− 3.66).

Find n.

7. Let K = 11 + 111 + 1111 + · · · + 111 · · · 25times. Find the remainder when K isdivided by 4.

8. There are in all 30 students in the class who all appeared for the examination. Riya’sroll numbers is 20.a) Average marks of all 30 students marks =65.b) Average marks of students with roll numbers 1 to 20 = 63.c) Average marks of students with roll numbers 20 to 30 =70 Find Riya’s marks.

9. ABCD is a square. E is a point as shown in figure such that 4DCE is equilateral.Area of 4DCE = 16

√3 units. Find area of square ABCD.

E

CD

A B

10. ABCD is a rectangle whose length is 5 times its breadth. E,F are point on sidesAB and CD such that

AE = CF = AD = 6. Find area of 4DEF.

F

BEA

D C11. If the principle is increased by Rs. 10,000 then simple interest increases by Rs 2,100

in the period of 3 years. Find the rate of interest per cent per annum.

12. Let a and b be two consecutive multiples of 3. LCM of a, b is 546. Find a+ b

13. A alone completes a piece of work in 4 days and B alone completes it in 6 days. IfA and B work on alternate days. B starts on first day, how many days are requiredto complete the work?

14. LCM of 2 numbers a and 6a is 138. Find a.

15. Find the greatest number amongst 6185, 10148, 12111, 1574. Let n be the power (index)of that number. What is the sum of the digits of n.

16. A CFL bulb costs Rs. 100 and lasts for Rs. 2.5 years while a regular bulb costsRs. 15 and lasts for 5 months. By what percentage should the price of CFL bulbbe reduced to cost the same as regular bulb over the period of 2.5 years.

17. A goldsmith sells gold at Rs 3, 500 per gm and diamond at Rs 1, 000 per gm. Hesold a particular diamond ring made of gold weighing 5 gm for Rs. 13, 500. If theweight of the diamond in the ring is x gm, find 5x

18. Each square of the grid is filled with one of the number 1, 2, 3, 4 such that each row,column and both diagonals contain all 4 numbers. Mark the largest number formedby the digits in the first two squares (marked portion).

1

1

4

2

19. ABCD and AXY Z are exactly identical squares. ∠BAX as shown is 60. Find∠DBY .

60 Y

C

ZD

X

A

B20. 37 articles were sold at Rs.3,330 and the profit was equal to the cost price of 8

articles. Find the cost of each article.

21. The number 18a4b96 is divisible by 72. Find the greatest value of 10a+ b.

22. 4ABC is equilateral and 4ADC is an isosceles as shown. If ∠DAC = 40, Findm∠DCP

P

40

DC

A

B

23. In the figure given, P,Q,R, S and X, Y, Z,W are the midpoint of the sides of squareABCD and PQRS respectively. If AB = 10, find area of the shaded portion.

ZW

YX

R

Q

P

S

DC

A B

24. Fig 1 shows 6 equilateral triangle are arranged to form a regular hexagon of side a.In Fig 2, a regular hexagon of side 2a is formed with 24 equilateral triangles. If aregular hexagon of length 5a is formed by n equilateral triangles, find n

6.

Fig 2Fig 1

a

a

a

a

a a

a

a

a

a

aa

a

a

a

a a

a

April 2016

Q 1. If n = (2× 10100) + 3, then find the sum of the digits of n2.

Q 2. n is a natural number divisible by 15. If n2 = 12k522h5, then find the value ofk2 + 4h.

Q 3. ABCD is a rectangle; and P is a point on side AD. If the area of ∆ABP is 18,and the area of ∆BPC is 70, then find the area of ∆PDC.

A

D C

B

P

Q 4. Sixty cubes of size 1 × 1 × 1 are put together to form a cuboid of size 3 × 4 × 5.All the exterior faces of this cuboid are painted. Find the number of 1 × 1 × 1 cubes ofwhich exactly 2 faces are painted.

Q 5. Eleven batsmen score runs as follows:i. The first five players together score 4 times the total score of the remaining players;ii. The first six players together score 5 times the total score of the remaining players;andiii. The average score of all eleven players is 30.Find the score of the sixth batsman.Q 6. Find the angle between the minute and the hour hand at 5:40 pm.

Q 7. As shown in the figure, a strip with a constant width of 1 meter is paved along theboundary inside a rectangular ground, whose length and breadth are in the ratio 3 : 2.If the area of the paved region is 46 square meters, then find the outer perimeter of theground in meters.

Q 8. As shown in the figure, B1, B2, · · · , B11 are eleven equidistant points lying on astraight line, in that order. Point A is chosen so that AB1B11 is an equilateral triangle.A is joined to each of B1 to B11. Find the total number of acute-angled triangles in thegiven figure. A

B(11)B(10)B(9)B(7) B(8)B(6)B(5)B(4)B(3)B(2)B(1)

Q 9. A square array of numbers is said to be a magic square, if the sum of the numbers ineach of its row, column and main diagonals is equal. In the following 4× 4 magic square,find (a+ b+ c+ d) if the sum of the remaining 12 entries is 150.

ab

cd

Q 10. Find two digit natural number n such that the greatest common divisor of 2520and n+ 100 is 21.

Q 11. Hardik takes 50 minutes to reach his school from his home, when he walks ata constant speed. If he wants to reach his school in 40 minutes, then by what percentshould he increase his walking speed?

Q 12. ∆ABC is an equilateral triangle. D is a point on line BC such that C is themidpoint of BD. If AB = 4, then find AD2.

D

A

CB

Q 13. Area of an isosceles triangle is 120. Find the perimeter of this triangle, if thelength of its base is 16.

Q 14. Let a ∗ b denote the length of the hypotenuse of a right-angled triangle whoseremaining two sides have lengths a, b. If (12 ∗ 16) ∗ k = 25, then find the value of k.

Q 15. n is a natural number such that the least common multiple of n and 72 is 360.Find the smallest possible value of n, greater than 64.

Q 16. Find the value of[

7−3√7−√3

+ 5−3√5+√3

]2−√

140.

Q 17. As shown in the figure, M is the center of a circle; and AB,CD are chords ofequal length. DN ⊥MC. If m∠AMB = 48, then find m∠CDN .

N

C

A

D

B

M

Q 18. n is a two-digit number whose ten’s digit is a, and unit’s digit is b. When weinterchange the digits, the value of the number increases by 20%. Find the value of n.

Q 19. An ant is at point A of a segment AB, having length 12. The ant moves as follows:First it moves 3 units towards B, then moves 2 units towards A; again moves 3 unitstowards B, then moves 2 units towards A, and so on. Find the total distance travelledby the ant, when it reaches point B for the first time.

Q 20. In a party, each boy dances with exactly three girls, and each girl dances withexactly four boys. If a total of 35 students are present at the party, how many boys arethere?

Q 21. If m,n are distinct natural numbers, then find the value of1

1+2025m−n + 11+2025n−m +

√2025.

Q 22. A bag contains several 50-paise, 1-rupee and 2-rupee coins, in the ratio 8:6:7respectively. If the value of the contribution of 2-rupee coins is more by 12 rupees thanthe contribution of all the remaining coins, then find the total number of coins.

Q 23. In an examination, the ratio of the number of students who passed to the numberof students who failed is 4:1. If 20 more students had appeared, and 2 more had passed,then the ratio would have been 2:1. Find the number of students who appeared in theexam originally.

Q 24. Person A can do a piece of work in 26 days. Person B is 30% more efficient thanA. In how many days can B complete the same work?

Q 25. As shown in the diagram, two concentric circles have a common center M . P is apoint on the smaller circle. A line is constructed perpendicular to MP at P , meets thebigger circle in points A,B. Given AB = 12, then if the area of the region/ring betweenthe two circles is kπ, then find the value of k.

B

A

M

P

Standard VIII April 2015 Mathematics

Q1. Virat runs twice as fast as he walks. He travels from his house to school by walkingsome distance and by running some distance. On Monday his walking time is twice hisrunning time and reaches the school in 30 minutes. On Tuesday his running time is twicehis walking time. Find the time in minutes he takes to reach the school on Tuesday.

Q2. The fraction 3516

can be written in the form 3516

= 2 +1

x+1

y

where x, y are natural

numbers. Find (x+ y)2.

Q3. Let n = 10025 − 25. Let S denote the sum of the digits of n. Find the smallestnatural number k such that S + k is a perfect square.

Q4. If 1.236× 1015− 5.23× 1014 = a.bc× 10k where a, b, c are digits from 1 to 9 and k isa natural number. Find (a+ b+ c+ k).

Q5. Two adults have their birthday on the same day. On a particular birthday theproduct of their ages is 770. Find the sum of their ages on that birthday.

Q6. Mohit bought a number of balls. He was required to pay 5% tax on his purchase. Ifhe did not have to pay the tax he could have bought 3 more balls in the total amount hehad spent. How many balls did Mohit buy?

Q7. Two candles of length one feet each start burning at the same time. One of thecandles will burn down in 40 hours and the other in 24 hours. If after H hours one of thecandle has length 3 times the length of the other candle, find H.

Q8. 125 small cubes of size 1 × 1 × 1 are put together to form a cube of size 5 × 5 × 5.Two cubes of size 1×1×1 are said to be neighbours if they are placed such that their oneface of size 1× 1 touches each other. Find the number of 1× 1× 1 cubes having exactlyfour neighbours.

(Note that a cube has 8 vertices, 12 edges and 6 faces.)

Q9. In 4ABC, three points P1, P2, P3 are placed on segment BC and each joined tovertex A. The resulting figure contains all together 10 triangles. Find the total number oftriangles present in the figure if 12 points P1, P2, · · · , P11, P12 are placed on segment BCand each is joined to vertex A.

CB

A

P(3)P(2)P(1)

Q10. As shown in the figure 2ABCD is a square and 4EBC is an equilateral triangle.Find the measure of ∠DAE.

E

C

B

D

A

Q11.A polygon A1A2A3........A10 of 10 sides is inscribed in a circle, that is all the verticeslie on the circumference of the same circle. All the 10 sides are of equal length. Let Mbe the center of the circle.

Find the measure of ∠A3A1A2.

A(4)

A(5)A(6)

A(7)

A(8)

A(9)

A(10)A(1)

A(2)

M

A(3)

Q12. In 4ABC D is on segment BC such that BD = x and DC = 2x. M is themidpoint of segment AC. If area of 4ABD is 26 units find the area of 4BMA.

Q13. In 4ABC, D is the foot of the altitude from A on segment BC. If AD = 24,AC = 30 and BC = 28. Find AB.

D CB

A

Q14. As shown in the figure m∠DAC = x,m∠BCE = y andm∠ABC = z. Find 1

12(x+ y − z).

z

y

x

B

D

E

A

C

Q15. I have a 14 digit interesting number. The sum of its any three consecutive digitsis same. If its first digit is 4, its 5th digit is 7 and the sum of its all digits is 79 then findthe sum of its last 4 digits.

Q16. Let n = (7584)2 + 4(7584)(1208) + 4(1208)2. Find the smallest value of the natural

number m such that the product of m and n is a perfect cube.

Q17. Let m be the largest divisor of 723 other than itself. Let n be the largest divisorof 754 other than itself. If L.C.M. of m and n = paqbrc where p, q, r are distinct primenumbers then find the value of a+ b+ c.(Note that the largest divisor of 103 other than 103 is 500).

Q18. We define a new operation ∗ as given below.a ∗ b = a2 + b. For example, 8 ∗ 5 = 82 + 5 = 69.If n is a natural number and p is a prime number then find the smallest value of p satis-fying 8 ∗ p = n ∗ 6.

Q19. Find the value of (2√

20 + 4√

8)(6√

2−√

45).

Q20. If a2 − b2 = 132 and a+ b = 22 then find the value of a+ b2.

Q21. As shown in the following figure equilateral triangle of size 1 is formed using 3match sticks. To form an equilateral triangle of size 3 with all the equilateral triangle ofsize 1 inside it we require 18 match sticks. Find the total number of match sticks requiredto construct a size 6 equilateral triangle with all the equilteral triangle of size 1 inside it.

Q22. Consider the 8-digit number 3681m42n where m and n are digits from 0 to 9. Findthe value of m2 + n if given 8-digit number is divisible by 72.

Q23. Find the value of 100(1− 18)(1− 1

9)(1− 1

10)........(1− 1

20).

Q24. Integer k is 4th power of another integer. If 18 is a factor of k then find the smallestvalue of k

18.

Q25. Club G has several members. Average age of members of G increases by one yearif either five members each 9 year old leave G or new five members each 17 year old joinG. Find the present number of members in G.

Standard VIII April 2014

Mathematics

Q1. As shown in the figure 2ABCD is a square. 4PAB and 4QAD are equilateraltriangles. Find the measure of ∠AQP .

A

P

B

Q

C

D

Q2. 2ABCD is a rectangle. P and R are the midpoints of segment AB and segmentCD respectively. Segments DP and AR intersect at S. Segments CP and BR intersectat Q. If AB = 30 and AD = 8 then find the perimeter of 2PQRS.

QS

R

P BA

CD

Q3. A polygon A1A2A3 · · ·A15 of 15 sides is inscribed in a circle, that is all its verticeslie on circumference of the same circle. All the 15 sides are equal in length. If M is thecenter of the circle then find the measure of ∠MA1A2.

Q4. In 4ABC, segment CD is altitude, that is perpendicular drawn from vertex C. IfAB = 39, AC = 41 and altitude CD = 40 then find the length of segment BC.

A

D

CB

Q5. In 4ABC, D is the midpoint of segment BC. M is the midpoint of segment AD.If area of the 4CMD is 17, then find the area of 4ABC.

M

DCB

A

Q6. Find radius of a circle having the same area as that of trapezium as shown in thefigure. Height of the trapezium is 4 times π.

4

32

18

CD

BA

π

Q7. A can do a job in 45 days. B can do the same job in 90 days. How many days willbe required to complete the same job if they both work together?

Q8. There are two brothers. The age of the elder brother is x years and that of theyounger one is 42 years. x is 15 times the difference in the ages of the two brothers. Howold is the elder brother?

Q9. Find the measure of the angle between the hour hand and the minute hand of aclock at 6 hours 50 minute.

Q10.2x

3− 3x

4=

15− x3

. Find the value of x.

Q11. Division A has 15 students and division B has 20 students. Average score ofstudents in division A is greater by 2 as compared to the average score of students indivision B. The total marks of all the students in division B is 160 more than total marksof all the students in division A. Find the average marks of students in division A.

Q12. In a cricket match, Sachin scores 30 runs more than Virat. Suppose Sachin’s runsare decreased by 20% and Virat’s runs are increased by 28%. Then these two scoresbecome equal. Find the runs scored by Sachin.

Q13. Like addition, subtraction, etc., we define a new operation ∆. For example, if wewrite 4∆5 then its value will be 4 × 2 + 5 = 13, if we write 5∆4 then its value will be5× 2 + 4 = 14, and so on. In general, if a and b are two numbers then the value of a∆bcan be given by a∆b = 2a+ b. Now solve the following problem.

If a∆b = 18 and b∆a = 21, then find the value of (3a)∆(5b).

Q14. Let K = (2√

3−√

6)(2√

6 +√

12). Find the value of K2.

Q15. Find the value of2√

3

(2−√

3)2− 2

√3

(2 +√

3)2.

Q16. As shown in the following figures, a 1× 1 square is made using 4 match sticks. Toform a 2× 2 square with all the unit squares inside it, we require 12 match sticks. Findthe number of match sticks needed to construct a 6× 6 square with all the unit squaresinside it.

Q17. Let n = (413315)2 + (413315) + (413316). If we factorise n into prime factors,number 2 occurs t times. Find (t+ 25).

Q18. Let K = (6544)2 − (3456)2. K has three distinct prime numbers P,Q,R in itsfactorisation. If K is represented as K = P aQbRc, then find the value of (a+ b+ c).

Q19. Let n = 68k46215 where k is a digit between 0 to 9. For some values of k, thenumber will be divisible by 15 and for some other values of k it will not be divisible by15. Find the sum of all possible values of k such that n is divisible by 15.

Q20. A distance of 100 km was covered at an average speed of 60 km/hr. How muchextra time will be required to cover the same distance at an average speed of 40 km/hr?Express your answer in minute.

Q21. Seven cubes are glued together as shown in the following figure. Let the volumeof the resulting solid be 448 cubic centimeter. Let S be the surface area of the solid insquare centimeter. Find the value of (S − 392).

Q22. If a and b are real numbers such that 0 < b < a and a2 + b2 =34

15ab. Find the value

of 7×(a+ b

a− b

).

Q23. Let a = 1k05 be a four digit number. Let b = 139m be another four digit number.If the greatest common divisor (that is highest common factor) of a, b is 45 then find(k +m)2.

Q24. In my class there are only two types of students, Normal and Brilliant. 10% ofNormal students feel that they are Brilliant and 10% of Brilliant students feel that theyare Normal. When I asked each student what he/she feels it turned out that 30% studentsfeel that they are Brilliant. Find the actual % of Brilliant students in the class.

Q25. I have an 11 digit interesting number. The sum of its any three consecutive digitsis 13. If the first digit is 4 and the last digit is 2, then find the sum of all the digits ofthis 11 digited number.

Standard VIII April 2013.

Mathematics

Q1 ABCD is a square. Point E is inside the square such that 4EDC is equilateral.m∠EAD equals

(A) 600 (B) 650 (C) 700 (D) 750.

Q2 In trapezium ABCD, segment AB is parallel to segment CD. m∠B = 2m∠C.m∠C−m∠D = 500. Then m∠A equals

(A) 1700 (B) 1100 (C) 1200 (D) 1250.

Q3 In rectangle ABCD, AB = 12 and AD = 14. Point E is on segment BC such thatBE = 5. Then perimeter of 4AED equals

(A) 41 (B) 42 (C) 43 (D) 44.

Q4 4ABC and 4PQR are equilateral triangles centrally placed as shown in the fig-ure. Area of the shaded region is 11

√3 square units. BC = QR + 2. Then BC equals

P

R Q

A

C B

(A) 11 (B) 7√

3 (C) 12 (D) 8√

3.

Q5 M is center of the circle as shown in the figure.m∠ABM = 380 and m∠ACM = 160. Then m∠BMC equals

C

A

B

M

(A) 1070 (B) 1080 (C) 1090 (D) 1100.Q6 Two pullys are connected by a tight belt as shown in the figure. Radius of pully Ais 5 units. Radius of pully B is 3 units. Pully A completes 210 rotations in a given timeT .Then how many rotations will be completed by pully B in the same time T?

B A

(A) 126 (B) 360 (C) 128 (D) 350.

Q7 2ABCD is a square. AB = 18 cm. Point E is on BC such that BEEC

= 21. Then area

of 4AED equals

(A) 162 cm2 (B) 166 cm2 (C) 180 cm2 (D) None of These

Q8 (11.73)2 + (8.54)(11.73) + (4.27)2=

(A) 250.48 (B) 251.36 (C) 254 (D) N.O.T.

Q9(0.7)3 × (0.07)2 × (0.007)1

(7)2 × (0.0007)2=

(A) 49 (B) 4.9 (C) 0.49 (D) 0.049.

Q10 Consider a cubical box with sides 8x8x8. It is filled completely with cubical boxeswith sides 2x2x2. The total surface area of all 2x2x2 cubical boxes is

(A) 648 (B) 1536 (C) 512 (D) 1024.

Q11 Let n = (58738)2 − (41262)2. The sum of the digits of n equals

(A) 25 (B) 26 (C) 27 (D) 28.

Q12 If a = 41, b = a+1a−1 , c = b+1

b−1 , d = c+1c−1 , e = d+1

d−1 , f = e+1e−1 then f equals

(A) 2021

(B) 8180

(C) 4140

(D) 2120

.

Q13 We define a new operation denoted by Ω. If a and b are two numbers then aΩbmeans a+b

2. Now consider the following problem. If xΩ(xΩ14) = x then x equals

(A) 7 (B) 21 (C) 14 (D) 28

Q14 A car travels from point A to point B. Car travels first half the distance at a constantspeed of 30 km/hr. What should be the speed of the car in second half of the journey sothat total distance AB is travelled at an average speed of 40 km/hr.

(A) 50 (B) 60 (C) 55 (D) None of These

Q15 Group A has 30 members each having Rs.200. Group B has 20 members each havingRs.120. How much money should each member of A give to each member of B so thatafter the transaction all 50 members have exactly same amount with each of them. Notethat each member of group A gives same money to each and every member of the groupB.

(A) Rs 1.3 (B) Rs 1.4 (C) Rs 1.5 (D) Rs 1.6

Q16 n = 438K463876589112. Note that n has 16 digits. One of its digits is K. Find thesum of all those values of K for which n is divisible by 24.

(A) 18 (B) 12 (C) 15 (D) None of These

Q17 Find the number of integers between 1 and 201 which are either divisible by 6 ordivisible by 10 but not divisible by both.

(A) 47 (B) 49 (C) 41 (D) 39

Q18 Find the number of ways in which a student can select 2 toys from 10 distinct toys.

(A) 55 (B) 5 (C) 90 (D) 45.

Q19 When x2 + 10x + k is divided by x + 2 remainder is 25. Find remainder whenx2 + 10x+ k is divided by x+ 3.

(A) 20 (B) 21 (C) 22 (D) 23.

Q20 A keeps Rs. 4000 in bank at interest rate 8 pcpa (simple interest) for period of 5years. How much principal should B keep in the same bank such that after 5 years Breceives the simple interest which equals the total amount A receives.

(A) 5600 (B) 18000 (C) 16000 (D) 14000.

Q21 LCM of three numbers 36, a, 48 is b. GCD (i.e. HCF) of b and 36 is c. GCD(i.e.HCF) of b and 48 is d. Then LCM of c and d equals

(A) 140 (B) 144 (C) 112 (D) 96.

Q22 In 4PQR, S is mid point of segment QR.Given SP = SQ = SR. m∠Q

m∠R = 32, then m∠R equals

(A) 54 (B) 30 (C) 36 (D) 60.

Q23 Car designer wants to fix capacity of petrol tank. He finds the volume with followingassumptions.(i) Car will run 36 kilometers every day.(ii) 18 kilometers per liter is consumption of petrol.(iii) The gap between two consecutive petrol filling should be atleast 6 days.Then the minimum capacity of petrol tank should be

(A) 12 Ltrs (B) 11 Ltrs (C) 10 Ltrs (D) 14 Ltrs.

Q24 Which among the following is true.

(A) 6 <√

35 < 3√

217 (B) 3√

217 < 6 <√

35(C)

√35 < 6 < 3

√217 (D)

√35 < 3

√217 < 6 .

Q25

√10800 +

√16200 +

√27000√

2 +√

3 +√

5=

(A) 40√

3 (B) 30√

6 (C) 45√

2 (D)None of These

Standard VIII June 2012. Mathematics

Q1. At certain rate of interest, it takes 8 years for the amount to become twice theprincipal when computed by simple interest. If calculated at the same rate, how manyyears will be required for the amount to become thrice the principal?

(A) 10 (B) 12 (C) 16 (D) 24.

Q2. The value of (33 + 43 + 53)(43) is · · ·

(A) 1296 (B) 1396 (C) 1286 (D) 1306.

Q3. Same test was given to class A and class B. There are 60 students in class A. Averagemarks of class A is 90% and average of class A and class B together is 80%. If number ofstudents in class B is 40 then average of class B is · · ·(A) 60% (B) 63% (C) 65% (D) 68%.

Q4. 10% of 20% of 30% of 40% of 25000 is

(A) 50 (B) 55 (C) 60 (D) 70.

Q5. In an examination, the percentage of marks for passing is 40%. A student gets 37marks and claims that he has scored 5 marks more than minimum required marks forpassing. The maximum marks (out of out) one can get in that examination is · · ·(A) 75 (B) 90 (C) 120 (D) None of A,B,C.

Q6.

√48−

√27 +

√75√

98−√

8 +√

2=

(A)

√3√2

(B)

√3

2(C)

3√2

(D)3

2.

Q7. In 4ABC, AB = 5, BC = 12, CA = 13. D is the mid point of segment BC. Thelength of segment AD is · · ·(A) 7.8 (B) 7.9 (C)

√61 (D)

√63.

Q8. In 4ABC, if BC = 16, altitude BE = 8 (point E is on side AC) and altitudeAD = 10 (point D is on side BC) then the length of side AC is · · ·(A) 20 (B) 25 (C) 27 (D) None of A,B,C.

Q9. In 2ABCD, AB = 12, AD = 5, m∠A = 900. Area of 2ABCD is 69. Thendistance of C from diagonal BD is

(A) 5 (B) 6 (C) 7 (D) 8.

Q10. In 2ABCD, m∠A : m∠B : m∠C : m∠D is 1 : 2 : 3 : 4. Measure of smallest angleis

(A) 30 (B) 32 (C) 34 (D) 36.

Q11. 4ABC is acute angled triangle. AD is an altitude (perpendicular) from vertex Aon side BC.

D

A

B C

Point D is on side BC. BD = 5, DC = 9, AC = 15. The value of AB is

(A) 11 (B) 12 (C) 13 (D) 14

Q12. AB is a diameter of a circle with center M . C is a point on the circle.

C

A BM

If m∠CMB = 480, then m∠ACM is

(A) 22 (B) 23 (C) 24 (D) 25.

Q13. If x2 − 7x+ k is divided by x− 2 then the quotient is x− 5 and remainder is zero.Then the value of k is · · ·(A) 7 (B) 10 (C) −10 (D) None of A,B,C.

Q14. Ifx

2+x

3+x

4= 3− x

6then x equals · · ·

(A)12

5(B)

13

6(C)

18

7(D) None of A,B,C.

Q15.x+ 3

x+ 1=

2x+ 1

2x+ 5, then the value of 8x+ 19 is · · ·

(A) 5 (B) 6 (C) 7 (D) 8.

Q16. A person was hired with a salary of Rs. 430000/- per year and a laptop. He workedfor 10 months. As a part of his salary for those 10 months he received the laptop and Rs.350000/-. Then the price of the laptop in rupees is · · ·(A) 20000 (B) 30000 (C) 40000 (D) 50000.

Q17. Milk is available in the bags of two sizes a liters and b liters. Sachin wants to buy40 liters of milk. He can pick 1 bag of a liters and 3 bags of b liters. Else he can pick 7bags of a liters and 1 bag of b liters. Then b is

(A) 8 (B) 12 (C) 14 (D) 16.

Q18. 3(5x−4) · 5(18−7x) = 455625. In this equation value of x is

(A) 1 (B) 2 (C) 3 (D)4.

Q19. Each face of a brick has rectangular shape. If volume of the brick is 60 cm3, lengthof the brick is 5cm and bredth of the brick is 4cm. then total surface area of brick is

(A) 94cm2 (B) 48cm2 (C) 47cm2 (D) 96cm2.

Q20. The perfect square among the following numbers is

(A) 76179 (B) 76165 (C) 76166 (D) 76176.

Q21. 7425k4 is six digited number divisible by 3 and is not divisible by 4 then digit k is

(A) 1 (B) 3 (C) 5 (D) 7.

Q22. The greatest number among 2270, 3162, 6108, 2054 is

(A) 2270 (B) 3162 (C) 6108 (D) 2054.

Q23. The sum of the first 102 terms in the following expression is · · ·1− 3 + 5− 7 + 9− 11 + 13− 15 + · · ·(A) -100 (B) -100 (C) 102 (D) -102.

Q24. The garden has a shape of regular pentagon. 125 trees are planted along perimeterof garden such that distance between any two consecutive trees is same. Then number oftrees planted on one side of garden is

(A) 24 (B) 25 (C) 26 (D) None of A,B,C.

Q25. a, b are natural numbers.If a is divided by 17 the remainder is 8.If b is divided by 17 the remainder is 6.If a× b is divided by 17 then the remainder is

(A) 14 (B) 13 (C) 16 (D) 15.

Standard VIII April 2012. Mathematics

Q1. The number of years required for the amount to become twice the principal whencomputed by simple interest at the rate of 10 p.c.p.a. is

(A) 20 (B) 5 (C) 10 (D) None of A,B,C.

Q2. The value of (11 + 22 + 33)(75) is

(A) 128 (B) 218 (C) 821 (D) 281.

Q3. Same test was given to class A and class B. Average marks of class A of 40 studentsis 70% and class B of 60 students is 80%. Average of class A and class B together is

(A) 72% (B) 74% (C) 76% (D) 78%.

Q4. If a = 75% of 60% of 20 and b = 40% of 120% of 50, then a+ b equals

(A) 30 (B) 33 (C) 9 (D) 36.

Q5. In an examination, the percentage of marks for passing is 36%. A student gets 17marks and fails by 10 marks. The maximum marks one can get in that examination is

(A) 75 (B) 100 (C) 125 (D) None of A,B,C.

Q6.

√2 +√

8 +√

32√6×√

12=

(A) 7√

2 (B)√

6 (C)7

6(D)

√6

2.

Q7. Write True/False.

In 4ABC and 4PQR(i) if ∠A ∼= ∠P,∠B ∼= ∠Q,∠C ∼= ∠R then two triangles are congruent.

(ii) if Side AB ∼= Side PQ,∠B ∼= ∠Q, Side BC ∼= Side QR then two triangles arecongruent.

(iii) if Side AB ∼= Side PQ, Side BC ∼= Side QR, ∠C ∼= ∠R then two triangles arecongruent.

(A) TTT (B) TTF (C) FTT (D) FTF.

Q8. In 4ABC, if BC = 10, AC = 12 and altitude AD = 6 then the length of altitudeBE is

(A) 4 (B) 5 (C) 7 (D) 8.

Q9. In 2ABCD, AB = 6, AD = 8,m∠A = 90. Distance of C from diagonal BD is 4.Then area of 2ABCD is

(A) 40 (B) 42 (C) 44 (D) 48.

Q10. In 4ABC, BE and CF are altitudes and intersect at H.

H

F

E

CB

A

If m∠BAC = 70 then m∠BHC equals

(A) 105 (B) 110 (C) 115 (D) 120.

Q11. 4ABC is acute angled triangle. AD is an altitude (perpendicular) from vertex Aon side BC.

D

A

B C

Point D is on side BC. AB = 6, BC = 8, BD = 3. The value of AC2 is

(A) 49 (B) 52 (C) 64 (D) 81

Q12. AB is a diameter of a circle with center M . C is a point on the circle.

C

A BM

If m∠ACM = 20 then m∠ABC is

(A) 60 (B) 50 (C) 70 (D) 80.

Q13. If 6 + x2 − 7x is divided by x− 1 then the quotient is

(A) x− 5 (B) x− 6 (C) x− 4 (D) None of A,B,C.

Q14. Ifx

4+x

6+x

3=

5

6− x

2then x equals

(A)2

3(B)

4

3(C)

2

5(D)

3

2.

Q15.x+ 2

x− 1=x− 1

x+ 2, then the value of 4x2 + 7 is

(A) 5 (B) 6 (C) 7 (D) 8.

Q16. A person was hired with salary Rs. 160000/- per year and a golden ring. He workedfor 8 months. As a part of his salary for those 8 months he received the golden ring andRs. 100000/-. Then the price of the golden ring in rupees is

(A) 10000 (B) 20000 (C) 30000 (D) 40000.

Q17. Temperature in Centigrade (C) and Fahrenheit (F) are related to each other byformula C = 5

9(F −32). If the temperature is recorded in both Centigrade and Fahrenheit

shows the same number then the number is

(A) −30 (B) −40 (C) 0 (D) 30.

Q18. 7(5x−8) · 5(x+2) = 30625. In this equation value of x is

(A) 1 (B) 2 (C) 3 (D)4.

Q19. If the total surface area of a cube is 150cm2, then the volume of the cube is

(A) 64cm3 (B) 81cm3 (C) 125cm3 (D) 216cm3.

Q20. The perfect square among the following numbers is

(A) 534014 (B) 536030 (C) 535824 (D) 536088.

Q21. 5793k4 is six digited number divisible by 4 and 89732k58 is eight digited numberdivisible by 11 then digit k is

(A) 0 (B) 2 (C) 4 (D) 6.

Q22. The greatest number among 2192, 3144, 596, 1948 is

(A) 2192 (B) 3144 (C) 596 (D) 1948.

Q23. The sum of the first 767 terms in the following expression

1− 2 + 3− 4 + 5− 6 + 7− 8 · · · is

(A) 384 (B) -384 (C) 768 (D) 767.

Q24. The number of poles that can be erected on all sides of rectangular garden havinglength 50 meter and breadth 30 meter, if the distance between 2 consecutive poles is 2meter is

(A) 80 (B) 84 (C) 78 (D) 82.

Q25. a, b, c are natural numbers. If a is divided by 17 the remainder is 8. If b is dividedby 17 the remainder is 11. If c is divided by 17 theremainder is 12. If a+ b+ c is dividedby 17 then the remainder is

(A) 13 (B) 14 (C) 15 (D) 16.

Mathematics Practice Problems

Q1. The value of a+ba−b , if a

b= 4, is

(a) 0 (b) -1 (c) 53

(d) 43

Q2. Consider the expression, (1)1 − (−1)2 + (1)3 − (−1)4 + (1)5 − (−1)6 + · · ·.The sum of first 873 terms in the above equation is

(a) 873 (b) 0 (c) -1 (d) 1

Q3. The population of a city is X in 1991. It becomes 3 times every 10 years.The population of this city in the year 2021 will be,

(a) 3X (b) X (c) 9X (d) 27X

Q4. The measures of exterior angles of a quadrilateral are (2x−15)o, (x+ 45)o, (3x)o and(2x+ 10)o. What is the measure of the largest angle of the quadrilateral?

(a) 115o (b) 135o (c) 90o (d) 100o

Q5. If 25

thof a is equal to 3

4

thof b, find the ratio of a to b.

(a) 6 : 20 (b) 20 : 6 (c) 8 : 15 (d) 15 : 8

Q6. The sum of the ages of Sachin and Rahul is 25 years, that of Rahul and Sunil is 35years and that of Sachin and Sunil is 30 years. The ratio of Sachin’s age to Sunil’s age is,

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

Q7. The fee charged in Rupees from each student of a class is equal to 1/4 of the totalnumber of students in the class. The total monthly fee collected is Rs. 324. Then thetotal number of students in that class is,

(a) 81 (b) 36 (c) 16 (d) 18

Q8. The LCM of 2 consecutive even numbers is 364. The sum of these numbers is,

(a) 50 (b) 54 (c) 58 (d) 46

Q9. The average of 3 consecutive even numbers is 18. If these 3 numbers are arrangedin ascending order, then the odd number just before the middle number and the evennumber just after the largest number are,

(a) 15, 20 (b) 17, 20 (c) 17, 22 (d) 15, 22

Q10. 19.20.0016

=

(a) 12.00 (b) 0.0012 (c) 0.012 (d) 12000

Q11. 0.9×0.09×0.0090.0009×9 =

(a) 0.9 (b) 0.09 (c) 0.009 (d) 9

Q12. What will happen to the area of a square if the length of its side is halved?

(a) Area of the square will be halved (b) Area of the square will remain same (c) Area ofthe square will be 1

4of its original area (d) Area of the square will be doubled

Q13. Write True/False.

(i) Sum of 5 different integers can never be 0.

(ii) Every chord other than diameter of a circle is parallel to one of its diameters.

(iii) If ’a’ and ’b’ are any two integers, then, ’a - b’ is always less than both ’a’ and ’b’.

(a) TTT (b) TTF (c) FTT (d) FTF

Q14. If 5K

= 1√0.0025

then K =

(a) 0.5 (b) 0.25 (c) 0.01 (d) 5

Q15. If x−13

+ x+25

= 2 then x =

(a) 715

(b) 829

(c) 298

(d) 1315

Q16. Side of a square is 10. Its perimeter is reduced by 30%, hence area is decreased by

(a) 30% (b) 48% (c) 51% (d) 55%

Q17. Ratio of the present ages of two brothers is 4 : 5. After 10 years the ratio of theirages would be 6 : 7. Find the age of elder brother after 15 year.

(a) 35 (b) 40 (c) 50 (d) 25

Q18. If 81 = 27x, then x =.

(a) 34

(b) 3 (c) 1 (d) 43

Q19. How many times should 57

be added to 57, so that the sum is 5.

(a) 4 (b) 5 (c) 6 (d) 8

Q20. 2ABCD is square with side 10. P is point inside square such that 4PBC isequilateral. Area of 4PBC is

(a) 50√

3 (b) 25√

3 (c) 40√

3 (d) 100√

3

Q21. With reference to the figure find the area of 4ABC.

P

A

CB

15

13

14

4 4

4

(a) 84 (b) 80 (c) 100 (d) 70

Q22. Greatest common divisor of lcm of 18 and 12 and lcm of15 and 200 is

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

Q23. a2+3aa2+4a+3

× a2−2a−3a2−9 =

(a) aa−3 (b) a

a+3(c) a−3

a(d) a+1

a+3

Q24. Value of x if x−1x−2 −

x−2x−3 = x−3

x−4 −x−4x−5

(a) 27

(b) 34

(c) 72

(d) 45

Q25. The average of marks in the class of 50 students is 75. But particular student’smarks were recorded 67 instead of 77. If this correction is taken into account what willbe new avarage of marks?

(a) 76 (b) 75.2 (c) 75.5 (d) 76.2

Q26. Age of father today is 6 times age of son. After 20 years age of father will be 2times age of son. How old was father when son was born?

(a) 30 (b) 35 (c) 20 (d) 25

Q27. A number consists of two digits. The digit at unit’s place is 4 times that in ten’splace. If digits are interchanged the new number when increased by 2 equals 3 times theold number. Then the number is

(a) 19 (b) 14 (c) 28 (d) 12

Q28. Which of the following is the greatest?

2500, 3300, 5200, 4100

(a) 2500 (b) 3300 (c) 5200 (d) 4100

Q29. (64)2+(36)2+(128×36)(64×64)−(36×36) =

(a) 725

(b) 1 (c) 257

(d) 62549

Q30. The digit in the unit’s place of number (6191 + 345201 − 17646) is

(a) 2 (b) 0 (c) 3 (d) N.O.T.

Q31. The value of the expression (243n5 )×(32n+1)9n×3n−2 =

(a) 27 (b) 127

(c) 9 (d) N.O.T.

Q32. In4ABC,m∠BAC = 80. The bisectors of ∠ABC and ∠ACB intersect each otherat point I, then m∠BIC is

(a) 170 (b) 130 (c) 85 (d) N.O.T.

Q33. Circular garden has area 616 sq. meters. The cost of fencing this garden at therate of Rs. 200/meter is Rs.

(a) 17600 (b) 4400 (c) 8800 (d) N.O.T.

Q34. A freight train 1 KM long is travelling at a speed of 20 KMPH. It enters a tunnelone KM long at 1 pm. In how many minutes does the rear of the train emerge from thetunnel.

(a) 3 (b) 6 (c) 12 (d) 1

Q35. Ajay earns 25% more than Bhaskar. By how much percent is Bhaskar’s income lessthan that of Ajay?

(a) 2 (b) 0 (c) 3 (d) N.O.T.

Q36.√3+√12+√75√

2+√18

=

(a) 2√

3 (b)√

6 (c)√

12

(d)√32

Q37. (√3−√2)(√3+√2)

(√7−√5)(√7+√5)

=

(a) 12

(b) 2 (c) 23

(d) 1

Q38.2√3√2+5√6

(√2)(√3)

=

(a) 6√3√2

(b) 9 (c) 6 (d)√52

Q39. What should be the digit in place of k if 6732k36 is divisible by 8.

(a) 1, 3, 5, 7, 9 (b) 0, 2, 4, 6, 8 (c) Any of the 10 digits (d) N.O.T.

Q40. Surface area of a circle having radius√

6π

equals surface area of a cube with side

x. Then x equals

(a) 2 (b) 1 (c) 3 (d) N.O.T.

VIII Std- Answer Key

April 2019

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans 8 99 51 25 45 12 55 10 19 69 4 18 80 37 22

Que 16 17 18 19 20 21 22 23 24

Ans 65 31 15 28 72 98 16 72 12

April 2017

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans 37 5 11 2 51 20 3 80 64 72 7 81 5 23 13

Que 16 17 18 19 20 21 22 23 24

Ans 10 8 43 90 74 80 10 25 25

April 2016

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans 16 72 52 24 11 70 50 25 50 47 25 48 50 15 90

Que 16 17 18 19 20 21 22 23 24 25

Ans 12 24 45 48 20 46 63 85 20 36

April 2015

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans 24 64 40 25 57 60 20 36 91 75 18 39 26 15 24

Que 16 17 18 19 20 21 22 23 24 25

Ans 10 22 23 36 78 63 68 35 72 20

April 2014

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans 15 34 78 50 68 10 30 45 95 20 40 80 70 72 48

Que 16 17 18 19 20 21 22 23 24 25

Ans 84 29 13 12 50 88 28 64 25 45

April 2013

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans D A B C B D A D C B A D C B D

Que 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Ans A C D A D B C A C B D B B C A

Que 31 32 33 34 35 36 37 38 39

Ans C C A B D A C A A

June 2012

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans C A C C D A C A B D C C B A A

Que 16 17 18 19 20 21 22 23 25

Ans D B B A D C C D A

April 2012

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans C A C B A C D B C B B C B A D

Que 16 17 18 19 20 21 22 23 24 25

Ans B B B C C B B A A B

Mathematics Practice Problems

Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans C D D A D B B B C D B C D B C

Que 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Ans C B D C B A A B C B D C A C B

Que 31 32 33 34 35 36 37 38 39 40

Ans A B A B D B A C A B