First Step Program (Std V) Preparatory Program- Ganit Pravinya Test Paper Year 2013 Solve the following problems with Proper Procedure and Explanation. 1. Solve : 1 1 5 (7 3) 4 20 3 4 4 4 4 2. Find Value of M. M 9.6666 9.666 9.66 9.6 9.03 (10.05 7.05) 2 3. Solve the following. M D C L XVIII (IX V) X 7. Write down the two digit numbers upto 60 such that the digit 0 or 3 or both will not be used. How many such two digit numbers are there. 8. Simplify : 217 94 205 291 589 893 779 1843 9. Draw a regular hexagon of perimeter 19.8 cm and insert a equilateral triangle in it. 10. In the given adjoining figure, P, Q, R, and S are midpoints of sides of a square ABCD. If side of a square is 32 cm then find the area of the shaded region. 4. Solve: 1 1 1 2 4 3 x 2 13 2 6 3 5 5. Simplify : 1 3 1 4.125 2 7 4 8 16 4 6. In Yeshwantrao Chavan School 1 7 th of the 11. The time required to climb Singhagad is three times the time to come down. A man takes half past four hours to climb Sinhagad. His average speed to climb and come down is 3 km per hour. Then find the distance he had to climb. total students in fifth, 1 5 th of the total students in sixth, 1 4 th of the total students in seventh, 1 3 rd of the total students in eight were present and 31 students were absent on one day then find the total number of students in that school? 12. Find two numbers such that the product of those two numbers is 1014 and their division is 6. 13. Write down three numbers in the sequence 18, 21, 26, 33, 44 14. Divide 70 in three parts such that 3 is added to one part 3 is subtracted from second part and 1
third part is divided by 3 then, these three numbers are equal find them. 6) Write down the perimeter of the whole figure. 15. Write next two numbers in the sequence 3, 12, 37, 86, 167... 16. A Merchant purchased 10 dozen apples at the rate of Rs. 9 per apple. Out of which 45 apples are sold at the rate of Rs. 12 per apple and 2 dozen apples are sold at the rate of Rs. 10 per apple. One less than a dozen apples were rested. At what rate the remaining apples be sold so that the merchant has no loss in the transaction. 17. Which is the least number added to the sum of the three digit smallest prime number and three the digit greatest prime number so that it is a perfect square 18. AB = 5cm, AF = 13cm and DE = 8cm, PO = 6cm. then write the answers of the following. 1) Write the diameter of a circle 2) Write down the perimeter of ABF 3) Write down the perimeter of rectangle BPQF. 4) Write down the perimeter of square BCFE 5) Write down the perimeter of CDE 19. Write down three digit numbers using 7 and 5 repetition is allowed. Write the sum of the smallest and greatest numbers. 20. In a School the salary of a clerk is 5000 more than the peon's salary. Liabrians salary is double the salary of the peon. 3 Assistant teachers salary is more than the liabrarian's salary by Rs. 2000, Rs. 4000, Rs. 6000. Head master's slalary is equal to the sum of the salaries of first and second assistant teacher. If the salary for one month of a school is Rs. 1,63,000. Then find the difference in the salary of Headmaster and the peon. ****** 2
3. Observe the adjoining fig. and state 1) No. of quadrilaterals 2) No. of triangles. 4. A drum contains water upto 3 4 th of its capacity, 2014 1. Find the sum of three digit largest prime number and smallest three digit prime number. Find the factors of the sum. Which number should be added to the sum of the factors so as to get the square of nine. 2. In the adjoining fig ABCD is a trapezium side AD II side BC, l (AB ) = /(GE), l (AD) = 12cm l BC = 20 cm, l (AB) = 6 cm, l (DF) = 7 cm and BGEF is square. Find the perimeter of the whole Figure. if 9 liters of water is drawn from it then the drum remains half filled. Then find the amount of water in the drum at the beginning and capacity of the drum. 5. There are 17 numbers such that the next number exceeds the preceding number by 5. The sum of all 17 numbers is 816. Find the number at the middle. 6. Four Prime numbers are written in ascending order such that the product of first three prime numbers is 4199 and the product of last three prime numbers is 7429. Find the sum of these prime numbers and hence find the smallest integer by which the sum of prime numbers is multiplied so that the resulting product should be the smallest perfect square and the resulting product should be a perfect cube. 7. Write two lowest two digit perfect squares in Roman and write the difference between them in Roman. 3
8. Find the sum of all numbers up to 100 having the digits at unit place, 3, 5 and 7. 9. The product of two consecutive numbers is 510510 Then find the numbers. 10. Draw ABC = 120 By using Compass divide the ABC as follows : ABD = 30, DBE = 30, EBC = 60 11. Find all two digit numbers when divided by 15 leave remainder 8. Hence find the numbers whose sum of digits is same and find the sum of such numbers. 12. Simplify : 1 1 1... 1 2 2 3 19 20 19. Find next three numbers of the sequence 3, 35, 99, 195... 20. A person expends 1 12 on milk, 1 4 part on food 1 3 of his monthly salary part on education and travelling and 1 6 part on medical, though his monthly saving is Rs. 1000. Find his monthly salary and expenditure on each item. 13. 4 7 of a pole is the mud. When 1 3 of the part in mud is pulled out still a 8m. long part remains in the mud. Find total length of the pole. 14. Sum of four numbers is 144. Out of these four numbers if 5 is added to secong number, 5 is subtracted from third number and fourth number is multiplied by 5 the answers are equal to the first number. Find the four numbers. 15. The sum of digits of three digit prime number is equal to the two digit smallest prime number find such three digit prime numbers upto 200. 16. Find the value of m. 7 8 0.6 m (22.5 0.025) 3 2 5 15 (3.57 2.47 4.312) (36.08 0.15) 17. if I I = MY and MY MY = WHY. Then write the number WHY (I, M, H and Y are different digits) 18. The sum of two fractions is 14 5 12 If one of them is 7 2 3 then find the other. 4
7. Complete the magic square using Roman numbers, (vertical, horizontal and diagonal sums are equal) 2009 1. Which numbers between 11 to 25 are divisible by the sum of the digits in that number? 2. Which digit in the units place in the product. 1 3 5 7 9... 15? 3. Add: 3.5 litre + 2.470 litre + 3 litre + 505 ml. + 3540 ml. 4. How many angles are there in the figure? How many of them are acute angles? 5. Which is the eighth number in the series 1 1 1 1,,,,... 2 4 8 16? What is the product of the first & the eighth number? 6. Observe the following divisions. Which of these is correct? why? 8. Evaluat: 0.6 0.55 0.444 0.3333 0.22222 0.111111 9. Write all the numbers that can be written using each of the digits 0 to 5 only once and which are divisible by 9 10. and * represent mathematical operations. If 18 9 * 5 = 10 11. In the figure three triangles are obtained using four lines. How many triangles can be obtained using such six lines at the most? Draw the figure How many triangles can be obtained at the most using eight lines? Do not draw the figure. 5
19. 1) In the adjoining figure, place the compass on the point of intersection "p of the diagonals of the rectangle and draw a circle with vadius equal to length of segment PA Through which of the vertices this circle pass? 12. Anjanabai has a farm of of rectangular shape with length 40 m. and breadth 30 m. Fencing with a gate of 2m length has to be made at the rate Rs. 300 per metre around the farm what is the expenditure? 13. Product of two numbers is 1890. what is the minimum sum of such two numbers? What is maximum sum? How many such pairs are there? what is the sum of all two digit divisors of 1890? 14. Evaluate : 0.2 125 0.04 5 0.008 25 15. 1) How many triangles are there? 2) How many quadrilaterals are there? 3) How many hexagons are there? 2 ) Draw a circle parsing through vertices of the rectangles given below. 3) The diagonal of rectangle "KLMN' is 8cm. What is the radius of the circle passing through vertices of rectangle "KLMN. 16. Sum of my age and vijay's age is 54. My age is twice the difference of our ages find our ages. 17. The rent of a four storey building is Rs. 31,200 The rent of each floor is 2 3 of the floor just below, find the rent of each floor. 18. Ganpatrao owns a square piece of land with side 20 m He has built 2 rectanglar and 2 square houses in this land. Between any two houses there is a road 2m. wide Draw a suitable figure. Find the total area of these houses. 6
7. In the product which digit are presented by A,B and C. 8. 8. What is the digit in the unit place in the product 2010 1. Add and represent the sum in Roman numerals MCCCLXXV and MCCIV 2. How many triagngles are there in the figure write their names. 3 3 3 3... (101 times 3) 9. ABCD is a rectangle P, Q, R, S, are mid points of side AD, AB, BC, CD, AB = 30 cm, BC =18 cm. Find the area of shaded region and remaining part. 3. Write all the possible two digit numbers using 0,1,2,3, for any number of times and find their sum. 4. Find m if 0.002 0.25 0.003m 0.6415 0.087 0.1 1.2308 5. Evaluate = 0.5 10.8 4.4 (10.9 3.7) 5 6. Determine smallest and largest among 1 625 5 125 25,,,, 3 576 16 369 62 10. 3360 is the product of there consecutive numbers. Find the numbers 11. A paper of area 1 sq.m is cut into small pieces of area 1 sq. mm each. These pieces are arranged in a line one after the other. What will be the length of this arrangement in decameter. 12. Write the four consecutive terms that will follow 3 7 12 18,,,,... 7 10 19 30 13. 35 + 42 + 49 +... 203 =? 14. A clock sounds one stroke of a bell every half an hour. Every hour the number of stroke is equal to the time for e.g. 5 strokes at 5 o'clock In a 7
period of 24 hours how many times the clock will sound one stroke. 15. When a number is divided by the other number, the quotient is 5.. H C F of the 7 numbers is 152. What is the sum of the numbers? If the numbers are greater than 5000 and smaller than 8000 then what is their H.C.F. 16. Write a five digit greatest number in which all digits are different and divisible by 110. 17. A train departed from a station A on 29-11 - 2009 at 11.30 p.m. and reached station B on 1-12-2009 at 7.30 a.m. It halted on 8 stations during the journey. It halted 20 min each on 3 stations, 30 min each on 3 stations and 45 min. each on remaining stations. Find the distance between A and B if the speed of the train is 70 Km / hr 18. 1,4,8,13,19,26... Write the there consecutive terms that will follow 1,4,8,13,19,26 19. Once the headmaster of Siddheshwar high school reported to the education officer out of total number of students 1 3 rd students are in 8 to 10th standard 1 6 th students are in 11 th standard. The number of students in 12 th standard is 2 3 rd of that in 11 th standard and 280 students are in 5 th to 7 th standard, what is the total number of students in the school. 8
2011 1. If 3 7 = 2, 8 12 = 4 and 6 10 = 12, 15 10 = 30 Then [(6 11) + (13 11)] 10 =? 2. In a four digit number all digits are odd numbers The digit in thousand's place is three times the digits in unit's place. The difference in the place values of the digits in hundred's place and ten's place is 430 Then find the numbers. 3. Observing the figure below fill in the empty squares with proper numbers of school from the home is half the distance of school from stadium The distance of stand from home is half the distance between home and school. The distance between market and home is 1 7 times the distance between home and school. Then find the distance from market to stand. IF Ashok reguires 1 minute to reach the market from the home then at what time will he reach the school if be starts at 11 o' clock from home. 9. In figure A, B, C, D, E, F, G, H, I, J, K, L, are numbers all these numbers are muliples of 5 The largest of these numbers is 60 and is at B The smallest of these number is at A. The numbers at A, C, E, G, I, and K are successive multiples of 5 Also C + D + E = G + H + I = K + L + A = 80 and the number at F is larger than the number at J by 10 Then find all these numbers. 4. Simplify : 2 1 3 156 154 4 5 10 20 9 9 3 3 10 2 5 5. Write next four numbers m the sequence. 4, 6, 12, 14, 20, 22... 6. The Sum of three numbers is 70 If 3 is added to the first number, 3 is subtracted from the second number and the third number is divided by 3 then the result is the same find the numbers. 7. The sum of two numbers is 40 and their multiplication is 384 find the smaller number of the two numbers. 8. Ashok has to go through market and bus-stand while going from home to school The stadium is further 420 m away from the school. The distance 10. In the adjoining figure two squares are drawn. The diagonals of one square are also drawn. Then find 1) Number of triangles. 2) Number of squares. 3) Number of rectangles. 9
11. The sum of digits of a two-digit number is 9. The number obtained by interchanging the digits is smaller than the original number by 27 find the two digit number. 12. ABCD is square. Points E,F G and H are mid points of sides AB, BC, CD and AD respectively point J is mid point of seg IF and K is mid point of seg IG If the side of the square is 20 cm, find the area of the shaded region. 13. Simplify : 1 1 1 41 143 221 187 11 13 17 14. From the sum of three digit, largest prime number and three digit smallest prime number their difference is subtracted. State the relation of the result with the smaller prime number. 15. Find the smallest number such that, when it is divided by 9 the remainder will be 1 and when it is divided by 8 the remainder will be 4 16. Find x : 1 17 1 2 9 3 1 13X 5 3 0.5 4 25 2 3 5 5 4 19. Write the following numbers is descending oder. 5 1 25 20,,, 18 82 213 91 20. Three friends have decided to share the mangoes in a box among themselves. When the first friend divided the mangoes in three equal parts there remains one mango, he took his share and one mango. When the second friend divided the remaining mangoes in there equal parts again there remains one mango, he took his share and one mango. When the third friend divided the remaining mangoes in three equal parts, again there remains one mango, he took his share and one mango. When the remaing two parts are distributed. The three friends got 2 mangoes each find the number of mangoes in the box. 17. Find all the two - digit numbers from 1 to 50 which will not require any of the digits 0 18. Simplify : 2 2 2 2 2 2 2 2 3 15 35 63 99 143 195 255 10