1. If Tupai Dada had distributed the cake equally between his relatives & friends , what would be each one's share ?
2. If the cake was of the form pf a square and you can cut the cake only in square pieces, how many minimum square pieces need to be cut so that every body has the exact share of cake as stated above in second paragraph?
3. If Tupai dada has 40% share of the cake which has 3 cherries in it what is the probability that he finds only 1 cherry in his portion of cake?
4.What was the approximate worth of Tupai Dada's piece of cake?
5.A shopkeeper purchases a lamp for some amount & sells it for Rs. 412 , making a profit of p%. If his cost price and selling price of the lamp get interchanged , he would be at a loss of p2 % . what is the approximate value of p?
If f(x) = (x+2) / (3-x) 6. Find the value of f(-1) + f(1/2)
7. A piece of spring is joined along three point ( a, a ) , (a + 28, a) , (a + 4 , a + 11) to form a triangle . A circle of same area as the triangle is rotated to form a sphere. Find the volume of the sphere in cu cm.
8. P(x) is a polynomial in x. when p(x) is divided by ( x - 1), the remainder is 5 and when p(x) is divided by (x + 1) , the remainder is 7. what would the remainder be when p(x) is divided by (x+1) , the remainder is 7. What would the remainder be when p(x) is divided by (x - 1)(x + 1 )?
9. To err is human. Instead of mixing 2 protons with 2 neutrons, you mix 4 protons with 3 neutrons. Each proton makes 5 plutons and each pluton makes 0.5 gluttons. Each neutron makes 2 zutons and each zuton makes 3 plutons. How many more glutton would you find?
10. A man stand at a point A on the bank of a river and looks at the top of a tree which is exactly opposite to him on the other bank. The angle of elevation is 45 degree. He walks 200 meters away from the tree and looks at the top of the tree and finds the angle of elevation to be 30 degree. Calculate the height of the tree and the width of the river?
11. Side AB of a triangle ABC is 80 cm long, whose perimeter is 170 cm . If Ð(ABC) = 60 degree , the shortest side of triangle ABC measures
12. Beginning with what number do the terms of the sequence Xn = n2 - 5n + 6 , n Є N , satisfy the inequality X n+1 > X n ? ii. 2021 > 2120
13. Three runners A, B and C run a race with runner A finishing 12m ahead of runners B and 18m ahead of ruuner C, while runner B finishes 8m ahead of runner C. each runner travels the entire distance at a constant speed. What was the length of the race?
14. A change-making machine contains one-rupee , two-rupee and five-rupee coins. The total number of coins is 300. The amount is Rs. 960. If the numbers of one-rupee coins and two-rupee coins are interchanged , the value comes down by Rs.40. The total number of five-rupee is
15.In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs, 18 min, 15 sec of watch time. What is the time gained or lost by this watch in one day ?
16. The 2000th letter in the sequence ABCDEDCBAABCDEDCBAABCDEDCBA . . . Is
17. Harinder had five regular solids of different shapes and all of equal volume. They were, a Tetrahedron, a Cube, a Sphere, a Septahedron and an Octahedron . If he has to paint all these solids at a cost Rs. 2.50 per unit area then which of the above mentioned solids will prove to be the costliest to paint ?
18. If m is a positive integer, for how many values of m 72/(m2 -“ 3) or 72/(m3 - 3) is an integer ?
19. A man invest Rs. 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8%, so that he can earn a total of 6% per annum?
20. A is set of positive integers such that when divided by 2, 3, 4, 5 , 6 leaves the remainders 1, 2 , 3, 4 ,5 respectively . How many intgers between 0 and 100 belong to set A ?
21. (BE)2 = MPB , where B , E , M and P are distinct integers . then M =
22.Find the area bounded by the lines y = |x - 1| and y = 4.
23. We define a relative prime due to a day for which the number of the month and the number of the day have no common factors other than 1. For example 22/5 (22 May) is such a day because 22 and 5 have no common factors other than 1 . The month with the smallest number of relatively prime day is
24. ABCD is a rectangle. X and Y are two points on the sides AB and BC respectively. If areas of triangle DAX, triangle YCD and triangle XBY are 5, 4 and 3 respectively ; what is the area of quadrilateral ABCD ?
25. How many ways are there to place a 5 by 5 square on an 8 by 8 chessboard so that each vertex is at the center of some field ?( solutions obtained from each other by reflection or rotations are not considered different )
26. n3 is odd. Which of the following statement(s) is (are) true ? i. n is odd ii. n2 is odd iii. n2 is even
27. Let f be a function such that for all integers x and y applies f(x +y) = f(x) + f(y) + 6xy +1 and f(x) = f(-x) . then , f(3) equals
28. From a circular sheet of paper with a radius of 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion ?
29. A person starts counting from the thumb , then the fore finger , then middle finger, and then the ring finger followed by the little finger. Then again the ring finger followed by the middle finger and so on. Which finger would he finish at when he counts 6449 ?
30. The fee charged by TIME for the students of MBA is 25% less than that charged for the students of MCA. If the total amount received from MBA os 50% more than that from MCA , the number of students in MCA course is what percent of that in MBA?
