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1 If x satisfies the inequality |x-2| + |x-3| + |x-4| ? 9, thena.0 ? x ? 6b.x ? 0 or x ? 6c.x ? -2 or x ?3d. none
2 What is the value of b for which the region bounded by the x – axis and y = -|2x| + b has an area of 72 ?a. 6b. 12c. 18d. 24
3 What is the radius of a circle inscribed in a triangle whose sides measure 21cm , 72 cm and 75 cm ?a. 9 cmb. 37.5 cmc. 28.5 cmd. 14cm
4 Rajat cut out two identical triangular pieces of cardboard, each of area 3000 sq.cm , and then placed them upon a table, one on top of the other such that the triangles completely coincide with each other. Now, if he rotated one of the two triangles by 180 degree about a vertical axis passing through its centroid, find the area that is common to both the triangles.a. 100 sq.cmb. 150 sq.cmc. 200 sq.cmd. 1331/3 sq.cm
5 Find the value of x for which [3/x] + [4/x] = 5 . [ a ] indicates the largest integer lesser than or equal to a .a. 1 < x ? 3/2b. 1 < x ? 4/3c. o < x < 3/2d. o < x< 4/3
6 A certain city has a circular wall around it, and this wall has four gates pointing north , south , east and west. A house stands outside the city , 3 km north of the north gate, and it can be seen from a point 9 km east of the south gate. What is the diameter of the wall that surrounds the city?a. 6kmb. 9kmc. 12kmd. None
7 In the land of OZ the people use a number system to a base n, n ? 10. Kirk , an inhabitanat of the land, one day received thrice this actual wage when the accountant accidently reversed the two digit of his wage . Find the decimal equivalent of Kirk’s correct wage.a. 12b. 36c. 13d. 35
8 A can complete a piece of work in 4 days, B takes double the time taken by A , C takes double that of B , and D takes that of C to complete the same task. They are paired in groups of two each. One pair takes two-third the time needed by the second pair to complete the work. Which is the first pair?a.A and Bb.A and Cc.B and Cd.A and D
9 In a quadrilateral ABCD , ?ABC = ?DCB = 120? , AB = 3 cm , BC = 4 and CD = 5 cm. Find the area of the quadrilateral ABCD.a.(45?3)/4b.(47?3)/4c.(23?3)/2d.None
10 A trader uses a faulty balance and sells sugar weighing only 960gms. Instead of 1 kg. and makes 4.166 profit. How much profit or loss percentage would he make if the balance was not faulty, and his selling price remained unchanged ?a. 4% profitb. 4% lossc. 1/6% profitd. 1/5% loss
11 nC4, nC5, nC6 are in A.P. value of n can bea. 14b. 11c. 27d. 8
12 Number S is obtained by squaring the sum of digits of a two-digit number D. If the difference between S and D is 27 , then the two-digit number D isa. 24b. 54c. 34d. 45
13 ection for questions 23 to 26
If the following are the movements of a person on a grid, answer the questions that follow:
R(X) = Take 2 steps to the right from the present position.
R(Y) = Take 3 steps to the right followed by 1 step forward from the present position.
L(X) = Take 1 steps to the left from the present position.
L(Y) = Take 1 steps to the left followed by 1 step backward from the present position.
F(X) = Take 2 steps forward from the present position.
B(X) = Take 2 steps backward from the present position.
23. What is the position of the Mr. A in the relation to his original position after taking these sequences of steps. R(X) followed by F(X)a. North Eastb. South Westc. North Westd. South East
14 L(Y) followed by B(X) followed by R(Y)a. North Eastb. South Westc. North Westd. South East
15 L(X) followed by R(X) followed by L(Y)a. North Eastb. South Westc. North westd. None
16 L(X) followed by R(X) followed by L(Y)a. North Eastb. South Westc. North westd. None
17 Prateek added two distinct three – digit numbers, each of which leaves remainders of 7 and 8 , when divided by 8 and 9 respectively. What is the maximum possible sum that Prateek could have obtained?a.1796b.1798c.1870d.1782
18 During Holi A, B , C decided to fill water ballons. The bucket being an old one had a leak. The tap and the garden hose filled the bucket , their normal ability being 10 min. & 15 min. respectively. When the bucket should have been full they discovered the leak and plugged it. If the time taken to fill the bucket post plugging was 2 min . how long should it take to empty the bucket with the leak working alone ?a.17 minb. 18minc. 16 mind. None
19 Now the balloons had to be filled . B is the slowest took thrice the time A & C took working together, but C took only twice the time of A & B together. So they decided to work together taking 10 min. how long does each take ?a. 24, 40 , 30b. 24, 30, 40c. 30, 40 , 24d. None
20 When the leak was plugged the colour solution had 20% colour in it. After plugging the leak, the filled bucket was to be made a 25% solution. If the capacity of bucket is 15 kg, what is the quantity of colour to be added?a.1.75b.2.75c. 3.75d. 1.25
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