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Directions for questions 1 to 20: Answer the questions independently of each other.

1. Using the principles of reﬂection of points, ﬁnd out the equation of the curve that is the reflection of y=e^{x}, in the line y = x.

(a) y=\log_{e}x+e^{x}

(b) y=-e^{x}

(c) y=\log_{e}x

(d) y=\log_{e}x-e^{x}

2. A number when divided by 4 gives a number which is 3 more than the remainder obtained on dividing the number by 34. Find the least such number.

(a) 64

(b) 132

(c) 256

(d) None of these

3. In a convex polygon, the interior angles are in A.P. with the smallest angle as 120 degrees and common difference as 5. What is the number of sides of the polygon?

(a) 16

(b) 13

(c) 15

(d) 9

4. A tournament is held between 10 players, A to J. Each player plays against each other player only once. A win gets 2 points, a draw 1 point, and a loss 0 points. What is the total of all the points  scored by each player?

(a)45

(b) 90

(c) 18

(d) 36

5. A 10% sugar solution is one in which 10 gm sugar is dissolved in 100 dm3 water. Water evaporates on heating the solution. On heating, 1 kg of the 10% solution is reduced to 0.5 kg. What is its  concentration now? [1 dm3 = 1 gm]

(a) 20%

(b) 18.2%

(c) 22.2%

(d) 21.18%

6. A square is of side 1 cm. The midpoints of its sides are joined to form another square. The midpoints of the second square are joined to form a third and this sequence of formation is continued  indefinitely. Find the sum of the areas of the square.

(a) 1 cm^{2}

(b) 2 cm^{2}

(c) Infinity

(d) None of these

7. In the above diagram C1 and C2 are the centres of the circles 1 and 2 respectively and C1 lies on the smaller circle. Radius of the smaller circle is r. Given that \frac{AB}{BC}=\frac{2}{1} and BP\bot AC . Find the value of C1P in terms of r.

(a) 1.2r

(b) r

(c) 0.8r

(d) Cannot be determined

8. Find the co-ordinates of the foot of the perpendicular from point (5, 7) on the line x + 7y — 10 = 0.

(a) (-25, 5)

(b) (\frac{103}{25},\frac{21}{25})

(c) (\frac{15}{19},\frac{25}{19})

(d) (3, 1)

9. If If \phi(n) denotes n^{3}+3n^{2}+3n, find \phi(n+1).

(a) 2n^{3}+6n^{2}+3

(b) 3n^{3}+12n^{2}+4n+1

(c) n^{3}+6n^{2}+12n+7

(d) n^{3}+4n^{2}+5

10. In the Punjab battalion, there are 18231 soldiers. The Commander of the battalion wants to make the soldiers stand in rows and columns. At least how many soldiers will have to be removed from the group, so that there are as many columns of soldiers as there are soldiers in each row?

(a) None

(b) 2

(c) 6

(d) 8

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11. A cube whose surface is EFGH is placed on a cube with surface ABCD such that vertices E and A of the two blocks coincide and side EF coincides with side AB. EF = 1 unit and AB = 2 units.  Now, keeping vertex F fixed, the smaller cube is rolled along the larger cube till G coincides with B. Then keeping G fixed, the smaller block is again rolled till GH coincides with BC. How much  distance is traversed by point E?

(a) π units

(b) \sqrt{2}\Pi

(c) (\sqrt{2}+\frac{1}{2})\Pi

(d) None of these

12. x^{3}-x^{2}-4=0 is an equation of degree 3. If one of the roots is 2 and the other two roots are ‘a’ and ‘b’, then what could be the value of (a + b — ab)?

(a) 3

(b) -3

(c) 2

(d) -2

13. If three numbers a, b and c are in A.P., then a^{2}(b+c), b^{2}c(c+a),c^{2}(a+b) are in:

(a) G.P.

(b) A.P.

(c) H.P.

(d) None of these

14. In \Delta ABC, equations of sides AB and CA are 7x + 2y = 8 and 5x + 4y = -2 respectively. Point D\equiv \left( \frac{22}{5},\frac{9}{5} \right) is such that AD\bot BC and D lies on BC. Then, area of \Delta ABC is:

(a) 21 sq. units

(b) 18 sq. units

(c) 36 sq. units

(d) None of these

15. Based on the figure below, what is the value of q, if p = 13?

(a) 17.9

(b) 17.7

(c) 17.5

(d) 17.3

16. A construction company xyz has 2 plants P and Q located in different cities. xyz has received two projects A and B simultaneously in different cities. xyz satisfies the requirement of the project  from its plant. The cost of transportation per truckload is given below in Rs.

Project requirements (truckload/day): A needs 45, B needs 10.
Plant production (truckload/day): P makes 35, Q makes 20
(What is the minimum transportation cost per day for supplying each project?

(a) Rs.675

(b) Rs.625

(c) Rs.600

(d) Rs.650

17. Around a circular ground a circular road is to be painted. The expected expenditure is Rs.1 1088. The diameter of the inner circle is 224 m. Find the width of the circular road if the rate of painting is 50 paise per sq.m.
(a) 28 m

(b) 32 m

(c) 140 m

(d) 45 m

18. Find the probability that atleast one row is empty if seven As are to be filled in the grid shown below. (No cell can hold more than one A.)

(a) \frac{49}{120}

(b) \frac{1}{5}

(c) \frac{51}{60}

(d) \frac{11}{30}

19. A person spent Rs.9.l0 in buying oranges at the rate of 3 for 10 paise and apples at 25 paise for a dozen. If he had bought five times as many oranges and a quarter of the number of apples he would have spent Rs.26.50. How_.many oranges did he buy?

(a) 192

(b) 153

(c) 163

(d) None of these

20. There are 3 clubs A, B and C in Bandra with 40, 50 and 60 members respectively. While 10 people are members of all three clubs, 70 are members of only one club. How many belong to exactly 2 clubs?

(a) 30

(b) 40

(c) 20

(d) 25