ACE OF PACE (MAIN SOLUTION CODE 01 & 02)

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1 CE OF PCE (MIN SOLUTION CODE & ). The product of a rational and an irrational number is always rational (B) irrational (C) both (D) can t say (B) Product of rational & irrational irrational. Divide: by (B) 4 (B) (C) 4 (D) 5. If x = + then x + x = (B) 9 (C) 9 (D) (B) x x x x If x + x = a + b and x x = a b then ab = (B) a = b (C) ab = (D) a + b = x a b.. () x x a b... () x x a b x ab 5. For what value of K is the polynomial x 4 + x + kx + x + is exactly divisible by (x + )? k = (B) k = (C) k = (D) k = (B) f

2 4 k 4 k k CE OF PCE (MIN SOLUTION CODE & ). Nidhi Singh has Rs.5, Rs., Rs.5, Rs. and Rs. notes in her purse. If in it all she has is Rs. find the number of each types of notes (in same order),, 4, 5, (B),,, 4, 5 (C),, 4,, 5 (D), 4, 5,, Therefore option 7. If gets % more than B, then B gets % less than (C) 9 % less than (D) (B) % more than 9 % more than (C).B B. 9 % less than. If a shopkeeper makes the price of goods 5% more than their cost price and allows the discount of 4%, then percentage of gain or loss is % (B) 5% (C) % (D) 5%.5x.4.5x.9x There fore % 9. In the given figure the value of x is D (D) (B) 4 E (C) x B (D) 9

3 CE OF PCE (MIN SOLUTION CODE & ) D 9 4 E 9 7 B. If cost price of chairs is equal to selling price of chairs then the percentage of gain or loss is 7 % loss (B) 7 % gain (C) % loss (D) % gain Let the cost of one chair be x. & selling price be y. x y y x x y % loss x 75 % 7 %. In the given figure, BCD is a trapezium in which B 7 cm,d BC 5cm, DC x cm and the distance between B and DC is 4 cm. Then the value of x is D L x cm M C 5 cm 4 cm 5 cm 7 cm B cm (B) cm (C) 9 cm (D) Cannot be determined D M 7 N C DM CN 5 4 DC 7 7 B

4 . If cot = then the value of sin cos sin cos CE OF PCE (MIN SOLUTION CODE & ) 7 (B) (C) (D) 7 cot tan cot cos sin cot sin cos cot 7 4. The perimeter of a rhombus is 5 cm and one of its diagonals is 4 cm. The length of the other diagonal is 4 cm (B) cm (C) cm (D) cm is (B) a a b a 4a 5 a cm a b b 5 b 5 other diagonal 4. Ram and Shyam start walking in opposite directions from a point Ram covers kms and Shyam covers 4 kms. Then Ram turns right and walks 4 kms and shyam turns left and walks kms. How far is each from the starting point? 4 kms (B) 5 kms (C) kms (D) kms (B) Distance from O 4 5

5 CE OF PCE (MIN SOLUTION CODE & ) km O 4 km km 4 km Shyam Ram 5. How many digit integers are there in which the sum of the digits equals? (B) 7 (C) (D) 9 (C) to 9 will have 7 as the number whose sum of digits 9 will have, -9 will have 5 and so on till 9 will have. Hence numbers.. Which is the smallest? 5 (B) (C) square root of 4 (D) cube root of (D) Cube root of is which is the smallest number. 7. It takes two painters days to paint a house. The older painter would only take days to do the job on his own. How many days would the younger painter take to paint the house on his own? (B) 9 (C) (D) (B) Old painter takes days to paint the house. So he paints / rd of the house in days. Hence the younger painter paints / rds of the house in days and entire house in 9 days.. Richa s age was double that of Nitesh years ago. If Richa was years older to Nitesh then, try to guess how old Richa is today. (B) 4 (C) (D) x y... () & x y... () Solving x, y 4 9. In the following question, four different groups of letters are given in the form of four alternatives. Out of these groups three are alike in a certain way, while one is different. Find out the odd one. STV (B) NOR (C) HJK (D) FHI (B) NOR. Showing the lady in the park, kash said, She is the daughter of my grand fathers only son. How is kash related to that lady? Brother (B) Husband (C) Father (D) Uncle Brother

6 CE OF PCE (MIN SOLUTION CODE & ). In a certain code il be pee means roses are blue, sik hee means red flowers and pee nut hee means flowers are vegetables. How is red written in that code? hee (B) sik (C) be (D) cannot be determined (B) Sik. Sunita is taller than Seema and Renu, Renu is shorter than Radha and Gauri. Bina is taller than Radha and shorter than Sunita. Sunita is not the tallest and Renu is not the shortest. Who is the tallest? Sunita (B) Bina (C) Gauri (D) Data inadequate (C) Gauri. man eats coconutes in days. Together with his wife they eat the same amount in days. How many days will it take wife to eat all the coconuts by herself? 4 (B) (C) (D) (D) Man east coconut per day. In days man eats coconuts. So wife eats the remaining coconuts in days. Hence for coconuts wife will take days. 4.. B, C, D, E, F and G are playing cards sitting in a circle. (i) F is nd to the right of G. (ii) B is neighbour of F but not of E. (iii) E is neighbour of C, is 4th to the right of G. (iv) D is between E and. Who is fourth to the left of G? D (B) E (C) C (D) Can t be determined (C) 5. In a class of students, Ravi occupies fifth position from the top and 5th from the bottom in a test. How many students are there in the class? (B) (C) 9 (D) 5 (C) 9. How many 9 s are there of the following number series which are immediately preceded by and followed by? Nil (B) (C) (D) 4 (B) 7. If means, means X, X means + and + means then x 4 + = 4 (B) (C) (D) (B) 4 4

7 CE OF PCE (MIN SOLUTION CODE & ). If the wages of men for 5 days be Rs.7, the wages of 9 men for days are Rs. 7 (B) Rs. 4 (C) Rs. 5 (D) Rs. 9 (B) 7 Wage of man for day 5 7 wages of 9 man for days In an election between two candidates, one got 55% of total valid votes. % of the votes were invalid. If the total number of votes was 75, the number of valid votes that the other candidate got was 7 (B) 9 (C) (D) No. of valid votes 75, no. of valid votes other candidate got 45, 7. In BC, B, BC 7, C and side BC is extended, as shown in the figure, to a point P so that PB is similar to PC. The length of PC is P C 7 B 7 (B) (C) 9 (D) (C) P C 7 PB ~ PC P B PB PC 7 PC C P P P PC 7 & PC P PC 7 4 PC 9 PC 9 B

8 CE OF PCE (MIN SOLUTION CODE & ) n. If = 79, the value of n is: 4 (B) (C) (D) (D) n n n. If every side of a triangle is doubled, the area of the new triangle is k times the area of the old one. k is equal to (B) (C) 4 (D) (C) k 4. Two cities and B are km. apart. car goes from to B with a speed of 4 km. p.h. and returns to with a speed of km. p.h. Its average speed is? 45 km. p.h. (B) 4 km. p.h. (C) 5 km. p.h. (D) 55 km. p.h. (B) t 9 4 t average speed 4km p.h If a + b + c=; bc + ca + ab = ; abc =, then the value of ( - a)( b)( - c) is (B) (C) (D) None of these (C) a b c a b c ab bc ca abc 5. The sum of the roots of a quadratic equation is 7/ and product is 5/. The equation is x + 7x 5 = (B) x 7x + 5 = (C) x + 7 x (D) x sx s 7 5 x x x 7x = (D) x + 7x + 5 =

9 CE OF PCE (MIN SOLUTION CODE & ). If is one root of the equation x + kx =, then the value of k is (B) (C) (D) k k 7. If the difference of the squares of two numbers is 45, the square of the smaller number is 4 times the larger number, then the numbers are 9, or 9, (B) 5, or 5, (C) 9, 5 or 9, 5 (D) none of these x y () y 4x... () x 4x 45 x 9x 5x 45 x 9x 5 x 9, 5 x 5 & y. In a class test, in mathematics, students scored 75 marks, students scored marks, scored 4 marks and scored marks. The average of their score is (approximately). 57 (B) 5 (C) 55 (D) The value of cot cos sec 45 4 sin is 4 (B) (C) (D) none of these If the line x y = K passes through the origin then the value of K is (B) (C) (D) (B) k k Directions for Question 4: In the following question, four terms are given, marked, (B), (C) and (D). Three of these are identical in some way and one is different from the rest (odd). Identify the term that is different or odd (B) 445 (C) 74 (D) 45

10 CE OF PCE (MIN SOLUTION CODE & ) (D) 4. The line ax + by + c = cuts the Y axis at c, b c x y b c, b (B) c, b (C) c, b (D) (, c) 4. If BUTTER = and TOST = 5, then MILK will be? 7 (B) 5 (C) (D) (C) 44. In the following question four positions of the same dice have shown. You have to see these figures and answer the number opposite to the number? 4 5 (i) (ii) (iii) (iv) 4 (B) (C) 5 (D) 45. number of friends decided to go on a picnic and planned to spend Rs. 9 on etables. Four of them, however, did not turn up. s a result, the remaining one had to contribute Rs. 4 each extra. The number of those who attended the picnic was: (B) (C) (D) 4 9 x x x x 4 4. group of rmy persons consisting of captains and soldiers is travelling in a train. For every 5 soldiers there is one captain. The number of captains in the group is: 5 (B) (C) 75 (D) 7 (C) 5x x x Which of the following system of equations has unique solution? x + y =, x + y = (B) x 5y =, x 5y = 9 (C) x y =, x y = (D) None (C)

11 CE OF PCE (MIN SOLUTION CODE & ) 4. Find the quadratic polynomial which is exactly divided by (x ) and (x + ). x x + (B) x + x (C) x x (D) None (C) x x x x 49. The points (a, 4a); (a, a); and (a + a, 5a) are the vertices of a right angle triangle (B) equilateral triangle (C) isosceles triangle (D) None (B) Equilateral triangle 5. The Co-ordinates of the midpoint of the line joining the points (, ) and (5, ) is (, 4) (D) Mid point 5, 4, 4 (B), 4 (C) (4, ) (D) (4, )

following instructions: Mark (a) if the question can be answered by using FIRST statement alone.

following instructions: Mark (a) if the question can be answered by using FIRST statement alone. Que:31 Que:32 Que:33 Que:34 Mark (c) if the question can be If a and b are positive numbers, is b>a? 1. A 2 >b. 2. A 2 >b 2. Mark (c) if the question can be Which of the four numbers a, b, c and d is the