Study Notes

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STUDY NOTES FOR SSC & STaTE LEvEL ExamS

CGL MAINSQ.1. A certain sum of money was given on loan on

simple interest. It trebles in 25 years. What is the rate of interest?

(A) 10% (B) 15% (C) 8% (D) 12%Q.2. In a school of 1000 students, 630 play Hockey

and 450 Cricket. How many play both Hockey and Cricket?

(A) 80 (B) 20 (C) 100 (D) 120Q.3. A solid wooden box has dimensions 4 m, 3 m and

2 m. What is the area of its surface? (A) 96 m2 (B) 52 m2

(C) 124 m2 (D) 154 m2

Q.4. In how many years will Rs 400 double itself at 8% simple interest?

(A) 8 years (B) 16 years

(C) 1122

years (D) 12 years

Q.5. The average of 8 numbers is 15. If the average of 7 of these number is 14. Find the 8th number.

(A) 20 (B) 30 (C) 15 (D) 22Q.6. What will be the compound interest accrued on an

amount of Rs. 16,500 at the rate of 14 p.c.p.a. at the end of three years?

(A) Rs. 7945.476 (B) Rs. 7022.415 (C) Rs. 6825.281 (D) Rs. 6928.114Q.7. One fourth of sixty percent of a number is equal

to two fifth of twenty percent of another number. What is the respective ratio of the first number to the second number?

(A) 4 : 7 (B) 8 : 13 (C) 5 : 9 (D) 8 : 15Q.8. A 180 metres long train crosses a pole in 20

seconds. What is the speed of the train? (A) 15 m/s (B) 9 m/s (C) 18 m/s (D) 12 m/sQ.9. What will be the area of a circle with circumference

equal to 66 cm? (A) 398.5 cm2 (B) 389.5 cm2

(C) 346.5 cm2 (D) 463.5 cm2

Q.10. Shankar started the business with an investment of Rs. 120000. After 3 months, Anoop invested Rs. 190000 in Shankar's business. At the close of the year, profit earned was Rs. 175000000. What

would be the share of Anoop in the profit? (A) Rs. 80000000 (B) Rs. 85000000 (C) Rs. 90000000 (D) Rs. 95000000Q.11. Present age of Suresh is twice his daughter's age.

After 6 years since now ratio of the age of Suresh and his daughter's age will be 23 : 13. What is present age of Suresh?

(A) 40 years (B) 20 years (C) 46 years (D) 36 yearsQ.12. What is the relation between x and y. If x2+7x+12

= 0 and y2+9y+20 = 0? (A) x > y (B) x < y (C) x > y (D) x < yQ.13. Length of a rectangle is twice its breadth. Area

of the rectangle is 18 metre2. What would be its perimeter?

(A) 9 m. (B) 18 m. (C) 25 m. (D) 28 m.Q.14. The average weight of a class of 20 students is 45

kg. A new student whose weight is 40 kg replaces an old student of this class. hence the agerage weight of the whole class decreases by 1 kg. The weight of the replaced student is:

(A) 55 kg (B) 50 kg (C) 60 kg (D) 45 kgQ.15. Find the area of a regular octagon with each side

'a' cm -

(A) ( )22a 1 2+ (B) ( )2a 1 + π

(C) ( )2a 2 2+ (D) 23 a4

Q.16. The speed of rickshow, car and bike are in the ratio of 3 : 5 : 6. What is the ratio of time taken by each one of them for the same distance?

(A) 6 : 5 : 3 (B) 10 : 6 : 5 (C) 12 : 7 : 6 (D) 4 : 3 : 5Q.17. The profit percentage on the three articles A, B

and C is 10%, 20% and 25% respectively and the ratio of the cost price is 1 : 2 : 4. Also the ratio of number of articles sold of A, B and C is 2 : 5 : 2, then the overall profit percentage is -

(A) 18.5% (B) 21% (C) 18% (D) 17%Q.18. The difference between simple and compund

interest for the fourth year is Rs 7280 at 20% p.a. What is the principal?

(A) Rs 10000 (B) Rs 40000 (C) Rs 50000 (D) Rs 80000

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Q.19. The compound interest on a certain sum at a certain rate of interest for the second year and third year is Rs 21780 and Rs 23958 respectively. What is the rate of interest?

(A) 6% (B) 12% (C) 10% (D) 15%Q.20. A can do a piece of work in 5 days, B can do it in

10 days with the help of C, they finish the work in 2 days. In how many days C alone can do the whole work?

(A) 3 (B) 4 (C) 5 (D) 6Q.21. Amit has a right circular cylinder which he inserted

completely into a right circular cone of height 30 cm. The vertical angle of the cone is 600 and the diameter of the cylinder is 8 3 cm. What is volume of the cone?

(A) 30007

π (B) 3000 π

(C) 4860 π (D) 2530

7π

Q.22. In a ∆ PQR, points M and N are on the sides PQ and PR respectively such that PM = 0.6PQ and NR = 0.4PR. What percentage of the area of triangle PQR does that of triangle PMN form?

(A) 60% (B) 50% (C) 36% (D) 55%Q.23. The semi-perimeter of a right angled triangle is 126

cm and the shortest median is 53 cm. What is the area of a triangle which has the largest median as its longest side?

(A) 1560 cm2 (B) 1350 cm2

(C) 1060 cm2 (D) 1260 cm2

Q.24. Find the volume of a pyramid with a rectangular base measuring 6 cm by 4 cm and height 10 cm.

(A) 90 cm3 (B) 80 cm3

(C) 102 cm3 (D) 88 cm3

Q.25. The price of petrol is Rs 60 per litre and the price of spirit is Rs 40 per litre. In what ratio the petrol and spirit be mixed such that the profit after selling the mixture at Rs 75 per litre be 25%?

(A) 1 : 1 (B) 5 : 1

(C) 3 : 2 (D) None of these

Q.26. The marked price of an article is increased by 25% and the selling price is increased by 16.66%, then the amount of profit doubles. If the original marked price be Rs 400 which is the greater than the corresponding cost price by 33.33%, what is the increased silling price?

(A) Rs 240 (B) Rs 360

(C) Rs 420 (D) Rs 600

Q.27. In a trapezium ABCD, AB is a parallel to CD, BD is perpendicular to AD, AC is perpendicular to BC. If AD = BC = 15 cm and AB = 25 cm, then the area of the trapezium is :

(A) 192 cm2 (B) 232 cm2

(C) 172 cm2 (D) 200 cm2

Q.28. 2x = 4y = 8z and xyz = 288, then value of 1 1 1

2 x 4 y 8 z+ + is :

(A) 1112 (B)

1196

(C) 2996

(D) 2348

Q.29. If a, b, c are positive real numbers, the least value

of (a + b + c) 1 1 1a b c

+ + is:

(A) 1 (B) 9 (C) 12 (D) 11Q.30. Mittal purchased a car for Rs 3,00,000 and a bike

for his son for Rs 1,00,000. he sold the car at a profit of 10% and bike at a loss of 20%. What is the net gain or loss?

(A) 2% gain (B) 2.5% loss (C) 1.5% loss (D) 2.5% gainQ.31. Krishna can do a work in 100 days while Mohan

can do the same work in 20 days. They started work together. After 3 days Krishna left the work and Mohan completed it. For how many days Mohan worked more than the number of days requied when both worked together?

(A) 143 (B)

134 (C)

325 (D)

233

Q.32. A can finesh a piece of work in 12 days while B can do it in 15 days. If both work at it together, what time will they take to do the work?

(A) 6 days (B) 8 days

(C) 263 days (D)

1105

days

Q.33. If sec x = P, cosec x = Q, then : (A) P2 + Q2 = PQ (B) P2 + Q2 = P2Q2

(C) P2 - Q2 = P2Q2 (D) P2 + Q2 = - P2Q2

Q.34. Each interior angle of a regular polygon exceeds is exterior angle by 1320. How many sides does the polygon have?

(A) 9 (B) 15 (C) 12 (D) 14Q.35. If z, y, z are real numbers such that x+y+z=4 and

x2+y2+z2 = 6. x, y, z lie in :

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(A)

3 , 22

(B)

2 , 23

(C) 20,3

(D) None of these

Q.36. If a + b + c = 3, a2+ b2+ c2 = 6 and 1 1 1a b c

+ + =1

where a, b, c are all non-zero, then abc is :

(A) 13 (B)

23 (C)

32 (D) 1

Q.37. ABC is a right triangle, right angled at B. AD and CE are the two medians drawn from A and C

respetively. If AB = 5 cm and AB = 3 5

2 cm, find the length of CE -

(A) 2 5 cm (B) 2.5 cm

(C) 5 cm (D) 4 2 cm

Q.38. When (x3- 2x2+ px - q) is divided by (x2 - 2x - 3), the remainder is (x - 6). The values of p and q are:

(A) p = -2, q = - 6 (B) p = 2, q = - 6

(C) p = -2, q = 6 (D) p = 2, q = 6

Q.39. = 2 and = 6, the values of x and y are:

(A) x y

xy+

(B)1 1,2 4

−

(C) 1 3,2 2

− (D) 1 3,2 4

− −

Q.40. The ratio of water and alcohal in two different containers is 2 : 3 and 4 : 5. In what ratio we are required to mix the mixtures of two containers in order to get the new mexture in which the ratio of alcohol and water be 7 : 5?

(A) 7 : 3 (B) 5 : 3 (C) 8 : 5 (D) 2 : 7Q.41. A person takes a loan of Rs 200 at 5% simple

interst. He returns Rs 100 at the end of one year. In order to clear his dues at the end of 2 years, he would pay :

(A) Rs.125.20 (B) Rs. 110.50 (C) Rs.115.50 (D) Rs. 118.00Q.42. What is the time period for which Rs 8000 amounts

to Rs 12000 at 20% p.a. of simple interest? (A) 4 years (B) 2.5 years (C) 3.25 years (D) 6 yearsQ.43. Kareena can do a piece of work in 9 days and

Karishma can do the same work in 18 days. They started the work. After 3 days Shahid joined them,

who can complete alone the same whole work in 3 days. What is the total number of days in which they had completed the work?

(A) 12 (B) 8 (C) 4 (D) 6Q.44. In a circle of radius 17 cm, two parallel chords

are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is :

(A) 23 cm (B) 30 cm (C) 15 cm (D) 40 cmQ.45. Area of quadrilateral ACDE is 36 cm2, B is the

mid-point of AC. Find the area of ∆ ABE if AC || DE and BE || DC.

(A) 10 cm2 (B) 9 cm2

(C) 12 cm2 (D) can't be determinedQ.46. ABCD is a parallelogram. ÐDAB = 300, BC = 20 cm

and AB = 20 cm. Find the area of parallelogram. (A) 150 cm2 (B) 200 cm2

(C) 400 cm2 (D) 260 cm2

Q.47. The area of the four walls of a room is 2640 sq m and the length is twice the breadth and the height is given as 11 m. What is the area of the ceiling?

(A) 2800 m2 (B) 3200 m2

(C) 3204 m2 (D) 3100 m2

Q.48. If the perimeter of a square and a rectangle are the same, then the areas A and B enclosed by them would satisfy the inequality :

(A) A > B (B) A > B (C) A < B (D) A < BQ.49. In a ∆ ABC, AB =10 cm, BC = 12 cm and AC =

15 cm. Find the length of median AD. If G is the centroid, find length of GA.

(A)

5 57 , 73 7 (B) 5 7 , 4 7

(C)

10 8, 733 (D) 84 7 , 7

3

Q.50. If =34, then the value of 1xx

− is :

(A) 1 (B) 2 (C) 3 (D) 4

Q.51. If

44

1xx

+ =119, then the value of 3

31x

x −

is :

(A) 49 (B) 27

(C) 36 (D) 63

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Q.52. Due to an increase of 30% in the price of egg, 3 eggs less are available for Rs 9.10. The present rate per egg is :

(A) 91 Paise (B) 78 Paise

(C) 48 Paise (D) 84 Paise

Q.53. By selling 12 apples for a rupee, a man loses 20%. How many for a rupee should he sell to gain 20%?

(A) 8 (B) 10

(C) 15 (D) 16Q.54. In a triangle ABC, O is the centre of incircle PQR,

∠ BAC = 650, ∠ BCA = 750, find ∠ ROQ B

CA

QR

P

O

(A) 800 (B) 1200

(C) 1400 (D)can't be determinedQ.55. If a + b + c = 13, what is the maximum value of

(a - 3) (b - 2) (c + 1)? (A) 26 (B) 27 (C) 30 (D) 19Q.56. If abcd = 81, what is the minimum value of a + b

+ c + d? (A) 18 (B) 9 (C) 12 (D) 36Q.57. Vijay travels half of his journey by train at the speed

of 120 km/h and rest half by car at 80 km/h. What is the average speed?

(A) 80 km/h (B) 96 km/h (C) 100 km/h (D) 120 km/hQ.58-61.Study the pir-chart carefully to answer the

question that follow - Percentage of students enrolled in different Hobby

classes in a school. Total number of students = 3600

Drama classes, 13%

Stitchingclasses,

11%

Painting classes, 15%

Dancing classes, 21%

Singing classes, 18%

Cooking classes, 22%

Q.58. The number of students enrolled in cooking classes is what percent of those enrolled in Dancing classes?

(A) 101.45 (B) 104.76 (C) 113.84 (D) 110.28Q.59. What is the total number of students enrolled in

stitching and Drama classes together? (A) 684 (B) 846 (C) 648 (D) 864Q.60. How many students are enrolled in painting

classes? (A) 550 (B) 480 (C) 540 (D) 520Q.61. Number of students enrolled in Painting classes

are what percent of those enrolled in singing classes?

(A) 78 (B) 92 (C) 83 (D) 72Q.62. In a hostel, there are 80 students and food stock is

for 30 days. If 30 new students join hostel, in how many days will the complete stock be exhausted?

(A) 2193 days (B)

71911 days

(C) 921

11 days (D) 23 days

Q.63. A book was sold at a discount of 10% on the printed price and was purchased at a discount of 20% on the printed price. If the profit in the complete deal was Rs. 10, then the printed price of the book was -

(A) Rs. 80 (B) Rs. 90 (C) Rs. 100 (D) Rs. 150

Q.64. If 1x 6x

, then 44

1xx

is -

(A) 1152 (B) 1154 (C) 1148 (D) 1150Q.65. The centroid of an equilateral triangle ABC is G.

If AB = 9 cm, the length of AG (in cm) is -

(A) 3 3 (B) 3 2

(C) 2 3 (D) 3

Q.66. A,B and C are three points on a circle. The tangent at C meets BA produced at T. Given ÐATC = 320

and ÐACT = 460, the angle subtended by AB at the centre of the circle is -

(A) 860 (B) 960

(C) 1120 (D) 1180

Q.67. The mid points of AB and AC of a DABC are respectively X and Y. If BC + XY = 12 units, then the value of BC - XY is -

(A) 2 units (B) 3 units (C) 4 units (D) 5 units

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Q.68. If AB is the a diameter of a circle. Whose centre is at O and C be any point an the circle. If CDAB and CD = 12 cm, AD = 16 cm, then BD is-

(A) 5 cm. (B) 7 cm. (C) 9 cm. (D) 11 cm. Q.69. The base of a right prism is a right angled isosceles

triangle whose hypotenuse is a cm. If the height of the prism is h cm. then its volume is -

(A) 2a h8 cm2 (B)

2a h4 cm3

(C) 2a h8

cm3 (D) 2a h

12cm3

Q.70. A train A is 180 m long, while another train B is 240 m. long. A has a speed of 30 km/h and B's speed is 40 km/hr. If the trains move in opposite directions, find when will A pass B completely?

(A) 21.6 sec. (B) 23.4 sec (C) 19 sec. (D) 28 sec. Q.71. If the difference between the compound interest

and the simple interest on a certain sum for 2 years at 8% per annum is Rs. 32, the sum is -

(A) Rs. 5000 (B) Rs. 5220 (C) Rs. 5500 (D) Rs. 6000

Q.72. If x = 3 13 1

and y = 3 13 1

then the value of

2 2x y

y x is -

(A) 48 (B) 52 (C) 56 (D) 101Q.73. If the angle of elevation of the sun is 600 , then the

ratio of the height of a wall and its shadow is -

(A) 1 : 3 (B) 3 : 1

(C) 2 : 3 (D) 3 : 2

Q.74. I f s inq -cosq=0, f ind the va lue o f s in .

cos2 2

(A) 0 (B) 1

(C) 2 (D) 2 2

Q.75. tan100 tan150 tan 750 tan 800 =? (A) 0 (B) 1 (C) -1 (D) 3 2

Q.76. If sin 5q=cos4q, where 5q and 4q are acute angles, find the value of q.

(A) 100 (B) 220

(C) 300 (D) 600

Q.77. If sec 5A = cosec (A+360), where 5A is an acute angle, find the value of A.

(A) 50 (B) 70

(C) 90 (D) 130

Q.78. If tan2q= 1-a2 , then the value of secq + tan3 q cosecqis-

(A) 3

2 2a 1 (B) 32a

(C) 322 a (D)

32 22 a

Q.79. A solid cylinder of metal 8 m high and 4 m, diameter is melted and recast in to a cone of diameter 3 m. Find the height of the cone.

(A) 39 m. (B) 42.66 m. (C) 53.40 m. (D) 51 m. Q.80. The ratio between the speed of two trains is 8:9.

Second train covers 360 km. in 4 hours. Distance covered by first train in 3 hours is (in km)

(A) 60 (B) 120 (C) 240 (D) 480Q.81. In an isosceles triangle, the measure of each of

equal side is 10 cm and the angle between them is 450 , then area of triangle is -

(A) 25 cm2 (B) cm2

(C) cm2 (D) cm.Q.82. The area of a circle is increased by 22 cm its radius

is increased by 1 cm. The original radius of The circle is -

(A) 3.2 cm (B) 3.5 cm (C) 3 cm (D) 6 cm Q.83. A rectangular tank of length 10 m, breadth 5 m

and depth 6 m is full of water. How much water must be taken out of the tank to reduce the level of water in the tank by one metre?

(A) 30 m3 (B) 60 m3

(C) 50 m3 (D) 100 m3

Q.84. The volume of the metal of cylindrical pipe is 748 cm3. The length of the pipe is 14 cm and its external radius is 9 cm. Its thickness is -

(A) 1 cm (B) 2.3 cm (C) 3.7 cm (D) 5.2 cm Q.85. Volume of two ones are in the ratio 1 : 4 and their

diametrs are in the ratio of 4 : 5, ratio of their heights is -

(A) 1 : 5 (B) 16 : 25 (C) 5 : 4 (D) 25 : 64

Q.86. is equal to -

(A)

(B)

(C)

(D)

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Q.87. Out of seven given numbers, the average of the first four numbers is 4 and that of the last four number is also 4. If the average of all the seven numbers is 3, fourth number is-

(A) 3 (B) 4 (C) 7 (D) 11

Q.88. If x = 3+ , then the value of is- (A) 38 (B) 36 (C) 34 (D) 24

Q.89. If = 1, a 0, b 0, the value of a3+b3 is-

(A) 0 (B) 1 (C) – 1 (D) 2

Q.90. If cos4 – sin4 = , then the value of 2cos2

– 1 is -

(A) (B)

(C) 1 (D) 0

Q.91. If = 3 and 0o < < 90o, then the

value of is- (A) 30o (B) 45o

(C) 60o (D) None of these

Q.92. If tan 62o = , then find the value of tan 28o.

(A) (B)

(C) a (D) b

Q.93. If tan = – 1, and < < , then find the value of sec .

(A) 1 (B) – 1 (C) (D) –Q.94. If the ratio of the shadow of the tree and tree is

:1, find the angle of elevation of the sun. (A) 30o (B) 45o

(C) 60o (D) 90o

Q.95.

(A) x (B)

(C) x5 (D) x-5

Q.96. If x – = 5, then the value of 2 is-

(A) (B)

(C) (D) Q.97-100. The Bar Graph given here shows the population

(in lakh) of a city in various census years. Observe the graph and answer the question based on it.

Q.97. The percent increase in population from 1961 to 1971 is -

(A) 6.71% (B) 7.40%

(C) 9.63% (D) 6%

Q.98. In which census year, the percent increase in population is highest as compared to that in the previous census years?

(A) 1961 (B) 1971

(C) 1981 (D) 1991

Q.99. In which census year, the percent increase in population is least as compared to that in the previous census year?

(A) 1961 (B) 1971

(C) 1981 (D) 1991

Q.100. Per year increase in population from the year 1981 to 1991 is -

(A) 28000 (B) 34000

(C) 28680 (D) 32400

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Q.1.(C) 2P = ⇒ R = 8%

Q.2.(A) Required number of students = 450 + 630 - 1000 = 80Q.3.(B) Surface area = 2(4×3 + 3×2 + 2×4) = 2(12 + 6 + 8) = 52 m2

Q.4.(C) 400 =

⇒ T = 12.5 years ⇒ years

Q.5.(D) 8th number = 15 × 8 - 14 × 7= 120 - 98 = 22

Q.6.(A) C.I. = 16500 – 16500

=

= Rs 7945.476

Q.7.(D) =

⇒ =

⇒ = , ⇒ x : y = 8 : 15

Q.8.(B) Speed of train = = 9 m/sQ.9.(C) 2π r = 66

⇒ r = = 10.5

∴ Area of circle = ×10.5×10.5= 346.5 cm2

Q.10.(D) Investment of Shankar for 1 month Investment of Anoop for 1 month

= = =

∴ Share of Anoop in the profit

= ×175000000 = Rs 95000000

Q.11.(A) Let the present age of daughter be x years ∴ Present age of Suresh = 2x years

⇒ 26x + 78 = 23x + 136, ⇒ 3x = 60, ⇒ x =20 ∴ Present age of Suresh

= 2 × 20 = 40 yearsQ.12.(C) x2 + 7x + 12 = 0 ⇒ x2 + 4x + 3x + 12 = 0 ⇒ (x + 4) (x + 3) = 0, ⇒ x = – 4, x = – 3 and y2 + 9y + 20 = 0, ⇒ y2 + 5y +4y + 20 = 0 ⇒ (y + 5) (y + 4) = 0, ⇒ y = – 5, y = – 4 ∴ x > yQ.13.(B) l = 2b lb - 18 m2

∴ 2b2 = 18, ⇒ b = 3 m. ∴ l = 2 × 3 = 6 m. ∴ Perimeter of rectangle = 2(6 + 3)= 18 m.Q.14.(C) Total weight = 20 × 45 = 900 kg ∴ Required weight = 900 – 20×44 + 40 = 900 – 880 + 40 = 60 kg

Q.15.(A) Area of Octagon = 2a2 (1 + ) cm2

Q.16.(B) Required Ratio = = 10 : 6 : 5

Q.17.(B) CP of A + B + C 2x×y + 5x×y + 2x×y = 20xy total profit = 0.2xy + 2xy + 2xy= 4.2xy

Profit % = ×100% = 21%Q.18.(C) Difference between CI and SI for nth year

=

⇒ 7280

= , ⇒ P = 50000 Rs

Q.19.(C)

⇒

⇒

⇒ r = 10%

ExpLANAtIoN/CGL MAINS

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Q.20.(C) (A+B)'s one day work = =

(A+B+C)'s one day work =

∴ C's one day work = -

= = =

∴ Required time = 5 daysQ.21.(B)

A BM

E C D

O

600

∠ AOB = 600 =AB = cm

OC = 30 cm, tan 600 = , OM = MB

OM = ×4 = 12 cm, ∴ CD = 10

∴ Volume of cone =

= × ×30 = 3000π cm3

Q.22.(C)

Q R

M N

P

6 6

44

Ratio of area of ∆ PQR : ∆ PQR = 3×3 : 5×5 = 9 : 25

∴ Required % = ×100 = 36%Q.23.(D)

A

B C

D

BD = 53 cm

∴ AD = CD = BD = 53 cm ∴ AC = 2 × 53 = 106 cm AB + BC + AC = 2 × 126 = 252 cm ∴ AB + BC = 146 cm

A

B C

D5 6 cm

AB = 56 cm, BC = 90 cm

∴ Arc of ∆ BCD = ×90×28 = 1260 cm2

Q.24.(B) Volume = ×6×4×10 = 80 cm3

Q.25.(D)

60

60

20 0

40SpiritP etro l

Such a mixture is not possibleQ.26.(C) Let profit be x% Rs and CP be 100 Rs ∴ SP = (100+x) Rs, MP = 133.33 Rs According to question Profit = 2x, CP = 100, SP = (100+x)

∴ (100+x) - 100 = 2x

⇒ 700 + 7x - 600 = 12x ⇒ x = 20% CP Profit SP MP 100 20 120 133.33 300 60 360 400 300 120 420 ∴ SP = 420 RsQ.27.(A)

A B

CD

1515

25 In ∆ ACB,

AC = = = 20 and in ∆ ADB, BD = = 20

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∴ DM = = 12 cm

∴ AM =

∴ AM = = 9 cm

∴ MN = 25 - 18 = 7 cm

∴ Area of trapezium = ×(32)×12 = 192 cm2

Q.28.(B) 2x = 4y = 8z

⇒ 2x = 22y = 23z

⇒ x = 2y = 3z = K (Let)

xyz = , ⇒ K 12

∴ =

= =

Q.29.(B) >

and >

⇒ ×

> ×

⇒ (a+b+c) > 9

Q.30.(D) Total CP = 300000 + 100000 = 400000 Rs

Total SP = +

= 330000 + 80000 = 410000 Rs

∴ Profit% = = 2.5%

Q.31.(A) Work done by together = 15×3 = 45% No. of days in which B completed rest 55% work

alone = = 11 days

Total no. of days in which B worked = 3 + 11 = 14 Required no. of days when working together =

=

∴ Required difference = 11 - = days

Q.32.(C) Required no. of days = = days

Q.33.(B) sec x = P, cosec x = Q

⇒ cos x = , sin x =

∴ sin2x + cos2x =

⇒ 1 = , ⇒ P2 + Q2 = P2 Q2

Q.34.(B) +1320 = , ⇒ n = 15

Q.35.(B) x + y + z = 4 and x2 + y2 + z2 = 6 ⇒ y + z = 4 - x, y2 + z2 = 6 - x2

yz =

= yz = x2 - 4x + 5

y and z are the roots of t2 - (4 - x)t + (x2 - 4x + 5) = 0 ∴ (4 - x)2 - 4(x2 - 4x + 5) > 0

⇒ (3x - 2) (x - 2) < 0, ∴ x

Q.36.(C) = 1 ⇒ = 1

⇒ bc + ca + ab = abc (a+b+c)2 = a2+ b2+ c2+ 2(ab+bc+ca) ⇒ (a+b+c)2 = a2+ b2+ c2+ 2abc

⇒ (3)2 = 6 + 2abc ⇒ abc = Q.37.(A)

A

B C

E

D

[11]



AC = 5 cm, AD = cm

AE = BE & BD = CD AB2 = AC2 = 25 - BC2........(I) and

AB2 = AD2 - BD2 = - BD2

= .......(II), From (I) & (II)

AB2 = 25 - = , CE2 = BE2 + BC2

⇒ CE2 = + BC2 ,⇒ CE2 = + BC2

⇒ CE2 = = = 20, ⇒ CE =

Q.38.(C)

⇒ x(p + 3) - q = x - 6, ⇒ (p + 3) = 1 ⇒ p = - 2, q = 6

Q.39.(A) .......(I), ........(II)

From (I) and (II)

= 2, = 6, = 8

y = and x = -

Q.40.(B) W1 : A1 , W2 : A2 , WN : AN

2 : 3 4 : 5 5 : 7

, ,

= , ,

72180

80180

75180

5180

318 0

⇒ 5 : 3Q.41.(C) Amount to be paid in first year

= +200 = 210

Principal for IInd year = 210 - 100 = 110 ∴ Amount paid in IInd year

= 110 + = 115.5 Rs

Q.42.(B) 12000 - 8000 = ,⇒ t = 2.5 yrs

Q.43.(C) Efficiency of Kareena and Karishma = 11.11 + 5.55 = 16.66% Work done in 3 days = 3×16.66 = 50% Rest work done by Kareena, Karishma and

Shahid = = 1 day

Efficiency of Shahid = 33.33% Total time = 3 + 1 = 4 daysQ.44.(B) OA = OC = 17 cm

AP = ×16 = 8 cm

OP = =15 cm

B

DC

A

O1717

P

Q

Now, PQ = OP +OQ = 23 cm ∴ 15 + OQ = 23 cm ∴ OQ = 8 cm

again CQ =

CQ =

∴ CQ = 15 cm ∴ CD = 2CQ = 30 cmQ.45.(C) 12 cm2

Q.46.(B) AD = BC =20 cm, AB = 20 cm

In ∆ADM, = sin 300 =

∴ DM = AD = 10 cm

[12]



∴ Area of parallelogram = base × height = 20 × 10 = 200 cm2

Q.47.(B) 1(2x + x) × 11 = 2640, 2x+x = 120, 3x = 120

x= =40, 2x2 = 2(40)2 =2×1600= 3200 m2

Q.48.(A) Let each side of a square be a and length and breath of the rectangle be l and b, then

4a = 2(l×b) ⇒ a =

∴ Area of the rectangle = l × b

and area of the square = a2 = (l+b)2

AM > GM, ⇒ > l ×b

⇒ Area of square > Area of rectangleQ.49.(D) By theorem AB2+AC2 = 2(AD2 + BD2) (BD = CE) 100 + 196 = 2(AD2 + 36)

A

D CB

G

⇒ AD2 = 112, AD = ,

⇒ AG = AD, ∴ AG = × = cm

Q.50.(B)

∴ 34 =

⇒ = 36 ⇒ = 6

Again, =

⇒ = 6 - 2 = 4, ⇒ = 2

Q.51.(C) =

⇒ = 121, ⇒ = 11

Again, =

∴ = 9 ⇒ = 3

∴ =

,⇒ = 36

Q.52.(A) By percentage change increase decrease

30%

i.e. = 3, ⇒ x = 13, ∴ 13 - 3 = 10

thus, the new price = = 91 paise

Q.53.(A) SP = paise, CP = x, SP = 0.8 x

= , ⇒ x = paise

Therefore, CP = paise

Thus, the new SP (with 20% profit)

= ×1.2 = paise

∴ Required answer = 8Q.54.(C) ∠ ABC = 180 = (65 +75) =400

∠ ORB = ∠ OQB = 900

∴ ∠ ROQ = 360 - (90 +90 - 40) ∠ ROQ = 1400

Q.55.(B) a + b + c = 13, ∴ (a - 3) + (b - 2) + (c + 1) = 13 - 3 - 2 + 1 = 9 For the maximum value of (a - 3) + (b - 2) + (c + 1)

(a - 3) = (b - 2) = (c + 1) = = 3

∴ (a - 3)(b - 2)(c + 1) = 3 × 3 × 3 = 27Q.56.(C) Minimum value of a + b + c + d for given product

abcd will be when, a = b = c = d

[13]



∴ Minimum value of a + b + c + d = 3 + 3 + 3 + 3 = 12Q.57.(B) Let the total distance be 2 D km, then

Total time =

∴ Average speed = = 96 km/h

Q.58.(B) Required % = = ×100 = 104.76%Q.59.(D) Total no. of students enrolled in Stitching and

Drama classes together = = 864

Q.60.(C) Required answer = = 540

Q.61.(C) Required%= ×100= = 83 %

Q.62.(C) Let food stock will be exhausted in x days m1 = 80, D1 = 30, m2 = 80 + 30 , D2 = x m1 d1 = m2 d2 , 80 × 30 = 110 × x

days

Q.63.(C) Let printed price of the book = Rs. 100 Then selling price = 90% of 100 = 90 and cost price = 80% of 100 = 80 Req. Profit = 90 - 80 = 10 Printed price = Rs. 100

Q.64.(B) ,

,

,

Q.65.(A)

A

BG

D C

AB = 9 cm. , BD = cm. ,

= , AG = = cm.

Q.66.(C)

AB

Co

46 032 0 T

ATC = 320 , ACT = 460

CAT = 1800 - (460 +320 ) = 1020

CAB = 1800 - 1020 = 780

ABC = ACT = 460

BCA = 1800 -( ABC + CAB) = 1800 - (460 + 780) = 560

BOA = 2 × BCA = 2 × 56 = 1120

Q.67.(C)

y

A

B C

x

BC + XY = 13, BC + ,

and XY =

BC - XY = 8 - 4 = 4 unitsQ.68.(C)

A B

C

16 xD12O

Let DB = x, In ACD

AC = = cm. , In BCD

BC = , In ABC

(16+ x)2 = (20)2 + , 256+x2 +32x = 400

+ 144 + x2 , 32x = 288, x = 9 cm.

Q.69.(B)

A

B C

x a

x Let AB = x = BC In ABC AB2 + BC2 = AC2 x2 +x2 = a2

2x2 = a2 ,

Volume of prism = Area of base × height

[14]



cm3.

Q.70.(A) Total distance = 180 + 240 = 420 m.

Speed = m/sec.

Req. time = = 21.6 sec.

Q.71.(A) Req. Diff. = , 32 =

= Rs. 5000

Q.72.(B) x =

and

= (4)3 -3(4) = 52Q.73.(B)

A

B

C x

h

60 0

, ,

Q.74.(C) sin - cos = 0 on squaring

sin2 + cos2 - 2sin cos = 0 2sin cos = 1

sin = sin +cos

= Q.75.(B) tan100 tan 150 tan 750 tan 800

=tan (900 - 800 ) tan (900 -700 ) tan 750 tan 800

= cot 800 cot 750 tan 750 tan 800

= (cot800 tan 800 ) cot750 tan 750) = 1 × 1 = 1Q.76.(A) sin 5 = cos4 ,

5 = 900 - 4 , 9 = 900, = 100

Q.77.(C) sec 5A = cosec (A+360 ) sec5A = sec[900 - (A+360)] sec 5A = sec(540 -A)

5A = 540 , A = 90

Q.78.(D) sec + tan3 cosec

= =

Q.79.(B) Volume of cone = Volume of cylinder

,

= = 42.66 m.

Q.80.(C) Speed of the second train km/hr.

Speed of first train = 80 km/hr

Req. distance = 80 × 3 = 240 km.

Q.81.(C) A

B Ca

450

c b

AB = AC = 10 cm.

Area =

cm2

Q.82.(C) Let the original radius be r cm. According to the question

(r+1)2 - r2 = 22, (2r+1) ×

, , r = 3 cm.

Q.83.(C) Volume of water taken out = 10 × 5 × 1 = 50 m3

Q.84.(A) Let the thickness of pipe be x cm According to the question 92 × 14 - ×14 (9-x)2 = 748 × 14 [81-(81+x2 -18x)] = 748 ×14 (-x2 +18x) = 748

, -x2 + 18x = 17

x2 - 17x + 17 = 0, x2 -17x - x + 17 = 0 x(x -17) - 1 (x - 17) = 0

[15]



x = 1, or 17, x = 1Q.85.(D) Let the heights of the cones be h1 and h2 respectively

,

Q.86.(D) =

=

=

= =

Q.87.(D) Fourth number = (4×4+4×4 – 3×7)= (16+16 – 21) = 11

Q.88.(C) x = 3+

= = 3 –

x2 + = (3+ – 3– )2 – 2 = 36 – 2 = 34

Q.89.(A) , a2 + b2 = ab

a2 +b2 – ab = 0, a3 + b3 = (a+b) (a2 – ab + b2) = 0

Q.90.(B) cos4 – sin4 = , (cos2 +sin2 ) (cos2 – sin2

) = , cos2 – sin2 =

cos2 – (1 – cos2 ) = , 2cos2 – 1 =

Q.91.(C) , cos2 = 3cot2 – 3cos2

4cos2 = 3cot2 , 4cos2 = 3

cos2 = 0, 4 – = 0, 4sin2 = 3

sin = , sin = sin60o = = 60o

and cos2 = 0, = 90o

Q.92.(B) tan28o = tan (90o – 62o) = cot 62o =

Q.93.(D)

lies in 2nd quadrant and sec is negative in 2nd quadrant.

sec = – = – = –

Q.94.(A) Let AB be a tree and BC its shadow.

In ACB, tan = , tan = , = 30o

Q.95.(A) = = = x

Q.96.(D) 2 = 2

= 25+4 = 29

2 = 2

= 2× ×5 = 10Q.97.(B) Population in 1961 = 32.40 lakh, Population in 1971

= 34.80 lakh, Increase = 34.80 – 32.40 = 2.4 lakh

Incrase % = ×100 = 7.40%

Q.98.(A) Percentage increase in 1961

= ×100 = 84%

Q.99.(B) Percentage increase in 1971

= = 7.40%

Q.100.(B) Total increase = 45.60 – 42.20 = 3.4 lakh

Annual increase = = = 34000

[16]



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