1 UNIT - I Arithmetics/1.Maths(1-33).pdf · 4. In how many years will a sum of money become four fold at 15% p.a.S.I. A) 5 B) 10 C) 15 D) 20 5. A sum of money becomes triple itself

1SRIGAYATRI NTSE Material

MATHEMATICS CLASS - X

UNIT - IArithmetic

1

NUMBER SYSTEM

1. If x>y>0, which of the following is lesser than yx ?

A) 2 B)

xy

C)

yx

D)

2yx

E)

2yx

2. If a2 - 81 = 0 then which of the following could be a value of a?A) -9 B) 6 C) 3 D) -3 E) -6

3. If x,y and z are positive integers adn 0.2x = 3y= 2z, what could be the ordering of x,y and z ?A) x > y > z B) y > x > z C) x > z > y D) x < y < z E) z < y < x

4. If n is a negative integer, what is the ordering of p, q and r from greatest to least. p = n2 -2.1; q = n3 -2.1;r = (n -2.1)2

A) p > q > r B) p > r > q C) q > p > r D) q < r < p E) r < p < q5. If x,y and z are three prime numbers and 19 < x < y < z < 35, find x + y - z

A) 21 B) 12 C) 23 D) 29 E) 526. If the product of three consecutive integers is 60, and one of them is a perfect square, find the first integer

A) 3 B) 4 C) 5 D) 9 E) 127. If x,y and z are three consecutive integers, and z>y>x, If z = x2, which of the following could be the value of

x?I. 2 II. 0 III. -1A) only I B) only II C) only III D) only I and II E) only I and III

8. Which of these is not a divisor (factor) of 112?A) 7 B) 8 C) 12 D) 14 E) 28

9. How many positive three-digit integers have the hundreds digit equal to 3 and the units digit (ones digit)equal to 4 ?A) 10 B) 19 C) 20 D) 190 E) 200

AVERAGES1. Average of first five multiples of 3 is

A) 6 B) 4 C) 3 D) 92. A ship sails out to a mark at a rate of 10 kmph and sails back at the rate of 15 kmph. What is the average

rate of sailing? (in kmph)A) 13 B) 12 C) 14 D) 12.5

3. The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, then the average of theremaining numbers isA) 36.5 B) 37 C) 37.5 D) 37.25



4. The average temperature on Tuesday, Wednesday and Thursday was 370C. Average of Wednesday, Thursday,Friday was 380C. If temperature on Friday was 390C, find temperature on TuresdayA) 600C B) 550C C) 430C D) 360C

5. There are 2 sections in a class A & B. Section A scored an average of 25 marks in an exam, Section Bscored an average of 20 marks in the exam. Calculate the average of the entire class if there are 4 students& 5 students respectively.A) 26 B) 21.2 C) 22.2 D) 29

6. The average weight of 15 students in a class in 20kg. When teacher's weight is included the averageincreases by 1. Find the weight of teacher?A) 36 B) 34 C) 33 D) 28

7. A batsman makes a score of 75 runs for 14 innings & thus increases his average by 2 runs. Find his averageafter 14 innings.A) 56 B) 49 C) 38 D) 29

PERCENTAGES

1. Which is greatest in

2 216 %, ,0.17?3 15

A)

216 %3

B)

215

C) 0.17 D) All are equal

2. Rama's salary was decreased by 50% & subsequently increased by 50%. What is % change?A) 25% increase B) 25% decrease C) No change D) None

3. In an examination, 35% of the students passed and 455 failed. How many students appeared for theexamination ?A) 160 B) 240 C) 350 D) 700

4. The value of a machine depreciates at the rate of 10% per annum. If its present value is Rs. 1,62,000. Whatwill be its worth (in Rs.) after 2yrs?A) 150000 B) 145000 C) 131220 D) None

5. A man spends 35% of his income on food, 25% on children's education and 80% of remaining on houserent. What % of his income is he left with?A) 6 B) 7 C) 8 D) 9

6. The population of a town is 27648. If it decreases by 4% per annum, find out the population 3 years ago.A) 31250 B) 32400 C) 35000 D) None

7. A number decreased by 15% gives 51. Find the numberA) 46 B) 60 C) 30 D) 59

RATIO AND PROPORTION

1. a : b = 5 : 9, b : c = 4 : 7, find a : b : c ?A) 20 : 36 : 63 B) 36 : 63 : 20 C) 36 : 20 : 63 D) None

2. Find mean proportional between 0.08 & 0.18 ?A) 0.6 B) 0.12 C) 0.13 D) 0.19

3. If x:y = 2:1, then x2 - y2 : x2+y2 is ?A) 6:5 B) 4:3 C) 3:5 D) 9 : 3

4. If 76 is divided into four parts proportional to 7,5,3,4 then smallest part is?A) 6 B) 8 C) 10 D) 12



5. Salaries of Sushma & Jaya are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratiobecomes 40:57. What is Jaya's present salary (in Rs.) ?A) 36000 B) 34000 C) 32500 D) None

6. If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrorsto unbroken mirrors?A) 2:1 B) 3:1 C) 3:2 D) 7:5

PARTNERSHIP1. A and B enter into a partnership. A contributes Rs. 800 and B contributes Rs. 1000. If the profit at the end

of the year amounts to Rs. 936. What would be the share of B(in Rs.) in the profit?A) 450 B) 480 C) 500 D) 520

2. Three persons A,B and C shared profits in the ration 2:3:4. If B received Rs. 10,000 more than A, then findthe share of C (in Rs).A) 60000 B) 40000 C) 30000 D) 28000

3. Kavitha is a working partner and Sunitha is a sleeping partner in a business. Kavitha puts in Rs. 5000 andSunitha puts in Rs. 6000. Kavitha received 12 1/2% of the profit for managing the business and the rest isdivided in proportion to their capitals. What amount each get out of a profit of Rs. 880.A) 420, 460 B) 460, 420 C) 350, 300 D) none

4. A,B and C invested capitals in the ratio 2:3:5 the timing of their investments being in the ration 4:5:6. In whatratio would their profits be distributed?A) 30:15:8 B) 8:15:30 C) 30:8:15 D) none

ALLIGATION AND MIXTURES1. 6kg of rice at Rs. 6/kg and 4kgs of rice at Rs. 7 / kg are mixed together and the mixture is sold at 10% profit.

What is the selling price of the mixture per kg(in Rs.) ?A) 7.04 B) 7.4 C) 7.0 D) 7.7

2. In what proportion must rice at Rs. 6.20 per kg be mixed with rice Rs. 7.20 per kg, so that the mixture beworth Rs. 6.50 a kg?A) 2:5 B) 6:4 C) 7:3 D) 3:7

3. From a cask of milk, containing 40 liters, 8 liters are drawn out and the replaced with water. If the sameprocess is repeated a second and a third time, how much milk (in liters) will be left in the cask?A) 86.5 B) 73 C) 37.5 D) 20.48

PROFIT AND LOSS1. If a radio is purchased for Rs. 490 and sold for Rs. 465.50, find the loss percent.

A) 6 B) 4 C) 3 D) 92. Find C.P (in Rs.) when SP = Rs. 51.70, loss = 12 %

A) 36 B) 40.25 C) 58.75 D) 693. If cost price is 96% of selling price, then what is the profit percent?

A) 6 B) 4.17 C) 3.20 D) 2.54. A dishonest dealer professess to sell his goods at cost price but uses a weight of 960 grams for a kg. wt.

Find his gain percent.A) 52 B) 40 C) 25/6 D) 19/2

5. Shiva buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs.5800, his gain or lass % is?A) 13 B) 24/11 C) 35 D) 60/11

6. A man purchases 11 books for Rs. 10 and sells 10 books for Rs. 11. How much profit or loss does he make?A) 21% gain B) 21% loss C) 30% gain D) none



7. Each of two cars are bought at the same price. By selling them, a profit of 10% is made on the first and aloss of 10% on the second. Find loss or profit % in the overal! transaction.A) 20% gain B) 20% loss C) No loss/gain D) none

8. By selling a table for Rs. 750 a man losses 25%. Find the cost price of the tableA) Rs. 910 B) Rs. 1000 C) Rs. 1050 D) None

SIMPLE INTEREST1. Find S.I. on principal Rs. 452 for 3 years, rate of interest being 5%

A) 67.8 B) 78.6 C) 80 D) None2. Find principal when S.I. Is Rs. 312.75/- calculated for 2 years 3 months at 6.25% p.a.

A) 2000 B) 2050 C) 2224 D) None3. Certain sum of money amounts to Rs. 312 at 4% interest & Rs. 324 at 8% interest. Find Time.

A) 3yrs B) 2yrs C) 1 yr D) none4. In how many years will a sum of money become four fold at 15% p.a.S.I.

A) 5 B) 10 C) 15 D) 205. A sum of money becomes triple itself in 8 years at S.I. In how many years will it become six times it self at

the same rate?A) 5 B) 10 C) 15 D) 20

6. A sum of money becomes triple itself in 5 years at S.I.In how many years will it become six tiems at thesame rate?

A)

1122

B) 12 C) 10 D) none

COMPOUND INTEREST1. On what sum of money will be Compound Interest be Rs. 102 in 2 years at 4% p.a.?

A) Rs. 750 B) Rs.1000 C) Rs. 1250 D) none2. Find the amount on Rs. 10,000 in 9 months at 4% p.a. If the interest is calculated quarterly?

A) Rs. 9500 B) Rs. 10000 C) Rs. 10303 D) none3. The C.I. and S.I. on a sum of money for 2 years are Rs. 816 and Rs. 800 at the same rate. Find the sum and

rate of % p.a.?A) 4%, 10,000 B) 10,000, 4% C) 9,000, 3% D) none

4. At C.I. a certain sum becomes double itself in 3 years. In how many years will it become 9 times?A) 3 B) 6 C) 9 D) 12

5. Find the amount on Rs. 8000 in 3 years, the rate of interests being 10%, 20%, 25% per year respectively.[Hint: A = P(1+r1/100)(1+r2/100)(1+r3/100)]A) Rs. 12,500 B) Rs. 13,000 C) Rs. 13,200 D) None



ALGEBRAIC EXPRESSIONS

EVALUATE ONE VARIABLE IN TERMS OF ANOTHER

1. 9a + 12a2 - 5a =A) 16a B) 16a2 C) 12a2 - 4a D) 12a2 + 4a E) 26a2

2.

( )( )2 2 2 22 4 6x y x y+ =

A)

2 212x y

B)

2 214x y

C)

2 2 2 22 4 6x y x y+ +D) 2 2 2 28 6x y x y+ + E) 4 4 2 28 6x y x y+

3. If 23 9 15

6cc+ = , what is the value of c?

A) 12 B) 2 C) 3 D) 6 E) 124. If 2x-3 = 9, what is x2-4x+2 ?

A) 12 B) 14 C) 16 D) 32 E) 36

5. What is the value of

( )

1

12 ?

2a ab b

−

−

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

A) 1 B) 2 C) 2a D) 4 E) a2/b2

6. The fraction

39

xx−−

is equivalent to

A)

13x −

B)

19x −

C)

13x +

D)

33

xx−+

E)

33

xx+−

7. The fraction

2

214 338 33

x xx x+ ++ −

is equivalent to

A) -1 B) 35

xx+−

C)

33

xx−+

D)

311

xx++

E)

311

xx−+

UNIT - IIAlgebra

2



8. If fg+2f-g = 2-(f+g), what is the value of 'g' in terms of b?

A) -1 B)

1f

C)

4f

D) 2-2f E)

2 3 ff−

9. If

4 1 10xy

⎛ ⎞+ =⎜ ⎟

⎝ ⎠

, what is the value of y in terms of x?

A) 14

x− B) 14

x C)

49

x

D)

23

x

E)

32

x

ALGEBRAIC FACTORS1. What are the factors of x2 - x - 6 ?

A) (x-3) (x-2) B) (x-3)(x+2) C) (x+3)(x-2) D) (x-6)(x+1) E) (x-1)(x+6)2. What is one factor of x2 - 4 ?

A) x2 B) -4 C) (x-1) D) (x+2) E) (x-4)3. What are the roots of x2+8x-48 = 0 ?

A) -6 and -8 B) -6 and 8 C) 4 and -12 D) -4 and 12 E) -4 and -124. If (x-2) (x+6) = -16, what is the value of x?

A) -6 B) -4 C) -2 D) 6 E) 7

5. If

5 66 44

x xx

+ = − +

, what is one possible value of x ?

A) -5 B) -4 C) 3 D) 5 E) 116. What are the factors of 2x3+8x2-192x ?

A) 2(x-8)(x+12) B) 2x(x-8)(x+12) C) x(2x-8)(x+24)D) 2x(x+16)(x-12) E) 2(x2-8x)(x2+12x)

7. For what values of x is the expression 3x2-3x-18 equal to 0 ?A) x = -3, x = 2 B) x = -3, x = 6 C) x = 3, x = -1/2 D) x = 3, x = -6 E) x = 3, x = -2

8. Four times the cube of a number is equal to 48 times the number minus four times the square of thenumber. If the number is greater than 0, what is the number?A) 3 B) 4 C) 5 D) 6 E) 8

9. Which of the following is equivalent to 6x2-11x-2?A) (6x-1) (x+2) B) (3x-1) (2x+2) C) (3x+1) (2x-2) D) (6x+1) (x-2) E) (x+1) (6x-2)

10. What is one value of makes the fraction

2

325

125xx

++

undefined?

A) -25 B) -5 C) -1 D) 5 E) No such value

RADICALS AND EXPONENTS

1. 3 3a a

A)

4a a

B) a5 C) a6 D)

5a a

E) a9



2.

( )( )

33

2

27

27

y

y=

A)

33

B)

3

C)

33

y

D) y E)

3y

3.

23

5mn

−

=

A)

3

5mn

B)

5

3nm

C)

10

6nm

D)

7

5nm

E)

10

6nm

4.

( )32

9 pr

pr −=

A)

3pr

B)

3pr

C)

3 pr

D) 3pr E) 3p2r2

5. If 23 6a =

, then 43a =A) 3

B) 6

C) 3 6

D) 6 6

E) 36

6. What is the value of

( ) aba b

−

, if a =

13

and b = 9 ?

A)

19

−

B)

13

C) 1 D) 3 E) 9

7. If

( )2 48c d =

and c = 2, what is the value of d?

A)

2 3

B)

2 6

C) 6 D)

4 6

E) 12

8. What is the value of (x-y)(2xy)(3yx), if x = 2 and y = -2 ?A) 6 B) 8 C) 12 D) 24 E) 384

9. If a is positive, and a2 = b = 4, what is the value of

4

ab ba

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

?

A)

11.024

B)

132

C)

116

D)

14

E)

12



LINEAR EQUATIONS AND INEQUALITIES

1. If -6x2 + 5x - 7 = 7x + 2 + 3x2 - 9x2. Find x

A) 9 B)

29−

C)

29

D)

92−

E)

92

2. If 4b+12 = 16, find 18-3bA) 12 B) 14 C) 15 D) 16 E) 18

3. Given the equations below, what is the value of x ? 2x+y = 6 ;

4 122y x+ =

A) -2 B) 0 C) 1 D) 3 E) 6

4. Given the equations below, what is the value of b?

7 254ba− + =

; b + a = 13

A) -3 B) 4 C) 12 D) 13 E) 16

5. Given the equations below, what is the value of b? 9a-2(b+4)=30;

14 3 32

a b− =

A) 2 B) 4 C) 6 D) 8 E) 10

6. If

23 4x >

, which of the following must be true?A) x >8 B) x<8 C) x > 2 D) x < 2 E) x <4

7. Which of the conditions would make 5x-5y > 0A) y > 0 B) x > 0 C) x = y D) x < y E) x > y

8. What is the greatest integer value of p for which 4p - 40 < 0 ?A) 11 B) 9 C) 4 D) 10 E) 40

9. If x =2 > 5 and x- 4 < 1, and x is an integer, what is the value of x ?A) 2 B) 3 C) 4 D) 5 E) 0

QUADRATIC EQUATIONS1. The condition that the equation ax2+bx+c = 0 be quadratic is

A) b2 - 4ac > 0 B) b2 - 4ac < 0 C) b2 - 4ac = 0 D)

0a ≠

2. If one root of the equation ax2+bx+c=0 be reciprocal of other, thenA) a = b B) b = c C) a = c D) b = 0

3. The product of the roots of the equation mx2 + 6x + (2m + 1)=0 is -1 then m =A) 2/3 B) -3/2 C) 1/3 D) -1/3

4. If the roots of x2+kx+1 = 0 are equal, then k =A) 1/2 B) 2 C) 1 D) -2

5. In a quadratic equation, the sum of the roots is 7 and the product of the roots is 12. The equation isA) x2-7x+12=0 B) x2-7x+5=0 C) x2-12x+5=0 D) None

6. If -7 is a root of x2+5x+a=0, then the second root isA) 1 B) 2 C) 4 D) a

7. If the roots of the equation 2x2-8x+7-k=0 are equal then k =A) -2 B) -1 C) 1 D) 2

8. If the difference of the roots of kx2+3x-4=0 is 5, then k =A) 0 B) 1 C) 2 D) -1

9. If ax2+bx+c=0 and x2+x+c=0 hava a common root, thenA) a+b+c=0 B) a=b or b=c or c=a C) a=b=c D) a+b+c=1



LINES AND ANGLES

1. In the given figure,

AB

is a line segmkent and, if

35

aa b

=+

. Find the value of b?

ba

A B

A) 36 B) 72 C) 108 D) 135 E) 180

2. If ( )027a +

and ( )013a + are supplementary angles. Find the value of a?

A) 25 B) 50 C) 60 D) 70 E) 90

3. In the given figure, AB and

CD

interest at 'O', find the value of x?

BC

A D

x

140

A) 40 B) 50 C) 60 D) 80 E) 1004. In the figure above, if PQRS is a parallelogram, then find the value of y?

A B

CD0x

3y120

A) 10 B) 20 C) 30 D) 40 E) 50

UNIT - IIIGeometry

3



5. In the figure given ABCD is a parallelogram. Find the value of DAC∠ ?

C D

A B

072

035

A) 350 B) 1450 C) 370 D) 730 E) 450

6. If a pair of angles forming a linear pair are in the ratio of 4:5, find the measure of the greater angle in the pair

A

CDBy

078052

A) 40 B) 50 C) 80 D) 90 E) 1007. In the given figure lines m and n are parallel and liens AB and CD are parallel respectively. Find the value of

x+y ?

m

n

B D

A C

y

x

A) 60 B) 90 C) 180 D) 360 E) Can't say8. Find the supplement and complement of 630.

A) 1800, 900 B) 1270, 370 C) 1170, 270 D) 1070, 170 E) 270, 1170

9. In the given figure find y, if l || m || n, p⊥ m and q

⊥

n

l m n

p

qy

A) 00 B) 450 C) 600 D) 900 E) 1800



10. In the given figure, I is parallel to m, find the value of a + b + x + y.

l

my

xa

b

A) 900 B) 1200 C) 1800 D) 3000 E) 3600

TRIANGLES

1. PQR is an isosceles triangle with PQ = PR . 030Q∠ = , find the measure of exterior angle QPX.

?QPX∠ = P

Q R

030

A) 300 B) 600 C) 900 D) 1000 E) 1200

2. ABCΔ is isosceles with AB=AC and D is a point in the interior of triangle ABC.

DBCΔ

is also isoscles

with DB = DC. If

030A∠ =

and 070BDC∠ = find ABD∠ .

A

B C

030

070

D

A) 200 B) 300 C) 450 D) 600 E) 700



3. In PQRΔ ,

050P R∠ = ∠ =

. Which of the two sides of the triangle are equal? Find Q∠ .A) 450 B) 600 C) 800 D) 900 E) 1000

4. Find the area of an equilateral triangle with side 4cm.

A)

24 3cm

B) 16cm2 C)

216 3cm

D) 16cm2 E)

248cm

5. Find the area of a right angled triangle with sides 9, 12 and 15 unitA) 2.5 cm B) 3.25 cm C) 4 cm D) 4.33 cm E) 3 cm

6. In the given figure

ABCΔ

is equilaterial, if

CDA∠

is 350 what is the measure of

DAC∠

?

A

B C D

A) 250 B) 350 C) 450 D) 600 E) 1200

7. In the given figure if DB = 5AD and EC = 5 AE and DE||BC. Find length of DE if BC = 24 cm.

B C

ED

A

A) 18 cm B) 9 cm C) 6 cm D) 4 cm E) 2 cm8. The perimeter of an isosceles triangle is 20 inches, its base measures 8 inches. Find the length of each of

its equal side.A) 7 B) 8 C) 6 D) 3 E) 9

9. A 25 foot ladder is kept against a wall. If the ladder slips down 4 feet alogn the wall so that the bottom of theladder is now 15 feet away from the base of the wall, how far away from the wall was the foot of the ladderoriginally?

h

b

A) 4 feet B) 7feet C) 12 feet D) 15 feet E) 25 feet10. In a right triangle one angle measures 300 and its hypotenuse measures 15 inches, find the length of the

shortest side of the triangle.A) 7.5 inches B) 6.5 inches C) 5.5 inches D) 5 inches E) 4.5 inches

11. If square of one side and hypotenuse of a right triangle are 64 and 17 respectively find the length of the thirdside of the triangleA) 22 B) 17 C) 15 D) 9 E) 8



1. The floor of an auditorium is in the shape of a rectangle around which vertical walls are raised. If the permiterof the floor is 110 m and the height of auditorium is 15 m. Find the cost of painting the four walls at the rateof Rs. 720/- per 100 sq. mA) Rs. 11880 B) Rs. 81180 C) Rs. 98890 D) None

2. A path of 1.5m width runs around and inside ar ectangular plot of 30 m x 18 m. Find the cost of leveling thepath at the rate of Rs. 1.25 per sq. mA) Rs. 125.25 B) Rs. 168.75 C) Rs. 149 D) None

3. The outer dimentions of a tank are 5m, 4m & 3m respectively. Find the cost of plastering the outer walls atthe rate of Rs. 15 per sq. mA) Rs. 760 B) Rs. 810 C) Rs. 860 D) Rs. 950

4. The edge of a cube is 12 cm. Find its volume (in cubic cm)A) 125 B) 625 C) 1331 D) 1728

5. In a ABCΔ , BC=8cm. The altitude from A to BC is 6cmA) 20 sq. cm B) 24 sq. cm C) 30 sq. cm D) 36 sq.cm

6. Find the area of rhombus whose diagonals are 24 cm & 18 cmA) 121 cm2 B) 169 cm2 C) 196 cm2 D) 216 cm2

7. Find the height of the adjacent trapezium if its area is 39 cm2

4.2 cm

8.8 cm

h

A) 2 cm B) 4 cm C) 6 cm D) 8 cm8. Find the area of circle whose diameter is 11 cm

A) 94 cm2 B) 94.99 cm2 C) 95 cm2 D) None9. Find the length of the arc of a sector with radius 5 m area 20 m2

A) 4 m B) 6 m C) 7 m D) 8 m

UNIT - IVMensuration - 2D

4



10. A path 2 m of uniform width runs across the rectangular plot of dimensions 10 m & 8 m. find the area of thepath

2 m

2 m 8 m

10 m

A) 24 sq.m B) 28 sq.m C) 32 sq.m D) 36 sq.m



1. What if the total no. of pets in the 4 households?

A) 14 B) 16 C) 15 D) 202. The given table shows credit points scored by five students in a six week course

Weeks I II III IV V VIStudentsA 10 24 20 11 6 18B 10 16 11 21 22 25C 12 23 22 21 18 26D 10 12 16 20 22 23E 24 15 16 13 12 8Which student has steady rate of progress in the course?

A) A B) B C) C D) D E) E3. In the given graphs, read the information and answer the question given. Employees in various departments

at company ABC. Total no employees in the company were 1000. What percentage of all the employees atcompany ABC work in the service department?

A) 16% B) 40% C) 14% D) 60 % E) 25%

UNIT - VData Interpretation

5



4. Scores in two test in 5 subjects. The graph shows the scores of a student in two tests in 5 subjects. Whatis the difference in percent of marks in the two?

A) 6 % B) 15 % C) 10 % D) 7% E) 12 %5. The following table gives the number of tourists visiting a city in a week and the bar-diagrm shwos the

occupancy percents in three different hotels A,B and C.Day Number of touristsMon 1750Tue 1800Wed 1700Thu 1650Fri 1950Sat 1900Sun 1600

The number of tourists stayed in hotel B was how much more than the number of tourists in hotel A onSaturday ?A) 390 B) 450 C) 285 D) 855 E) 570



6. The given bar graph represents the profit percent of a company A. If the income of company A in 2000 was35,000 dollars and in 2002 was 29,000 dollars. What is the ratio of the expenditures of the company forthese two years?

A) 75:74 B) 65:69 C) 174:175 D) 175:174 E) 35 : 297. In the given figure, sales of two products are given, what is the ratio of the total sale of the two products

A) 34:35 B) 35:34 C) 43:45 D) 45:43 E) 55 : 498. The given pie-chart shows the percentage of children interested ine ach field, find the number of students

who are interested in music from a group of 120 students

A) 48 B) 50 C) 25 D) 36 E) 30



TIME, SPEED AND DISTANCE

1. Express a speed of 36 kmph in metres per secondA) 10 B) 12 C) 14 D) 17

2. The speed of a train is 90 kmph. What is the distance (in km.) covered by it in 10 minutes?A) 15 B) 12 C) 10 D) 5

3. The speed of a bicycle is 36 kmph. Find the time taken (in sec) to cover a distance of 200m.A) 18 B) 19 C) 20 D) 21

4. A man coveres half of the journey at 70 kmph and the rest at 30 kmph. What is the average speed (in kmph)of the car for the whole journey?A) 42 B) 4.2 C) 40 D) None

TRAINS1. How many seconds will a train 200 m long running at the speed of 72 kmph takes to pass a tree?

A) 10 B) 20 C) 24 D) 602. How long (in second) does a train 125m long running at 72kmph take to cross a bridge of 75m?

A) 3 B) 10 C) 14 D) 153. In the above problem, if the trains are running in the same direction, In what time (in seconds) wil they be

completely clear of each other?A) 26 B) 50 C) 67 D) 99

TIME AND WORK1. P, Q and R can do a work in 20, 15 and 112 days respectively, in how many days can they together

complete the work?A) 16 B) 9 C) 5 D) 7

2. P and Q can do a piece of work in 12 days. Q and R can do it in 15 days, R and P in 20 days. In how manydays all of them can do the work?A) 10 B) 20 C) 15 D) 47

3. Akhil and Nihil can do a work in 30 days and 36 days respectively. They work together for 10 days and thenAkhil goes away. In how many days will Nikhil finish the work?A) 17 B) 19 C) 12 D) 14

4. P can do a work in 40 days and Q can do it in 30 days. They together undertook to do a piece of work forRs. 840. What is the share of R (in Rs.)A) 160 B) 360 C) 340 D) 440

5. Sixteen men can complete a work in 8 days. Three days after they started the work, 4 more men joinedthem. In how many days will all of them together complete the remaining work?A) 4 B) 5 C) 6 D) 7

UNIT - IArithmetic

1



PIPES & CISTERNS1. Pipe P can fill a tank in 24 hours and pipe Q can empty it in 36 hours. In how many hours the tank will be

filled if they work together?A) 24 B) 36 C) 72 D) 40

2. Pipe P can fill an empty tank in 4 hours while another tap can empty it in 6 hours. If both the pipes areopened at the same time, then how many hours it will take to fill up the cistern?A) 24 B) 32 C) 20 D) 14

3. A pipe can fill a cistern in 12 minutes and another pipe in 15 minutes, but a third pipe can empty it in 6minutes. The three pipes are kept opened together. Find (in min.) when the cistern will be emptied?A) 15 B) 30 C) 60 D) Never

SETS

1. If A and B are disjoint sets and n(A) = 10, n(B) = 5 then ( )n A B∪ =

A) 5 B) 10 C) 15 D) None2. If A= {1,2,3,5} then how many subsets does A have?

A) 12 B) 32 C) 24 D) 83. The cardinality of A if set A has 256 subset is

A) 1 B) 5 C) 8 D) 274. The symmetric difference of sets A and B is

A) ( ) ( )( (A B A B∪ ∩ ∩ B) ( ) ( )( (A B A B∩ ∪ ∩

C) ( ) ( )(A B B A− ∪ − D) None

5. Out of 50 staff members in an office 20 members prefer to drink tea only. 10 prefer to drink coffee only and5 prefect to drink neither tea nor coffee. The number of members who prefer to take atleast one of the twodrinks isA) 45 B) 15 C) 44 D) 11

PERMUTATION AND COMBINATION

1. If A and B are disjoint sets and n(A) = 10, n(B) = 5 then

( )n A B∪

=

A) 5 B) 10 C) 15 D) None2. If A = {1,2,3,4,5} then how many subsets does A have ?

A) 12 B) 32 C) 24 D) 83. The cardinality of A if set A has 256 subsets is

A) 1 B) 5 C) 8 D) 274. The symmetric difference of sets A and B is

A) ( ) ( )( (A B A B∪ ∩ ∩ B) ( ) ( )( (A B A B∩ ∪ ∩

C) ( ) ( )( (A B B A− ∪ − D) None

5. Out of 50 staff members in an office 20 members prefer to drink tea only. 10 prefer to drink coffee only and5 prefer to drink neither tea nor coffee. The number of members who prefer to take atleast one of the twodrinks isA) 45 B) 15 C) 44 D) 11



PERMUTATION AND COMBINATION

1. The value of 30!20!

A) 850 B) 870 C) 800 D) 820 E) None of these

2. The value of

203C

A) 125 B) 130 C) 120 D) 110 E) None of these3. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at tleast

3 men are there on the committee. In how many ways can it be done?A) 564 B) 645 C) 735 D) 5040 E) None of these

4. In how may different ways can the letters of the word 'CORPORATION' be arranged so that the vowelsalways come together?A) 810 B) 1440 C) 2880 D) 50400 E) None of these

5. In how many ways can the letters of the word 'LEADER' be arranged?A) 72 B) 144 C) 360 D) 720 E) None of these

6. How many 3-digit numbers can be formed from the digits 2,3,5,6,7 and 9, which are divisible by 5 and noneof the digits is repeated?A) 5 B) 10 C) 15 D) 20 E) None of these

7. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowelsoccupy only the odd poisitons?A) 32 B) 48 C) 36 D) 60 E) 120

8. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women ?A) 63 B) 90 C) 126 D) 45 E) 135

9. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowelsalways come together ?A) 10080 B) 4989600 C) 120960 D) none of these

10. What is the value of 1 x 1! + 2 x 2!+ 3 x 3! + .....n x n!, where n! means n factorial or n(n-1)(n-2) .......1A) n(n-1)(n-1)! B) (n+1)!/(n(n-1)) C) (n+1)! - n! D) (n+1)! - 1!

PROGRESSIONS AND SERIES1. If the A.M. between 2 and x is 5 then find x

A) 8 B) 6 C) 10 D) none2. Find the sum of 25 terms in the following sequence 2, 5/2, 3...

A) 125 B) 102 C) 200 D) 3603. Find the sum of all natural no.s between 100 and 1000 which are multiples of 5?

A) 98450 B) 89540 C) 54890 D) none

4. Which term of G.P.

2,2 2, 4, 4 2,

...is 64 ?

A) 18 B) 11 C) 12 D) 675. If the first term of a G.P. is 2 and sum of infinite term is 6 then find the common ratio

A) 3/2 B) 2/3 C) 4/5 D) none6. Find the geometric mean of 2 and 32.

A) 48 B) 64 C) 8 D) 97. In a H.P 4th term is 1/9 and 13th term is 1/27 find the 7th term.

A) 15 B) 5 C) 2 D) 6



FUNCTIONS

1. If f(x) = x2-10 and g(x) = 2f(x)+3, what is

( )2g

?

A) 5 B) 9 C) 10 D) 16 E) 192. If F(x-3) = x, what is F(14) ?

A) 0 B) 11 C) 14 D) 17 E) 21

UNIT - IIAlgebra

2



POLYGONS1. Find the length of the rectangle whose area is 4984 square units and width is 56 units.

A) 60 units B) 69 units C) 79 units D) 80 units E) 93 units2. The length of a rectangel is twice its width. Find the dimensions of the rectangle in inches if its area is 288

square inchesA) 24,12 B) 20,10 C) 16,8 D) 32,16 E) 50,25

3. The area of a square is 16 squre units. Find the length of its diagonal

A) 2 2 B) 2 C) 4 D)

4 2

E) 16

4. Find the area of a parallelogram with base 8 units and altitude 4.5 unitsA) 36 sq. units B) 96 sq. units C) 18 sq. units D) 24 sq.units E) 48 sq. units

5. Find the area of a right angled triangle (in square inches) with hypotenuse 25 inches and base 7 inches.A) 84 B) 42 C) 64 D) 80 E) 60

CIRCLES1. Find the circumference of a circle with diameter 42 units

A) 84 B) 108 C) 132 D) 146 E) 1682. The diameter of a wheel of a vehicle is 70 inches. It moves slowly. How far will it go in inchs in 48 revolutions?

A) 18000 B) 33600 C) 20000 D) 10560 E) 240003. The circumferences of two circles are in the ratio 2:3. Find the ratio of their areas

A) 4:9 B) 9:4 C) 2:3 D) 3:2 E) 4:64. A rectangular acrylic sheet is 34 inches long and 24 inches wide. From it, 64 circular buttons each of

diameter 3.5 inches have been cut out. Find the area of the remaining sheet (in sq inch)A) 816 B) 200 C) 100 D) 616 E) 300

5. If the circumference of a circle triples, the area of the circle becomesA) 9 times smaller B) 3 times smaller C) 3 times bigger D) 6 times bigger E) 9 times bigger

6. If the area of a circle is (121x)

π

square units, what is the circumference of the circle?

A)

( )11 x π

units B)

( )22 x π

units C)

( )11x π

units D)

( )22x π

units E)

1212

xπ

units

UNIT - IIIGeometry

3



1. The volume of a cube is 125 cubic cm Find its surface areaA) 25 cm2 B) 375 cm2 C) 150 cm2 D) 250 cm2

2. A cube of 6 cm side melted and smaller cubes of 2cm side are manufactured. Find the number of smallercubes so formed.A) 12 B) 27 C) 24 D) 8

3. The length, breadth & height of a cuboid are in the ratio of 4:3:2 and its volume is 3000 cubic m. Find itssurfae areaA) 1300 m2 B) 1500 m2 C) 1333 m2 D) 27000 cm2

4. The radius and height of a cylinder are in the ratio of 2:1 and its volume is 616 cubic cm. Find its curvedsurface areaA) 1848 cm2 B) 627 cm2 C) 612 cm2 D) 672 cm2

5. A cylinder of radius 2 cm is melted and 11 cubes of 2 cm side are manufactures. Find the height of thecylinder melted.A) 7 cm B) 15 cm C) 44 cm D) 11 cm

6. Volumes of two spheres are in the ratio of 729 : 343. Find the ratio of their volumesA) 49 : 81 B) 343 : 729 C) 7 : 9 D) 81 : 49

7. Find the volume of a hemisphere of diameter 14 cm.A) 19404 cm3 B) 19600 cm3 C) 9702 cm3 D) none

8. A cylinder of 10 cm radius and 10 cm height is melted and cones of 10cm diameter and 2.5cm height aremanufactured. Find the number of cones formed.A) 48 B) 30 C) 75 D) 24

9. If a solid sphere of radius is melted and cast into the shape of a solid cone of height, then the radius of thebase of the cone isA) 2r B) r C) 4r D) 3r

10. A cone, a hemisphere and a cylinder stand on equal based and have the same height. The ratio of theirvolume isA) 1:2:3 B) 2:1:3 C) 2:3:1 D) 3:2:1

UNIT - IVMensuration - 3D

4



STATISTICS1. The mean of 9,11, 13, P, 18 and 19 is P. Then find the value of P.

A) 14 B) 15 C) 16 D) 17

2. Find the mode of the given data 32, 30, 32, 16, 32, 16, 32, 30, 19, 30.

A) 32 B) 30 C) 32 & 30 D) 19

3. If x<y<z, z=ky, x=0, and the average of the numbers x,y and z is 3 times the median what is the value of K?

A) 3 B) 5,5 C) -2 D) 8 E) 6

4. The average of x,y and z is 8 and the average of y and z is 4. What is the value of x?

A) 16 B) 4 C) 24 D) 8 E) 32

5. A class of 30 students had an average of 92 kpoints on a science test out of maximum 100. If 10 studentshad a prefect score, what was the average score for teh remaining students?

A) 88 B) 56 C) 89 D) 92 E) 90

6. If 2P-8, P+4 and 3P-13 are all integers and P+4 is the median of these integers which of the following couldbe a value of P?

A) 6 B) 11 C) 8 D) 15 E) 13

7. If the average of x,y and 7 is 13, what is the average of x+3, y-5 and 6?

A) 7 B) 10 C) 12 D) 13 E) 6

8. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his averageafter 17th inning.

A) 30 B) 40 C) 39 D) 38 E) 87

9. The sum of three consecutive odd numbers is 38 more than the average of these numbers. What is the firstof these numbers ?

A) 13 B) 17 C) 19 D) Data inadequate E) None of these

10. Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first numberis ?

A) 15 B) 45 C) 48 D) 60.25 E) 55

UNIT - VData Analysis

5



PROBABILITY1. A coin is tossed six times. What is the probability of getting head at least once?

A) 63/64 B) 1/64 C) 27/64 D) 23/64

2. Two coins are tossed, what is the probability of getting at least one head?

A) 3/4 B) 1/3 C) 1/4 D) None

3. A die is thrown. What is the probability of getting 6 ?

A) 1/2 B) 1/3 C) 1/6 D) 0

4. Two dice are thrown. What is the probability of getting a doublet?

A) 5/36 B) 7/36 C) 11/36 D) 1/6

5. A bag contains 4 green, 6 black and 7 white balls. A ball is drawn at random. What is the probability that itis either a green or a black ball?

A) 10/17 B) 1/7 C) 7/17 D) 1/3

6. In the above question, what is the probability that none of them will win

A) 1/20 B) 4/9 C) 11/20 D) 9/20

7. Three mangoes and three apples are in a box. If 2 fruits are chosen at random. The probability that?

A) 13/22 B) 4/17 C) 37/66 D) 35/36

8. A bag contains 6 red, 4 white, and 8 blue balls. Three balls are drawn at random. What is the probability ofthe balls being of different colors?

A) 13/66 B) 4/17 C) 37/66 D) 35/36



1. If

ABCΔ

is right angled at C, then the value of

( )cos A B+

is

a) 0 b) 1 c)

12

d)

32

2. Given that

1sin2

α =

and

1cos2

β =

, then the value of

( )α β+

is

a)

0o

b)

30o

c)

60o

d)

90o

3. The value of the expression

2 22

2 2

sin 22 sin 68 sin 63 cos63 sin 27cos 22 cos 68

o oo o o

o o

⎡ ⎤++ +⎢ ⎥+⎣ ⎦

is

a) 3 b) 2 c) 1 d) 0

4. If

sin cos 0,θ θ− =

then the value of ( )4 4sin cosθ θ+

is

a) 1 b) 34 c)

12

d)

14

5. Value of

2 2 2sin 5 sin 80 sin 85o o o+ +

isa) 0 b) 1 c) 2 d) 3

6. If 3sin 3 cosθ θ= then value of tan 20 is

a) 2 b)

3

c)

13

d) 1

7. Which is not possible

a)

1sin2

θ =

b)

3cos2

θ =

c) tan 1θ = d)

1sec2

θ =

8. If

tan 45 cos60 sin 60 cot 60o o o ox =

, then x is equal to

a) 1 b)

3

c) 1 d)

12

UNIT - VITrigonometry

6



9. If

θ

is an acute angle such that

2sec 3θ =

, then the value of

2 2

2 2

tan cosectan cosec

θ θθ θ−+

is

a) 47 b)

34

c)

27

d)

17

10. The value of

cos1 cos 2 cos3 .....cos180o o o o

is

a) 1 b) 0 c)

1−

d) None of these

11. The value of

( ) ( )( ) ( ) ( )

( )cos 90 sec 90 tan tan 90cotcos 90 sin 90 cot 90

o o o

o o oec

θ θ θ θ

θθ θ θ

− − −+

− − −

is

a) 1 b) 1− c) 2 d)

2−

12.

2

2 tan 301 tan 30

o

o+

is equal to

a) sin 60o b)

cos60o

c)

tan 60o

d)

sin 30o

13.

sin 2 2sinA A=

is the true when

A =

a)

0o

b)

30o

c)

45o

d)

60o

14.

cosec15 sec15o o+ =

a)

2 2

b)

6

c)

2 6

d)

6 2+15. cos 4sin 1,sin 4cosθ θ θ θ− = + =a)

1±b) 0 c)

2±d)

4±

16. If

cos sina b cθ θ+ =

then

( )2sin cosa bθ θ− =

a)

2 2 2c a b− −

b)

2 2 2c a b− +

c)

2 2 2a b c− +

d)

2 2 2a b c+ −

17. If

2sin sin 1x xx+ =

then

8 6 4cos 2cos cosx x x+ +

a) 0 b) 1− c) 1 d) 2

18. If

( ) ( )2 2sec tan , sec tanx a y bθ θ θ θ= + = −

then 2 2x y =

a)

secab θ

b)

2 2 tana b θ

c)

2 4a b

d)

2 2a b

19. If

sin cos aθ θ+ =

and

sec cosec ,bθ θ+ =

then, the value of

( )2 1b a −

is equal to

a)

2a

b)

3a

c) 0 d)

2ab

20. If a

sec tan 1bθ θ+ =

and

2 2 2 2sec tan 5a bθ θ− =

, then

2 2 24a b a+

is equal to

a) 92 b) 2

9a c)

2b−

d) 9

Answers

1. a 2. d 3. b 4. c 5. c 6. b 7. d 8. a 9. d 10. b11. c 12. a 13. a 14. c 15. d 16. d 17. c 18.d 19. a 20. a



EXERCISE

1. A circle drawn with origin as the centre passes through

13 ,02

⎛ ⎞⎜ ⎟⎝ ⎠

. The point which does not lie in the

interior of the circle is

a)

3 ,14−⎛ ⎞

⎜ ⎟⎝ ⎠

b)

72,3

⎛ ⎞⎜ ⎟⎝ ⎠

c)

15,2

⎛ ⎞⎜ ⎟⎝ ⎠

d)

56,2

⎛ ⎞−⎜ ⎟⎝ ⎠

2. If the distance between the points

( )4, p

and

( )1,0

is 5, then the value of p is

a) 4 only b) 4±

c) 4−

only d) 0

3. The distance of the point ( )2,3P

from the x-axis is

a) 2 b) 3 c) 1 d) 5

4. The distance of the point ( )6,8P − form the origin is

a) 8 b) 2 7 c) 10 d) 6

5. The points

( ) ( ) ( )4,0 , 4,0 , 0,3−

are the vertices of a

a) right triangle b) isosceles trianglec) equilateral triangle d) scalene triangle

6. The point which lies on the perpendicular bisector of the line segment joining the points ( )2, 5A − − and

( )2,5B

is

a) ( )0,0 b)

( )0,2

c)

( )2,0

d)

( )2,0−

7. If the point ( )2,1 lies on the line segment joining points a

( )4,2

and

( )8,4B

, then

a) 13

AP AB= b) AP PB= c)

13

PB AB=

d) 12

AP AB=

UNIT - VIICoordinate Geometry

7



8. The perpendicular bisector of the line segment joining the point ( )1,5A and ( )4,6B cuts the y-axis at

a) ( )0,13 b)

( )0,13

c)

( )0,12

d)

( )13,0

9. If x is a positive interger such that the distance between points

( ), 2p x

and

( )3, 6Q −

is 10 units, then

x =

a) -3 b) 3 c) 9 d) 0

10. If points

( ) ( ),0 , 0,a b

and

( )1,1

are collinear, then

1 1a b+ =

a) -1 b) 1 c) 0 d) 2

11. The area of the triangle formed by

( ) ( ), , ,a b c b c a+ +

and

( ),c a b+

so

a) 0 b) abc c)

( )2a b c+ +

d) None of these

12. The permeter of a triangle with vertices ( ) ( )0,4 , 0,0 and

( )3,0

is

a) 5 b) 12 c) 11 d)

7 5+

13. If ( ) ( )5,3 , 11, 5A B − and

( )12,P y

are the vertuces of a right triangle right angled at P, then

a) -2,4 b) -2,4 c) 2, - 4 d) 2,4

14. If

( ) ( ), 2 , 3,2x −

and ( )7, 5− are collinear, then

x =a) 60 b) 63 c) -63 d) -60

15. If the area of the triangle formed by the points ( ) ( ), 2 , 2,6x x − and ( )3,1 is 5 square units

a)

23

b)

35

c) 3 d) 5

16. If the distance between the points

( )4, p

and

( )0,1

is 5, then

p =

a)

4±

b) 4 c) -4 d) 0

17. The perimeter of the triangle formed by the points

( ) ( )0,0 , 1,0

and

( )0,1

is

a)

1 2±

b) 2 1+ c) 3 d)

2 2+

18. If three points ( ) ( )0,0 , 3, 3 and

( )3,λ

form an equilateral triangle, then

λ =

a) 2 b) -3 c) -4 d) None of these

19. The coordinates of the point on X-axis which are equidistant from the points

( )3,4−

and ( )2,5 are

a)

( )20,0

b)

( )23,0−

c) 4 ,05

⎛ ⎞⎜ ⎟⎝ ⎠

d) None of these

Answers

1. d 2. b 3. b 4. c 5. b 6. a 7. d 8. b 9. c 10. b11. a 12. d 13. a 14. c 15. a 16. a 17. d 18. d 19. d



1. Which of the four statements given below, is different from the other ?

a)

:f A B→

b)

( ):f x x→

c) f is a mapping from A to B d) f is a function from A to B

2. If ( ) ( )1

n nf x a x= − , where 0a > and

n N∈

, then of

( )f x

is equal to

a) a b) x c)

nx

d)

na

3. Which of the following functions from Z to itself are bijections ?

a)

( ) 3f x x=

b)

( ) 2f x x= +

c)

( ) 2 1f x x= +

d)

( ) 2f x x x= +

4. If

{ } { }1,2,3 , ,A B x y z= =

, then the number of functions from A to B is

a) 6 b) 27 c) 12 d) 9

5. If :f R R→ is given by ( ) 3 3f x x= +

, then ( )1f x−

is equal to

a) 1/3 3x − b)

1/3 3x +

c)

( )1/33x −

d) 1/33x +

6. Which of the following functions from { }: 1 1A x x= − ≤ ≤ to itself are not bijections ?

a)

( )2xf x =

b)

( ) sin2xg x π⎛ ⎞= ⎜ ⎟

⎝ ⎠

c)

( )h x x=

d)

( ) 2k x x=

7. Which one of the following is a function ?

a)

( ){ }2, , ,x y x y R x y∈ =

b)

( ){ }2, , ,x y x y R y x∈ =

c)

( ){ }3, , ,x y x y R x y∈ =

d) ( ){ }3, , ,x y x y R y x∈ =

8. Which of the following are not bijective on R ?

a) ( ) ( ) ( )1 2f x x x= − − for

x R∈

b)

( )f x x=

for

x R∈

c)

( ) 2f x x=

for

x R∈

d)

( ) ( )4 2f x x +

for

x R∈

9. If

( ) ( ) ( ) ( ) ( ){ }3,4 , 4,5 , 5,7 , 7,3f x =

then which of the following ordered pair corresponds to f of

( )x

a)

( ){ }3,5

b)

( ){ }7,4

c)

( ){ }4,7

d)

( ){ }5,3

UNIT - VIIIFunctions

8



10. If

( ) 115

f x xx

= − +−

, then domain of

( )f x

can take values

a)

( )1,4x∈

b) ( )3,6x∈ c) x R∈ d)

( )2,5x∈

Answers

1.b 2. b 3. b 4. b 5. c 6. a,c,d 7. a,c,d 8. a,b,c,d 9. a,b,c,d 10. a,d



1. The inverse of 1 00 1⎛ ⎞⎜ ⎟⎝ ⎠

is

a)

0 11 0⎛ ⎞⎜ ⎟⎝ ⎠

b)

1 01 0⎛ ⎞⎜ ⎟⎝ ⎠

c)

1 00 1⎛ ⎞⎜ ⎟⎝ ⎠

d)

0 10 1⎛ ⎞⎜ ⎟⎝ ⎠

2. If

32

xA

y⎛ ⎞ ⎛ ⎞

=⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

and

1 2 13 1

A− ⎛ ⎞= ⎜ ⎟⎝ ⎠

, then the values of

x

and

y

are respectively

a) 11,8 b) 8,11 c)

8, 11− −

d) cannot e found

3. If

( )3 2 1A =

and ( )3 2 1TB = , then det ( )AB =a) 14 b) 13 c) 4 d) cannot be computed

4. If the determinant of

a bb c⎛ ⎞⎜ ⎟⎝ ⎠ is zero, then a,b,c are in

a) G.P b) A.P c) H.P d) none of these

5. If

( )( ) ( )

! 1 !2 ! 3 ! 24

x x t zx x y

+⎛ ⎞ ⎛ ⎞=⎜ ⎟ ⎜ ⎟+ + ⎝ ⎠⎝ ⎠

, then the values of x,y,z are respectively

a) 2,6,12 b) 1,6,2 c) 3,2,6 d) 5,3,4

6. If 2 8A A kl= + where

1 01 7

A⎡ ⎤

= ⎢ ⎥−⎣ ⎦

then k is

a) 7 b) -7 c) 1 d) -1

7. If the matrix

a bA

c d⎡ ⎤

= ⎢ ⎥⎣ ⎦

then

2A

is

a)

2 2

2 2

a bc d⎡ ⎤⎢ ⎥⎣ ⎦

b)

2

2

a bc ab bdac dc bc d⎡ ⎤+ +⎢ ⎥+ +⎣ ⎦

c) nonexistent d) none of these

UNIT - IXMatrices

9



8. If

1 1 11 2 01 3 0

A−⎡ ⎤

⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

then the value of

adj A

is equal to

a) 5 b) 0 c) 1 d) none of these

9. If

[ ]1 3 2 1

1 1 2 5 1 2 015 3 2 x

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥× =⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

then x is

a) 2 b) -2 c) 14 d) none of these

10. If

3 11 2

0 6A

⎡ ⎤⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦

and

5 4 64 1 25 1 1

B⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥− −⎣ ⎦

then

a)

A B+

exists b) AB existsc) BA exists d) none of these

Answers

1. c 2. d 3. a 4. a 5. b 6. b 7. b 8. c 9. b 10. c

Documents

1 UNIT - I Arithmetics/1.Maths(1-33).pdf · 4. In how many years will a sum of money become four fold at 15% p.a.S.I. A) 5 B) 10 C) 15 D) 20 5. A sum of money becomes triple itself