C Relations

SYLLABUS: MATHEMATICS

FOR GROUP ‘X’ (TECHNICAL TRADES)

1. Sets, Relations and functions

2. Trigonometric Functions

3. Inverse Trigonometric Functions

4. Complex Number and Quadratic Equations

5. Linear Inequalities

6. Mathematical Induction

7. Permutations and Combinations

8. Binomial Theorem

9. Sequences and Series

10. Cartesian system of rectangular co-ordinates

11. Straight lines and family of lines

12. Circles and family of circles

13. Conic sections

14. Three-dimensional Geometry

15. Matrices and Determinants

16. Limit and Continuity

17. Differentiation

18. Applications of Derivatives

19. Indefinite integrals

20. Definite Integrals

21. Applications of the Integrals

22. Differential Equations

23. Mathematical Reasoning

24. Linear Programming

25. Vector

26. Probability

27. Statistics

gaiNat

MATHEMATICS

Q.1. yaid sambanQa R [sa p`kar pirBaaiYat hO ik R={(x,y) : 2x+y=41, x, y N } tao R, inamna maoM sao iksa p`kar ka sambanQa hO ?

What is the nature of relation R, if R is defined as R ={(x,y) : 2x+y=41, x, y N } ?

(A) svatulya / reflexive (B) samaimat / symmetric

(C) saMkamak / transitive

(D) [namaoM sao kao[- nahIM / None of these

Ans:D

Q.2. cos24cos55cos125cos204cos 0 0 0 0 300 0 ?

(A)

2

1

(B)

2

3

(C) 3 (D) 0

Ans:A

Q.3. ?

1

1

sec 2

2

1

x

x

(A) 2 tan

-1

x (B) 2 x

2

(C) 2 cot

-1

x

(D) x

2

Ans:C

Q.4. Aitprvalaya 9x

2

– 16y

2

=144 kI naaiBayaaM &at krao .

Find the foci of hyperbola 9x

2

– 16y

2

=144.

(A) (0, 5) (B) ( 5, 0) (C) ( 5, 1) (D) (5, 1)

Ans:B

Q.5. ]sa i~Bauja kI p`kRit &at krao ijasako SaIYa- ibandu A(12, 8), B(-2, 6) va C(6, 0) hOM . Find the nature of the triangle whose vertices are A(12, 8), B(-2, 6) & C(6, 0).

(A) samaiWbaahu samakaoNaIya i~Bauja /Isosceles Right angle triangle

(B) samabaahu i~Bauja/Equilateral triangle

(C) ivaYamabaahu i~Bauja / Scalene triangle

(D) [namaoM sao kao[- nahIM / None of these

Ans:A

Q.6. xy Plaona pr p`%yaok ibandu P ( x, y, z ) ko ilae,, For every point P ( x, y, z ) on the xy - plane,

(A) x 0 (B) y 0 (C) z 0

(D) None of these

Ans:C

Q.7.

( 6 5 i ) 2

ka saMyaugma &at krao .

Find the conjugate of

( 6 5 i ) 2 .

(A) 60 11 i

(B)

11 60 i

(C)

11 60 i (D) 60 11 i

Ans:B

2

Q.8. C ( n, r ) 2 C ( n, r 1 ) C ( n, r 2 ) ? .

(A) C ( n 1, r ) (B) C ( n 2, r ) (C) C ( n 2, r 1 ) (D) C ( n 1, r 1 ) Ans:B

Q.9. ek gauNaao<ar EaoNaI ka n vaa^ pd

2 n hO tao [sako p`qama 6 pdaoM ka yaaoga &at kIijae . If

n th term of a G.P. is

2 n then find the sum of its first 6

terms.

(A) 126 (B) 124 (C) 190 (D) 154

Ans:A

Q.10.

6

1

3

x

x ko ivastar maoM

x 2 ka gauNaaMk &at kIijae .

Find the coefficient of

x 2 in the expansion of

6

1

3

x

x .

(A) 405 (B) 7290 (C) 2430 (D) 1215

Ans:D

Q.11. ?

0

0

0

2

b a

c a

c b

(A) a 2 b 2 c 2 (B) 4 a 2 b 2 c 2 (C)

4

1 a 2 b 2 c 2 (D) a b c 2

Ans:B

Q.12. yaid

1 0 0

0 1 0

0 0 1

A tao A 1 ?

If

1 0 0

0 1 0

0 0 1

A, then A 1 ?

(A) A (B) A (C) I (D) – I

Ans:A

Q.13. yaid [-ka[- ka GanamaUla hO tao

1

1

1

2

2

2

= ?

If is the cube root of unity, then

1

1

1

2

2

2

= ?

(A)1 (B) (C) 2 (D) 0

Ans:D

3

Q.14.

x

x x

x

sin( 2 ) sin(2 )

lim

0

= ?

(A) cos 2

2

1

(B) 1 (C) 2cos 2 (D) 0

Ans:C

Q.15. tansec 1 (x tan x ) ?

dx

d

(A) –

2

1

(B) 1 (C) – 1 (D)

2

1

Ans:D

Q.16. yaid x y y x c tao

2

2

dx

d y

&at krao .

Find

2

2

dx

d y

, if x y y x c .

(A)

c

2

(B) – 2

2

c

(C) 2

2

c

(D) 2

4

c

Ans:C

Q.17. ek Gana kI Baujaa maoM 3 saomaI/saokND kI dr sao vaRiw hao rhI hO . yaid Gana kI Baujaa 10 saomaI hO tao ]sako Aayatna maoM haonao vaalaI vaRiw kI dr (saomaI

3

/ saokoND maoM) &at krao .

An edge of a cube is increasing at the rate of 3 cm/sec. Find the rate at which does the volume increase (in cm

3

/sec) if the edge of the cube is 10 cm.

(A) 900 (B) 725 (C) 700 (D) 825

Ans:A

Q.18. yaid s t 3 4 t 2 5 kNa ka gait batata hO AaOr %varNa lauPt hao tao [saka vaoga ( [-ka[- p`it sakoND) mao If s t 3 4 t 2 5 describes the motion of a particle, then its velocity (in unit/sec) when the acceleration vanishes, is

(A)

9

16

(B)

3

32

(C)

3

4

(D)

3

16

Ans:D

Q.19. saM#yaaAaoM 8, 12, 13, 15, 22 ka maanak ivacalana &at krao . Find the standard deviation of 8, 12, 13, 15, 22.

(A) 3.54 (B) 3.72 (C) 4.21 (D) 4.6

Ans:D

Q.20. yaid ek isa@ko kao tIna baar ]Calaa jaata hO tao isa@ko maoM ek yaa dao SaIYa- Aanao kI P`aaiyakta &at krao . If a coin is tossed thrice, find the probability of getting one or two heads.

(A)

5

4

(B)

8

5

(C)

4

3

(D)

7

6

Ans:C

4

Q.21. yaid ibanduAaoM

A ( 60 i 3 j ),

( 40 8 )

B i j AaOr

C ( a i 52 j ) samaroK hOM tao a =?

If the points

A ( 60 i 3 j ), ( 40 8 )

B i j, and

C ( a i 52 j ) are collinear, then a is equal to

(A) 40 (B) -40 (C) 20

(D) -20

Ans:B

Q.22. sin x dx ?

3

3

2

(A) 1 (B)

4

3

3

(C)

4

1

2

(D) 0

Ans:B

Q.23. dx ?

cos x . sin x

cos x

2 2

2

(A) cot x tan x c (B) cot x tan x c (C) cot x tan x c (D) tan x cot x c Ans:A

Q.24. Avakla samaIkrNa e x y x e y

dx

dy 2 ka hla &at krao .

Find the solution of the differential equation e x y x e y dx

dy 2 .

(A) c

y

e x e y

3

3

(B) c

x

e x e y

3

3

(C) c

x

e x e y

3

3

(D) c

y

e x e y

3

3

Ans:C

Q.25. vak y 2 2 y x

AaOr y - Axa sao pirbaw xao~ ka xao~fla (vaga- maa~k maoM) &at krao . Find the area of the region (in sq.units) bounded by the curve y 2 2 y x

& y - axis.

(A)

3

8

(B)

3

4

(C)

3

5

(D)

3

2

Ans:B

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