8/17/2019 Class Xi Maths Test

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Grouop-A 

1 Mark

1.  Answer any eight.

i. If the rth

  term in the expansion of

63

2 x

  is independent of x,

which one of the following is the value of r?

(a) 4 (b) 5 (c) 6 (d) 3

ii. What is the eccentricity of a rectangular hyperbola?

iii. Which one of the following is the derivative of x  w.r.t log  x, (x>0)

(a) 21

(b) x (c) log x (d) ex

iv. If 3 3cos , sina t y a t     thendy

dx=

(a) tan t  (b) cot t  (c) 3cot t  (d) 3tan t 

v. In the expansion of6

1 x

  the middle term is

(a) 6C3

(b) 6C4   4

1 x

(c) 6C5   4

1 x

(d) 6C2x2

vi. Which one of the following is the length of the latus rectum of theellipse 4x2  + 3y2  =1?

(a)3

4

(b)4

3

(c)1

3

(d)1

4

vii. What is the derivative of sin   o y x   w.r.t. x?

viii. A and B are two events such that , 0.7 A B P A B , and

  0.2 P A     then  B  

ix. If x < 0, find log | |d 

 xdx

.

x. Write down the domain of definition of   1

| |

 f x

 x x

.

TEST

ON

MATHEMATICS

CLASS XI

TIME: 3 HRS FM: 80

8/17/2019 Class Xi Maths Test

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Grouop-B

2 Marks

2.  Answer any eight.

(i) A coin is tossed four times. First three outcomes were Head. Whatis the probability that the fourth outcome will be Head?

(ii) Use binomial theorem to find the value of 1023.

(iii) Reduce the equation y2  – 4x – 4y = 0 to standard form of a conic.

(iv) Find the focal distance of a point on the parabola y2  = 4ax in termsof abscissa of that point.

(v) Finddy

dx

  if y = xy

(vi) Find the equation of the parabola having vertex and focus at (–2, 3)and (1, 3) respectively.

(vii)Prove that tan 70 2 tan50 tan 20o o o .

(viii) If : cos : cos y A B , prove that tan tan tan2

 B x A y B x y

  .

(ix) If a and b  are two positive numbers such that 2 2 7a b ab , then

show that 1 1

log log log3 2

a b a b

.

(x) Find the maximum value of 3cos 4sin 5   .

Grouop-C

4 Marks

3. Obtain the equation of the parabola having focus at (3, –2), theequation of the directrix being 2x – y + 3 = 0.

4. For the ellipse x2  + 9y2  = 36, find the distance of any one end of

the minor axis from any one of its foci.

5. If 1 1 0 x y y x   then show that

2

1

1

dy

dx

.

6. Find the equation of the chord of the circle

x2

  + y2

  – 8x + 2y + 1 = 0, whose middle point is (5, 2).

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7. (i) If a, b, c are three rational numbers and if 2   is a root of thequadratic eqation ax2  + bx + c = 0, what is the value of b?(ii) Find the value of sin 18O. [1 + 3]

8. Iftan tan

tan1 tan tan

  

 

, then show that

sin 2 sin 2sin2

1 sin 2 sin 2

  

 

.

9. If  A B C      , then show that sin sin sin 4sin cos sin2 2 2

 B C  A B C  .

10. Solve: sin sin 5 sin 3 0, 0   .

11. If   be the area of the triangle ABC, then show that

 s s a s b s c

.

12. In any triangle ABC, prove that tan cot2 2

 B C b c A

b c

.

13. A and B are two fixed points whose coordinates are (2, 4) and (2, 6)respectively; ABP is an equilateral triangle on that side of thestraight line AB which is opposite to that containing the origin.Find the coordinates of P.

14. (i) Find the distance between the parallel lines 3x + 4y = 9 and6x + 8y = 15.

(ii) Prove that the sum of n terms of the series 1 11 111 1111 ...

is 10

10 181 9

n   n . [1+3]

15. Four integers are in AP; if their sum is 0 and product is 9, thendetermine the integers.

16. Obtain the derivative of cos2x w.r.t. x starting from the definition.