Mahatama Gandhi Birth and Then Chilhood and Some More Information

12013
11122 3 Hours / 100 Marks
Instructions –

Seat No.

(1) All Questions are compulsory. (2) Answer each next main Question on a new page. (3) Illustrate your answers with neat sketches wherever necessary. (4) Figures to the right indicate full marks. (5) Assume suitable data, if necessary. (6) Use of Non-programmable Electronic Pocket Calculator is permissible.

Marks 1. Attempt any TEN of the following: a) Define even and odd function. b) If f ( x) = ( x + 9) /
2

20

x - 3 find f (4) + f (5)

lim c) Evaluate x ® 0 sin 2 x° x é lim ê 1 – 1 d) Evaluate x ® 1 x - 1 x 2 ê ë
3x lim 2 x e) Evaluate x ® 0 3 – 2 tan x

ù ú xú û

P.T.O.

12013 æ 3 ö ÷ ç1 – ç 2x ÷ ø è
x

[2] Marks

f)

lim Evaluate x ® ¥

g) Find

dy 2x x 7 , if y = e + log5 + log 7 dx dy , if dx y = sin x

h) Find

(1 – cos x)
2

i)

1 ö æ ÷ Differentiate w.r.t. x ç x + xø è Differentiate w.r.t. x
x
2a

j)

- (2a )

2a

+a

2x

+ (2 x)

2a

k) The mean of 25 observations is 40. If each observation is increased by 2, find the new mean. l) Find median for the following table. Temperature °C No. of days 30 15 35 08 32 04 36 02 40 02

m) Find the coefficient of range 40, 52, 47, 28, 45, 36, 47, 50

12013 2.

[3] Marks Attempt any FOUR of the following: 16

a) If f ( x) = x 2 + 4, solve f ( x + 1) – f ( x – 1) – 12 = 0 æ 1 ö + t ÷ = f (t ) b) If f (t ) = 50 sin (100 p t + 0.4) prove that f ç è 50 ø lim c) Evaluate x ® ¥ æ 2 ö ç x + x +1 - x÷ è ø
3 2

lim x + 3x - 6 x + 2 d) Evaluate x ® 1 3 2 x + 3x - 3x - 1 lim tan x - sin x e) Evaluate x ® 0 3 x lim Evaluate x ® 3 æ log x - log 3 ö ç ÷ ç ÷ x -3 è ø

f)

P.T.O.

12013 3.

[4] Marks Attempt any FOUR of the following: 16

a) If y = 3 sin q – 2 sin 3 q
3 x = 3 cos q – 2 cos q find

dy p at q = dx 4

b) Differentiate tan

–1

æ 1 – x2 ö ç ÷ w.r.t. sin –1 æ 2 x 1 - x 2 ö ç ÷ x ÷ è ø ç è ø

dy log x c) If x y = e x - y prove that dx = (1 + log x) 2 d) Differentiate...