1223 words - 5 pages

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

...view middle of the document...

r.t. 54 x e) If y = e

m sin –1 x

prove that

2 (1 – x ) d y

2

dx

2

-x

dy 2 -m y=0 dx

f)

If r = a (2q - sin 2q) y = a (1 - cos 2q) p æ dy ö find ç ÷ at q = 4 è dx ø

12013 4.

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

a) A right angled triangle whose hypoteneous is 60cm long has its area maximum. What should be its dimensions. b) The cost per k.m. of an electric cable is C = 120 x + 600 x Rs. where ‘‘ x ’’ is the cross section in sq.m. Find the cross section for which the cost is the minimum. Find the minimum cost. c) Find the radius of curvature to the curve y = x3 at (1, 1) d) Show that x

n n

a

+ y b = 2 is the tangent to the curve.

æ xö æ yö ç ÷ + ç ÷ = 2 at (a, b) . èaø èbø e) Prepare a frequency distribution table for the data giving weights of 30 wooden logs. 132 166 134 119 151 114 138 124 130 132 142 121 144 147 126 104 143 129 108 111 155 131 157 137 122 148 139 135 136 145 f) Find median by graphically from the following distribution CI fi 5-10 5 10-15 15-20 20-25 25-30 30-35 35-40 40-45 6 15 10 5 4 2 2

P.T.O.

12013 5.

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

a) The mean weight of 150 students in a class is 60kg. The mean weight of boys is 70 kg and of girls is 55kg. Find the number of boys and girls in the class. b) The mode for the following data is 41.5. Find the missing frequency from the table Class: Frequency: 15-25 25-35 35-45 45-55 55-65 65-25 4 11 19 – 0 2

c) Find the mean for the following table. Daily income less than (Rs.) No. of persons 50 5 100 150 200 250 300 350 400 8 15 22 34 40 55 60

d) The runs scored by two bastman A and B in 5 one day matches are given below. A: B: 48 50 50 52 39 60 46 55 37 53

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