Section A
(Attempt all questions). 4x10= 40
1) a) Mr. D. K Vhora gets ₹6455 at the end of a year at the rate of 14% p.a. in a recurring deposit account. Find the monthly installment.
b) Solve the inequation and represent the solution set on the number line -2/3< -x/3 + 1≤2/3; x belongs to R.
c) Solve the following quadratic equation using formula (Correct to three significant figures): x² -3(x+3) = 0. (4+3+3)
2a) Prove the following identity:
Cosecx/(cosec x -1) + cosecx/(cosecx +1) = 2 sec²x.
b) A box contains 25 cards, numbered from 1 to 25. A card is drawn at random from the box. Find the probability that the number on the card is (i) even ii) Prime iii) multiple of 6.
c) i) Find the mean proportional of 8.1 and 2.5.
ii) Find the third proportion of 21/4 and 7. (3+4+3)
3a) The point p(3,4) is reflected on p' in the x-axis and o' is the image of o (origin) in the line pp' find:
i) The coordinates of p' and o'.
ii) The length of the segment pp' and oo'.
iii) The perimeter of the quadrilateral pop'o' (use graph sheet for this question)
b) If A= 3 4 B= 1 y & C= 7 0
5 x 0 1 10 5 Find x and y if 2A + B= C.
c) If A=(-4,3), B=(8,-6) in what ratio is the line joining AB, divided by the x-axis ? (3+4+3)
4). (4+3+3)
a)Find the mean by shortcut method:
Class interval frequency
05-10 10
10-15 6
15-20 4
20-25 12
25-30 8
30-35 4
35-40 2
40-45 1
45-50 3
b) For what value of k the equation (k -12)(x²+ 2x)+ 2= 0 has equal roots.
c) Find the mode and the median:
x: 10 11 12 13 14 15
f: 1 4 7 5 9 3
SECTION B
(Attempt only 4) 4x10= 40
5) a) Construct incentre of a triangle ABC, where AB= 6cm, BC= AC = 4cm.
b) Two vertices of a triangle are (3,5) and (-7,4). Find the third vertex, given that the centroid is (2,-1).
c) Is a, b,c are in continued proportion then prove that: (a+ b)/(b+ c) =a²(b - c)/c²(a - b).
6a) 90 pupils in a school have heights as below:
Height number of pupils
121-130 12
131-140 6
141-150 30
151-160 20
161-170 14
171-180 8
Using graph paper draw an ogive and estimate the median and inter quartile range.
b) If cosecx + cot x = p, then prove that cosx= (p²-1)/(p²+1). (6+4=10)
7)a) Solve the and draw the number line for the following in equation:
3≥ (x -4)/2 + x/3 ≥ 2; x belongs to R.
b) A letter is chosen from the words MONEY DATE. what is the probability that the word is chosen is i) a vowel b) a constant.
c) Find the matrix X If AX = B If
A= 4 B= -4 8
1 -1 2 (4+3+3=10)
8)a) SOLVE: 16{(a- x)/(a+ x)}³= (a+ x)/(a- x). (3+3+4=10)
b) There are two children in a family, find the probability that,
i) there is at least one girl in the family.
ii) Younger child is a boy.
c) A two digit number is 4 times the sum and three times the product of its digits. Find the numbers.
9) Shyam has a cumulative bank account and deposited ₹600 per month for a period of 4 years. If he gets ₹ 5880 as intrest at the time of maturity, find the rate of interest.
b) Solve:(using formula) 2x - 1/x = 7 (correct to 2 decimal places)
c) Use a graph paper and draw a histogram from the following data, hence estimate mode.
Class interval Frequency
00-05 10
05-10 14
10-15 28
15-20 42
20-25 50
25-30 30
30-35 14
35-40 12 3+3+4
10). 4+3+3
a) Ages of two persons A and B are in the ratio 4:3 five year hence, the ratio of their ages will change to 9:7. Find their present ages.
b) Find X and Y If the relation AB = C where A= X 3X B= 2 C= 5
Y 4Y 1 12
c) Prove: 1 - cos²x/(1+ sin x) = sinx.
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