SECTION A (40 MARKS)
Question 1). 2x5= 10
a) If Ram bought a watch for ₹2688 which includes 12% GST and a shirt for ₹440 which includes 10% GST. Find the printed price of the watch and shirt together, without GST
b) the point P(a,b) is reflected in the x-axis to obtain the point Q(3,4). Find a, b.
c) If a 3a 2 5
b 4b 1 = 12 , find a and b.
d) The mean of numbers 6,y, 7, x and 14 is 8. express y in terms of x. y= 13 - x
e) Given f(x) = x/(x² -1). Find f(1/3). 2/3
Question 2. 10 marks
a) Solve using the quadratic formula x² - 5x - 2= 0. Give your answer correct to 3 significant figures.
b) If (8a+5b)/(8c+5d)= (8a-5b)/(8c - 5d), prove that a/b= c/d
c) Find the value of k, if x- k is a factor of x³ - kx² + x + 4. -4
Question 3 Marks 10
a) Solve 1 < 3x -3≤ 12, x belongs to R and mark it on a number line.
b) Calculate the mean, median, and mode of the following numbers 11, 12, 10, 11, 12, 13, 14, 13, 15, 13.
c) Find the sum of the numbers between 2 to 200 divisibile by 4
Question 4 marks 10
a) If cosA= 4/5 and cos B= 24/25 ; evaluate
i) cosec² A.
ii) cot A + cot B
b) On a map drawn to a scale of 1:12500 a triangular plot of land has the following measurements: PQ = 10cm, QR= 8cm, Ang PRQ=90° . Calculate
i) The actual length of PQ in km.
ii) the area of the plot in square kilometre.
c) Find the probability of extra Sunday in February in leap year
SECTION B) 40 MARKS
Answer any four questions
Question 5. Marks 10
a) The work done by ((2x -- 3) men in (3x+1) days and the work done by (3x+1) men in (x+8) days are in the ratio of 11:15. Find the value of x.
b) John has a recurring deposit account of ₹1000 per month in a bank. What will he get after 12 months if the rate be 9% p.a
c) Find the mean of the following frequency distribution:
Class Interval. Frequency
0 - 30 3
30-60 7
60-90 15
90-120 14
120-150 7
150-180 4
Question 6. Marks 10
a) Two dice are thrown. Find the probability
A) The sum of the scores is 9
B) the product of the score is 12
C) the score on second die is greater than first
D) the sum of the score is a multiple of 4
E) the sum of the score is a perfect square.
b) Prove that: sinA/(1-cotA) + cosA/(1-tanA)= sinA + cosA
Question 7. Marks 10
a) A straight line passes through the points A(-2,8) and B(10, -4). It intersect the co-ordinates Axes point E and F. P is the midpoint of the segment EF, Find:
I) the equation of the line.
ii) the coordinates of the E and F.
iii) The coordinates of the point P.
b) In an auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of the rows was doubled and the number of seats in each row was reduced by 15, the total number of seats increased by 400. Find
I) the number of rows in the original arrangement.
ii) the number of seats in the Auditorium after rearrangement.
Question 8. Marks 10
a) Draw a histogram and hence estimate the mode for the following frequency distribution
Class Interval. Frequency
0 - 20 3
20- 40 8
40- 60 10
60- 80 6
80-100 4
100-120 3
b) A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite Bank 60°. When he moves 40m away from the bank, he finds the angle of elevation to be 30°. Calculate
I) the width of the river and.
ii) the height of the tree.
Question 9. Marks 10
a) If A=. 4 -2 B= 0 2 C= -2 0
6 -3 1 -1 1 -3
Find A² - A + BC
b) A vessel is in the form of an inverted cone. Its height is 15cm and the diameter of its top which is open, is 5cm. it is filled with water up to the rim. When lead shot, each of which is a sphere of a diameter 5mm are dropped Into the vessel, 1/3 of the water flows out. Find the number of lead shots dropped into the vessel.
c) Find the value of k for which the lines my - 7y + 5= 0 and 6x - 2y + 9 = 0 are perpendicular to each other .
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