SECTION -A (40 Marks)
1). 1x 10 = 10
i) Value of the quadratic polynomial p(x)= 2x²- 3x + 5 at x= -2
A) 9 B) 10 C) 11 D) 12
ii) Is 3x² - 4x +2 = 2x² - 2x +4 a quadratic equation. T/F
iii) (1- sin²x)sec²x is
A) 0 B) 1 C) sin²x D) tan²x
iv) Cosx sin(90-x)+ sinx cos(90- x) is
A) 0 B) 1 C) - sin x D) - sinx
v) If cos x= 4/5, value of tan x is
A) 1 B) 0 C) 3/2 D) none
vi) Find the diagonal of a cuboid 30cm long, 24cm wide and 18cm high.
A) 40 B) 42.42 C) 50 D) 52.52
vii) The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean ?
A) 8 B) 16 C) 10 D) 12
viii) Which term of the sequence -1, 3, 7, 11, .... is 95.
A) 30 B) 31 C) 32 D) 33
ix) If the sum of any pair of opposite angles of a quadrilateral is 180°, then the quadrilateral is
A) right angled B) equal C) cyclic D) opposite.
x) A tower is 100√3m hig5. Find the angle of elevation it its top from a point 100m away from its foot.
A) 30 B) 60 C) 45 D) 90
2) 1x 10= 10
i) Write the first three terms in aₙ= n²+1.
ii) How many numbers of two digit are divisibile by 3 ?
iii) The length of a chord of a circle is 4cm. If it's distance from the centre is 1.5cm, determine the radius of the circle.
iv) Find the length of a tangent drawn to a circle with radius 5cm, from a point 13cm from the centre of the circle.
v) An unbiased die is thrown. What is the probability of getting a number between 3 and 6. (1)
vi) One root of x²- 3x - c= 0 is -2, find the value of c.
vii) If the probability of winning a game is 0.3. what is the probability of loosing it ?
viii) Probability of a sure event is __
ix) f(x)= x²+ 3x - 10, g(x)= x -2. Find out whether g(x) is a factor of f(x) or note
x) Find the value of k when f(x)= x³ - 3x² - x + k, if g(x)= x+1 is a factor of f(x)
3) 2x 10= 20
i) Solve x/(x+1) + (x+1/x = 34/15, x≠0, x≠ -1.
ii) Find the sum of the deviations of the variate values 3, 4, 6, 8, 14 from their mean. (2)
iii) Find k if 2x² + Kx + 3= 0 has real roots.
iv) A two digit number is four times the sum and three times the product of its digits. Find the number.
OR
A journey of 240 km would take half an hour less if the speed were increased by 2km per hr. Find the usual speed.
v) Determine the general term of an AP whose 7th term is -1 and 16th term 17.
vi) The 7th term of an AP is 32 and its 13th term is 62. Find AP.
vii) A solid cylinder has total surface area of 462cm². Its curved surface area is one third of its total surface area. Find the volume of the cylinder. (π= 22/7).
viii) In a ∆ABC, AD is the bisector of ang.A, meeting side BC at D . If BD= 2.5cm, AB= 5m and AC= 4.2cm, find DC.
OR
D and E are the points on the sides AB and AC respectively of a ∆ABC such that AD= 8cm, DB= 12cm, AE= 6cm and CE= 9cm, prove that BC= 5DE/2.
ix) √{(- sinx)/(1+ sin x)}= secx - tan x.
x) An electric pole is 10m hig8. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of 45 with the horizontal the foot of the pole, find the length of the wire. (2)
SECTION - B (40 Marks)
4) Prove that the line segments joining the midpoints of the adjacent sides of a quadrilateral form a parallelogram. (3)
5) A ladder 15m long reaches a window is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street. (3)
6) AB and CD are two parallel chords of a circle whose diameter is AC. Prove that AB= CD. (3) OR
Equal chords of a circle subtends equal angles at the centre.
7) If x sin³a + y cos³a= sina cos a and x sin a = y cos a, prove x² + y² = 1. (3)
8) If A, B, C are the interior angles of a triangle ABC , prove that tan{(A+ C)/2}= cot(B/2). (3)
9) A man standing in the deck of a ship, which is 8m above water level. He observes the angle of elevation of the top of a hill as 60 and the angle of depression of the base of the hill as 30. Calculate the distance of the hill from the ship and the height of the hill. (3)
10) If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that 1/V = 2/S(1/a + 1/b + 1/c). (3)
11) Class interval. Frequency
0-10 7
10-20 10
20-30 15
30-40 8
40-50 10 find the mean. (4)
OR
Class interval. Frequency
1-10 8
11-20 10
21-30 15
31-40 8
41-50 18 find the median.
12) A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by 2cm. If the area of the base of the cuboid is 160cm² and its height 12cm, determine the radius of any of the spheres. (4)
13)a) If cotx = 1/√3, find the value of (1- cos²x)/(2- sin²x). (2)
b) The radius and slant height of a cone are in the ratio 4:7. If it's curved surface area is 792cm², find its radius. (π= 22/7). (2)
14) a) If P(A)= 1, then A is called
A) certain event
B) impossible event
C) possible event
D) absolute event. (1)
b) A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is
A) red
B) black or white
C) not black. (3)
15)a) 2(a²+ b²)x² +2(a+ b)x+ 1= 0.
b)Find the sum of (-5)+(-8)+(-11)+....+(-230). (1.5+ 1.5)
OR
16)a) AB and CD are two parallel chords of a circle such that AB= 10cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17cm, find the radius of the circle.
b) Two chords AB and CD of a circle intersect each other at P outside the circle. If AB= 5cm, BP=3 cm, and PD= 2cm, find CD.
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