General Instructions

1 . All question are compulsory .
2 . T his question paper contains 30 questions.
3 . Question 1-6 in Section A are very short answer type questions carrying 1 mark each.
4 . Questions 7-12 in Section B are short answer type questions carrying 2 marks each.
5 . Question 13-22 in Section C are long answer I type questions carrying 3 marks each.
6 . Question 23-30 in Section D are long answer II type questiona carrying 4 marks each.
7 . Use of calculators are not permitted .

---

Section A (Each Question 1 Marks)

Question 1 .
Simplify and identify whether this equation is quadratic or not (x - 3)(x + 3) = 2 .

---

Question 2 .
After how many decimal places will the decimal expansion of

19/200

terminate ?

---

Question 3 .
C(2,6) is the mid point of A(4,5) and B(0,

a/7

) . find a .

---

Question 4 .
If

cos²θ/1 - cos²θ

-

1/sin²θ

, find the value of this .

---

Question 5 .
If S_n of an A.P is 4n² + 1 ,find a .(first term)

---

Question 6 .
Find the ratio the x-axis divides the line segment joining the points A(1,-2) and B(3,2).

---

Section B (Each Question 2 Marks)

Question 7 .
The product of two numbers are 900. The L.C.M of these two numbers is 25 times of H.C.F . Find H.C.F.

---

Question 8 .
Find the 8^th term from the end of the A.P 17,14,11,8,------------- -40 .

---

Question 9 .
Point P divides the line segment joining the points A(-1,3) and B(9,8). Such that

AC/BC

=

k/1

. If P lies on the line x - y + 4 = 0, find the value of k .

---

Question 10 .
For what value of k, the equations x + 3y + 7 = 0 and 3x + 9y + k = 0 will represents coincident lines ?

---

Question 11 .
A box contains 35 marbles some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is blue is

3/5

. Find the green marbles in the box.

---

Question 12 .
All face cards of black colour are lost from the pack of 52 playing cards . The remaining cards are well - shuffled and then a card is drawn from them. Find the probability the drawn card is a king .

---

Section C (Each Question 3 Marks)

Question 13 .
Find the smallest number which when increased by 21 is exactly divisible by both 520 and 468.

---

Question 14 .
Solve the quadratic equation .
a²b²y² + b²y - a²y - 1 = 0

---

Question 15 .
The sum of the digits of a two digit number is 12 and the difference between the number that formed by reversing the digit is 18. Find the number.

---

Question 16 .
If P(x,y) is any point on the line joining the points A(a,0) and B(0,b), then show that

x/a

+

y/b

= 1

---

Question 17 .
If a cosθ - b cosθ = c, Prove that

a sinθ + b cosθ = ± √(a² + b² - c²)

---

Question 18 .
If an isosceles triangle ABC in which AB = AC = 6 cm is inscribed in a circle of radius 9 cm, find the area of the triangle .

---

Question 19 .
R and S are points on sides AB and AC respectively of triangle ABC. If AR = 9cm, RB = 18cm,
AS = 15cm and SC = 30cm. Show that BC = 3RS.

---

Question 20 .
figure shows a sector of a circle, center o, containing an angle θ^o . Prove that: Area of the shaded region is

r²/2

(tanθ -

πθ/180

)

---

Question 21 .
The height of a cone is 40 cm. A small cone is cut off at the top, through a plane parallel to the base . If its volume be

1/8

of volume of the given cone. Find the vertical height of small cone .

---

Question 22 .
Find the value of a , if the mean of the following distribution is 8.

x :	3	5	7	9	11	13
f :	6	8	15	a	8	4

---

Section D ( (Each Question 4 Marks))

Question 23 .
If ratio of the roots of equation px² + qx + q = 0 is a : b, Prove that

OR

Question 23 .
The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2

16/21

, find the fraction .

---

Question 24 .
The sums of n terms of three arithmetical progressions are S₁, S₂ and S₃ . The first term of each is unity and the common differences 1,2 and 3 respectively . Prove that S₁ + S₃ = 2S₂ .

---

Question 25 .
Prove that three times the square of any side of an equilateral - triangle is equal to four times the square of the altitude.

OR

Question 25 .
ABC is a triangle in which AB = AC and D is any point in BC . Prove that AB² - AD ² = BD.CD

---

Question 26 .
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at angle of depression of 30^o, which is approaching to the foot of the tower with a uniform speed . Six seconds later , the angle of depression of the car is found to be 60^o . Find the further time taken by the car to reach the foot of the tower .

---

Question 27 .
Draw a circle of radius 6 cm . Draw a tangent to this circle making an angle of 30^o with a line passing through the center .

---

Question 28 .
If the median of the distribution given below is 28.5, find the value x and y .

Class interval:	0-10	10-20	20-30	30-40	40-50	50-60
No. of students:	5	x	20	15	y	5

---

Question 29 .
A cylindrical pipe has inner diameter of 14 cm and water flows through it at 1540 litres per minute . Find the rate of flow in kilometres per hour .

---

Question 30 .
If secθ + tanθ = p , obtain the values of secθ, tan θ and sinθ in terms of p .

---