Section BQuestion Numbers 1 to 10 carry 1 mark each.
- In fig. I , S and T are points on the sides P Q and PR, respectively of ΔPQR, such that PT = 2 cm, TR =4 cm and ST is parallel to QR, find the ratio of the areas of Δ PST and Δ PQR.
- Has the rational number a terminating or a non-terminating Decimal representation?
- If α, β are the zeroes of a polynomial, such that α+β=6and αβ =4, then Write the polynomial.
- If the sum of first P terms of an A.P is αp²+bp, find its common difference.
- In fig. 2, Δ AHK is similar to Δ ABC. If AK =10 cm , BC = 3.5 cm and H K=7 cm, find AC.
- If 3x =cosec Ø and find the value of 3 .
- if P(2, p) is the mind –point of the line segment joining the points A (6,-5) And B (-2, 11), find the value of p.
- If A(1,2), B(4,3) and C(6,6) are the three vertices of a parallelogram ABCD, Find the coordinates of the fourth vertex D.
- The slant height of a frustum of a cone is 4 cm and the perimeters (circumferences) Of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum .
- A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting a red face card.
Question Numbers 11to 15 carry 2 marks each.
- if two zeroes of the polynomial x³-4x²-3x+12 are and - , then find its third Zero.
- Find the value of k for which the following pair of linear equations have Infinitely many solutions: 2x+3y =7; (k-1)x +(k+2)y = 3k.
- In an A.P ., the first term is 2, the last term is 29 and sum of the terms i Is 155. Find the common difference of the A.P.
- if all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
- Without using trigonometric tables, find the value of the following expression :
Find the value of cosec 30 º, geometrically.
Question Numbers 16 to 25 carry 3 marks each.Section D
- Prove that is an irrational number.
- The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes ½ find the fraction.
Solve the following pair of, equations
- In an A. P. , the sum of first ten terms is -150 and the sum of its next ten terms is -550 . find the A.P.
- In fig. 3, ABC is a right triangle, right angled at C and D is the mid – point of BC. Prove the AB² = 4 AD² - 3AC².
- prove the following :Or
Prove the following : (cosec A –sin A) (sec A-cosA )=
- Construct a triangle ABC in which BC =8 cm, <B =45º and <C =30º construct another triangle similar to Δ ABC such that its sides are ¾ of the corresponding sides of Δ ABC.
- Point p divides the line segment joining the points A(2,1) and B(5,-8) such that AP/AB =1/3 , if P lies on the line 2x-y + k = 0, find the value of k.
- If R(x,y) is a point on the line segment joining the point P(α,b) and Q (b,α), then prove that x + y = α +b.
- in fig. 4, the boundary of shaded region consists of four semicircular arcs, two smallest being equal. If diameter of the largest is 14 cm and that of the smallest is 3.5 cm, calculate the area of the shaded region.
find the area of the shaded region in Fig. 5, if AC = 24 cm, BC = 10 cm and O is the center of the circle. [Use π =3.14]
- Cards bearing numbers 1,2,3 , -----,35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing
a. a prime number less than 15.
b. A number divisible by 3 and 5.
Question Numbers 26 to 30 carry 6 marks each.
- Find the mean, mode and median of the following frequency distribution :
- Three consecutive positive integers such that the sum of the square of the first and the product the product of the other two is 46, find the integers.
The difference of squares of two numbers is 88. if the larger number is 5 less than twice the smaller number, then find the two numbers.
- prove that ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Using the above, prove the following: If the areas of two similar triangles are equal, then prove that the triangles are congruent.
- From the top of a 7m high building, the angle of elevation of the top of a tower is 60º and the angle of depression of the foot of the tower is 30º. Find the height of the tower.
- A mild container is made of metal sheet in the shape of shape of frustum of a cone whose volume is 10459 3/7 cm³. The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs. 1.40 per square centimeter.
A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of
Base of the cone is 21 cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy.