Here is the expected question paper for **Summative Assessment – II (SA-2) 2017 | CBSE Board**

**SECTION–A**

**Question number 1 to 4 carry 1 mark each.**

**1). **Two different coins are tossed simultaneously. What is the probability of getting at least one tail?

**2). **What will be the angle of elevation of the sun when the length of shadow on the ground of a vertical tower is [latex]\sqrt{3}[/latex] times its height?

**3). **If the angle between two tangents drawn from an external point P to a circle of radius r and centre O is 90°, then what is length of OP.

**4).** For what value of K will K+9, 2K-1, 2K+7 are the consecutive terms of an AP?

**SECTION–B**

**Question number 5 to 10 carry 2 mark each.**

**5). **AP and BP are tangents to a circle with centre O such that AP=5cm and ∠APB=60°, find the length of the chord AB?

**6).** In a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Then Prove that: AB + CD = BC + DA.

**7). **Find the value of ‘a’ if the points (a,3) (6,-2) and (-3,4) are collinear?

**8).** P and Q are the points with coordinates (2,-1) and (-3,4), find the co-ordinate of the point R such that PR is [latex]\frac{2}{5}[/latex] of PQ?

**9).** How many terms of the AP 27, 24, 21….. should be taken so that their sum is zero?

**10).** Find the value of K for which the quadratic equation 2kx^2–2 (1+2k) x+(3+2k) = 0 has equal roots?

**SECTION–C**

**Question number 11 to 20 carry 3 mark each.**

**11).** The king, queen & jack of diamond are removed from a deck of 52 playing cards and then well shuffled, now one card is drawn at random from the remaining cards. Determine the probability that the card drawn is?

(1) A face card

(2) A red card

(3) A king

**12).** Two poles of equal heights are standing opposite to each other on either side of the road, which is 100m wide from a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the heights of the poles.

**13).** Prove that the points (7, 10) (–2, 5) and (3,–4) are the vertices of an isosceles right triangle?

**14).** Final the roots of the equation

[latex]\frac { 1 }{ 2x-3 } +\quad \frac { 1 }{ x-5 } =1\quad x\neq \frac { 3 }{ 2 } 5[/latex]

**15). **Divide 56 in four parts in AP such that the ratio of the product of their extremes (1st and 4th) to the product of means (2nd & 3rd) is 5:6?

**16).** Find the area of the shaded region, where ABC is a quadrant?

**17).** AB is a chord of a circle, with centre O and radius 10 cm that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence find the area of major segment ALBQA. (Use π = 3.14)?

**18).** A hemispherical tank of diameter 3m, is full of water it is being emptied by a pipe at the rate of 25/7 liter per second. How much time will it take to make the tank half empty. [Use π =22/7]

**19).** A 20m deep well with diameter 7m is dug and the earth taken out from digging is evenly spread out to form a platform of dimensions 22m×14m. Find the height of the platform. [Use π = 22/7]

**20).** A toy is in the shape of a smaller solid hemisphere mounted on a bigger solid hemisphere. Radius of bigger hemisphere is 2cm and that of the smaller is 1 cm.Find the total surface area of the toy?

**SECTION–D**

**Question number 21 to 31 carry 4 mark each.**

**21).** In a carton there are 15 rectangular cards of which 7 are green and rest are white, 18 pentagonal cards of which 3 are green and rest are white. One card is selected at random from the carton. Find the probability that selected card is:

(a) a rectangle

(b) a pentagon

(c) a pentagon of green colour

(d) a rectangle of white colour

**22).** The angle of elevation of a cloud from a point P, 60m above the surface of a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake.

**23).** Draw a triangle ABC with side BC = 4 cm, ∠ B = 45° ∠A =105°, then construct a triangle whose sides are [latex]\frac{6}{5}[/latex]times the corresponding side of ΔABC.

**24).** ABCD is a rectangle formed by the points A (-1, -1), B (-1, 4), C (5, 4) and D (5,-1). P, Q, R & S are midpoints of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square, a rectangle, a parallelogram or rhombus. Justify your answer.

**25).** A manufacturer of TV sets produced 600 sets in the third year & 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find?

(1) The production in the 1st year

(2) The production in the 10th year

(3) The total production in first 7 years

**26).** A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6km/h more than the first speed. If it takes 3 hours to complete the total journey what is its first speed?

**27).** A rectangular park is to be designed whose breadth is 3m less than its length, its area is to be [latex]4m^{2}[/latex] more than the area of a park that has already been made is the shape of an isosceles triangle with its base as the breath of the rectangular park and of altitude 12m. Find the length and the breadth of the rectangular park.

**28).** Prove that the lengths of the tangents drawn from an external point to a circle are equal.

**29).** AB is a chord of a circle with centre O such that AB = 16 cm and radius of circle is 10 cm. Tangents at A & B intersect each other at P. Find the length of PA.

**30).** There is a right circular cone of height 30cm. A small cone is cut off from the top by a plane parallel to the base. If volume of the small cone is [latex]\frac{1}{27}[/latex] of the volume of given cone, find at what height above the base is the section made.

**31).** ABCD is a square of side 14cm. Semicircles are drawn with each side of square as diameter. Find the area of the shaded region [Use π =22/7]