SUMMATIVE ASSESSMENT II, 2012 II, 2012 MATHEMATICS / Class X / Time allowed : 3 hours Maximum Marks : 80

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1 SUMMATIVE ASSESSMENT II, 0 II, MATHEMATICS / Class X / X Time allowed : 3 hours Maimum Marks : General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section-A comprises of 0 questions of mark each, Section-B comprises of 8 questions of marks each, Section-C comprises of 0 questions of 3 marks each and Section-D comprises of 6 questions of 4 marks each. (iii) Question numbers to 0 in Section-A are multiple choice questions where you are to select one correct option out of the given four. (iv) There is no overall choice. However, internal choice have been provided in question of two marks, 3 questions of three marks each and questions of four marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted. (i) (ii) (iii) 0 (iv) 3 (v) 3 4 Page of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

2 SECTION A / Question numbers to 0 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 0. The two roots of a quadratic equation are and. The equation is : (A) 0 (B) 0 (C) 0 (D) 0 एक द व घ त सम करण क द म ऱ और ह यह सम करण ह : (A) 0 (B) 0 (C) 0. The 6 th term from the end of the AP 5,,, 4,..., 3 is : (A) 5 (B) (C) 9 (D) 6 5,,, 4,..., 3 (A) 5 (B) (C) 9 (D) 6 3. From a point Q, the length of a tangent to a circle is 4 cm and distance of Q from centre is 5 cm. The radius of the circle is : (A) 7 cm (B) 4 cm (C) 3.5 cm (D) 0 cm Q 4 Q 5 (D) 0 (A) 7 (B) 4 (C) 3.5 (D) 0 4. In given figure, AB is the chord of the circle and AOC is its diameter such that ACB55. If AT is the tangent to the circle at point A then BAT is equal to : (A) 60 (B) 40 (C) 50 (D) 55 AB AOC ACB55 AT A BAT Page 3 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

3 (A) 60 (B) 40 (C) 50 (D) Two tangents drawn at the ends of a diameter of a circle, if etended, will be at an angle of : (A) 30 (B) 0 (C) 0 (D) 90 (A) 30 (B) 0 (C) 0 (D) To draw a pair of tangents to a circle which are inclined to each other at an angle of 00, it is required to draw tangents at end points of those two radii of the circle, the angle between which should be : (A) 75 (B) 80 (C) 05 (D) (A) 75 (B) 80 (C) 05 (D) Eight solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 3 cm. The diameter of each sphere is : (A) 3 cm (B) 6 cm (C) cm (D) 8 cm 6 3 (A) 3 (B) 6 (C) (D) 8 8. A race track is in the form of a circular ring whose outer and inner circumferences are 396 m and 35 m respectively. The width of the track is : (A) 63 m (B) 56 m (C) 7 m (D) 3.5 m (A) 63 (B) 56 (C) 7 (D) The length of the shadow of a tower on the ground is equal to its height, then the angle of elevation of the sun is equal to : (A) 30 (B) 45 (C) 60 (D) 90 (A) 30 (B) 45 (C) 60 (D) The probability of getting a prime number in a single throw of a die, is (A) (B) 6 (C) 3 (D) एक प स क एक ब र उछ ऱन पर, एक अभ ज य स ख य क आन क प र ययकत ह : (A) (B) (C) (D) Page 4 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

4 . SECTION-B / Question numbers to 8 carry two marks each. 8 If and are the two roots of the quadratic equation and b. यद वद द व घ त सम करण क ज ए a b0, find a क द म ऱ तथ ह, त a तथ b क म न ज ञ त. If the sum of first q terms of an AP is qq, find the common difference of the AP. q qq 3. In given figure, if B90, BC5 cm and AC7 cm, then find the radius of the circle with centre O. a b0 B90, BC5 AC7 O 4. The cost of fencing a circular field at the rate of Rs. 4 per metre is Rs Find the area of the field. Use Find the volume of a right circular cylinder of height cm and the base radius 5 cm. 5 Page 5 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

5 6. If the distance between the points (7, 4) and (3, y) is 4 units, find the value of y. (7, 4) (3, y) 4 y 7. Find the distance of a point P (, ) from the midpoint of the line segment joining the points A (3, 5) and B (5, 7) A (3, 5) B (5, 7) P (, ) 8. Two coins are tossed together. Find the probability of getting () eactly one head () both heads. द यसक कक क एक स थ उछ ऱ गय प र ययकत ज ञ त क ज ए द वक () तथ यत: एक () द न आ ए OR/अथव A card is drawn at random from a well shuffled pack of 5 cards. Find the probability of getting (a) (b) a face card of red colour a jack of spades अच छ प रक र स फ ट गई 5 पत त क त श क गड ड स एक पत त य द च छय यनक ऱ गय यनम न क आन क प र ययकत ज ञ त क ज ए (a) (b) ऱ ऱ र ग क फ स क ड ह कम क ग ऱ म SECTION-C / Question numbers 9 to 8 carry three marks each Find the value of k so that the following quadratic equation has equal roots. k ( k) 0 k क वह म न ज ञ त क ज ए, ज सक यऱए यनम नयऱज त द व घ त सम करण क म ऱ सम न ह आए k ( k) 0 OR/अथव In p , find the value of p, so that (i) (ii) (iii) the roots are real the roots are not real the roots are equal p , म p क म न ज ञ त क ज ए, त द वक (i) (ii) (iii) म ऱ व स तववक ह ; म ऱ व स तववक न ह ; म ऱ सम न ह Page 6 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

6 0. Find the sum of first 40 multiples of A quadrilateral ABCD is drawn to circumscribe a circle (see fig.). Prove that ABCDADBC ABCD ABCDADBC. OR/ In given figure XY and X Y are two parallel tangents to a circle with centre O and another tangent AB with point of contact C is intersecting XY at A and X Y at B. Prove that AOB90. XY X Y, O C AB XY A X Y B AOB90. Draw a triangle of sides 4 cm, 5 cm and 6 cm and then construct a triangle similar to it whose sides are 3 of the corresponding sides of the first triangle Page 7 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

7 3. Find the area of the shaded region in the given figure, where ABCD is a square of side 4 cm and semicircles are drawn with each side of square as diameter. 7 ABCD A toy is in the form of a cone of radius 7 cm mounted on a hemisphere of same radius. The total height of the toy is 3 cm. Find the total surface area of the toy. 7 3 OR/ A juice seller was serving his customers using cylindrical glasses. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass, if the height of a glass was 0 cm, find the apparent capacity of the glass and its actual capacity. (Use 3.4) A tree is broken by the wind. The top struck the ground at an angle of 30 and at a distance of metres from the root. Find the height of the tree If the vertices of a triangle are (, 3), (4, k) and (9, 7) and its area is 5 sq. units, find the value of k. (, 3), (4, k) (9, 7) 5 k 7. Find the coordinates of the points which divide the line segment AB joining A (, ) and B (, 8) into four equal parts. Page 8 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

8 A (, ) B (, 8) AB 8. 5 cards numbered,, 3,, 5, are put in a bo and mied thoroughly. A card is drawn at random from the bo. Find the probability that the card drawn bears. ड ड () an even no. () a number divisible by or 3 5 क ड ज न पर,, 3,, 5 तक क स ख य ए यऱ ह ई ह, क एक बक कस म ड ऱ कर अच छ प रक र यमऱ य गय इस बक कस म स य द च छय एक क यनक ऱ गय प र ययकत ज ञ त क ज ए द वक यनक ऱ गए क पर अ द वकत स ख य () एक सम स ख य ह () य 3 स भ ज य स ख य ह SECTION-D / Question numbers 9 to 34 carry four marks each Solve for : 4 (,, 4) 4 क यऱए ह ऱ क ज ए : 4 (,, 4) 4 OR/अथव The sum of a number and its reciprocal is. Find the number. एक स ख य तथ इसक प रयतऱ म क य गफ ऱ ह स ख य ज ञ त क ज ए 30. Kartikay repays his total loan of Rs.,8,000 by repaying every month. Starting with the first instalment of Rs. 000, if he increases the instalment by ` 00 every month, what amount will be paid by him in the 30 th instalment? What amount does he still have to pay after the 30 th instalment?,8, Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. 3. From a solid cylinder whose height is.4 cm and diameter.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm. Page 9 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

9 .4.4 OR/ A container shaped like a right circular cylinder having diameter cm and height 5 cm is full of icecream. The icecream is to be filled into cones of height cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream A solid metallic right circular cone 0 cm high with vertical angle 60 is cut into two parts at the middle point of its height by a plane parallel to the base. If the frustum, so obtained be drawn into a wire of diameter cm, find the length of the wire An aeroplane, when 3000 m high passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplane from the same point on the ground are 60 and 45 respectively. Find the vertical distance between the two aeroplanes at that instant. (Use 3.73) 3000 ( 3.73 ) o 0 o - Page 0 of 0, DEVENDRA NAGAR, SECTOR-5, D/56, RAIPUR, C.G, HELPLINE : , Visit Us :

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