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T Board Question Paper: March 2020, , , , , , BOARD QUESTION PAPER: MARCH 2020, Mathematics Part - II, , , , Time: 2 Hours Max. Marks: 40, , Notes:, , i. All questions are compulsory., , ii. Use of calculator is not allowed., , iii. The numbers to the right of the questions indicate full marks., , iv. In case of MCQ’s [Q. No. 1(A)] only the first attempt will be evaluated and will be given credit., , Vv. For every MCQ, the correct alternative (A), (B), (C) or (D) in front of sub-question number is to be, , written as an answer., , vi. Draw proper figures for answers wherever necessary., , vii. The marks of construction should be clear and distinct. Do not erase them., , viii. Diagram i: tial for writing the proof of the theorem., Ss a, Q.1. A. Four alternative answers are given for every sub-question. Select the correct alternative, , , , and write the alphabet of that answer: [4], is Out of the following which is the Pythagorean triplet?, (A) (1,5,10) (B) (3,4,5) (©) (2,2,2) (D) (5,5, 2), , ii. Two circles of radii 5.5 cm and 3.3 cm respectively touch each other externally. What is the, distance between their centres?, , (A) 44cm (B) 2.2cm (C) 88cm (D) 89cm, iii. Distance of point (—3, 4) from the origin is 3, (A) 7 (B) 1 (Cc) -5 (D) 5, iv. Find the volume of a cube of side 3 cm:, (A) 27cm (B) 99cm? (C) 81cm (D) 3cm?, B. Solve the following questions: [4], i. The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas., , ii. Find the diagonal of a square whose side is 10 cm., , iii. CABCD is cyclic. If ZB = 110°, then find measure of 2D., , iv. Find the slope of the line passing through the points A(2, 3) and B(4, 7)., , ies (Any two): [4], , , , Q.2. A. Complete and write the following ac, , In the figure given above, ‘O” is the centre of the circle, seg PS is a tangent segment and S is, the point of contact. Line PR is a secant., , If PQ = 3.6, QR = 6.4, find PS., , Solution:, , , , PS? = PQ x Oo ...(tangent secant segments theorem), = PQ x (PQx [])

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= 3.6 x (3.6 + 6.4), , 6 x [], , =36, PS= O ...(by taking square roots), , , , ii. Ifsec 0 = 2 , find the value of tan 0., , , , Solution:, 1 + tan? 0 = sec” 6, a, 1+ tan? @= (2), 7, fant’p = 25, 49, _ 625-49, 49, 49, tan 0 = 7 ...(by taking square roots), , iii,, , , , , , In the figure given above, O is the centre of the circle. Using given information complete the, following table:, , , , Type of arc | Name of the arc | Measure of the arc, , Minor are | LC], Majorare | [_] LC], , , , , , , , , , , , , , , , B. Solve the following sub-questions (Any four): [8}, i. P, N,, R Q, In APQR, NM || RQ. If PM = 15, MQ = 10, NR = 8, then find PN., ii. M, Q, N' P, , In AMNP, ZMNP = 90°, seg NQ | seg MP. If MQ = 9, QP = 4, then find NQ.

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ii., , nw, , L, , In the figure given above, M is the centre of the circle and seg KL is a tangent segment. L is a, point of contact. If MK = 12, KL = 6V3 , then find the radius of the circle., , Find the co-ordinates of midpoint of the segment joining the points (22, 20) and (0, 16)., , A person is standing at a distance of 80 metres from a Church and looking at its top. The, , angle of elevation is of 45°. Find the height of the Church., , Complete and write the following activities (Any one): 13], D, , J ™~S, do,, , In the given figure, X is any point in the interior of the triangle. Point X is joined to the, vertices of triangle. seg PQ || seg DE, seg QR || seg EF. Complete the activity and prove that, seg PR || seg DF., Proof:, , In AXDE,, , PQ || DE «+-(Given), , xp _[ ] 7 ‘eon tt ;, , PD OE ...(Basic proportionality theorem)...(i), , In AXEF,, , QR || EF .-.(Given), , 4 - o w)--ii), , z- H ...[From (i) and (ii)], , seg PR || seg DF ...{By converse of basic proportionality theorem), , If A(6, 1), B(8, 2), C(9, 4) and DQ), 3) are the vertices of -ABCD, show that UABCD is a, parallelogram., Solution:, , Slope of line = ah., , ty 7, , Slope of line AB =, , Ooo, , i), , Slope of line BC -. (ii), , sna, Roly an, , Slope of line CD «.(iii), , ~, e

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Slope of line DA = ; «-(iv), , Slope of line AB = oO ...[From (i) and (iii)], line AB || line CD, , Slope of line BC = Ci ...[From (ii) and (iv)], , line BC || line DA, Both the pairs of opposite sides of the quadrilateral are parallel., OABCD is a parallelogram., , , , , , , , , , B. Solve the following sub-questions (Any fo): [6], i. If APQR, point S is the mid-point of side QR. If PQ = 11, PR = 17, PS = 13, find QR., ii. Prove that, tangent segments drawn from an external point to the circle are congruent., iii. Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance, 7.3 cm from the centre., iv. A metal cuboid of measures 16 cm x 11 cm x 10 cm was melted to make coins. How many, coins were made, if the thickness and diameter of each coin was 2 mm and 2 cm respectively?, (x= 3.14), Q.4. Solve the following sub-questions (Any fvo): [8], i. In AABC, PQ is a line segment intersecting AB at P and AC at Q = that seg PQ || seg BC., If PQ divides AABC into two equal parts having equal areas, find x., ii. Draw a circle of radius 2.7 cm and draw a chord PQ of length 4.5 cm. Draw tangents at points, P and Q without using centre., ii, A s D, P R, B Q c, In the figure given above UABCD is a square of side 50 m. Points P, Q, R, S are midpoints of, side AB, side BC, side CD, side AD respectively. Find area of shaded region., Q.5. Solve the following sub-questions (Any one): [3], , i:, , ii., , Circles with centres A, B and C touch each other externally. If AB = 3 cm, BC = 3 cm,, CA =4 cm, then find the radii of each circle., , Ifsin 0 + sin’ 0= 1, show that: cos? 0 + cos’ 0 = 1