www.InyaTrust.com BELTHANGADY TALUK MATHS TEACHERS WORKSHOP MINIMUM STUDY LEVEL QUESTION PAPER Time: 2hour TOTAL: SUBJECT: MATHEMATICS 50 1x7=7 I . Choose the best alternative from following options 1) If Tn = 5n + 1 , the value of S2 ---(A) 18 (B) (C) 19 (D) 20 n 2) The value of Cn is---(A) n (B) n! (C) 1 (D) 0 3) If a coin is tossed once, the probability of head occurs. 2 (B) (A) (C) (D) 4 4) The formula to find coefficient of variation. ∑ (A) (B) ∑ (C) . (D) ∑ 5) The value of sin 60 ------ (B) √ (D) √3 6) The two lines are mutually perpendicular, then, the product of their slop is -------(A) 0 (B) 1 (C) 2 (D) − 7) The degree of the polynomial 3x2 - 4x4 + 2x3 + 7x - 8. (A) 2 (B) 4 (C) 3 ( D) 1 II. Answer the following 1x5=5 8) If A and B is a non – empty sets, write the relation between n (A), n (B), n (A∩B), n (AUB). n(AUB) = n(A) +n(B) – n(A∩B) 9) State Thales Theorem. If a straight line is drawn parallel to a side of a triangle,then it divides the (A) √ (C) other two sidesproportionally. 10) Write the relation between Dividend, Quotient, Reminder and Divisor. a = bq + r [ 0≤ <q] where a=Dividend,b=Divisor,q=Quotient, R=Reminder 11) What is the distance between the circles of radius R and r touch each other Internally? d =R+r 12) Write the formula to find the Volume of a Cone. V= r 2h Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 1 www.InyaTrust.com III. Answer the following 2x 10 = 20 13) In a circle of radius 4.5cm draw two radii such that the angle between them is700 Construct tangents at the non-centre ends of the radii. 14) Construct a pair of tangents to a circle of radius 3cm, such that the angle between them is 1000. 15) Rationalize the denominator and simplify √ √ = = = = √ √ √ √ √ √ √ √ x √ √ √ √ √ √ √ √ √ − √ Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 2 www.InyaTrust.com 16) Find the product. √2 x √3 √2 = 2 = 2 = √2 √3 = 3 = 3 = √3 √2 x3 √4x27 √108 17) In a group of 50 students, 30 like tea, 25 like coffee and 16 like both. In a Venn diagram show how many like only tea. 18) How many 3 digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 without repeating any digit. The number of 3 digit numbers can be formed using the digits 1,2,3,4,5,6 Hundreds Tens ones 6 5 4 P1 P1 P1 6 5 4 =6x5x4 = 120 OR How many diagonals can be drawn in a hexagon? Formula - nC2 - n 6 C2 – 6 ! = ( )! - 6 ! =( ! )! ! - 6 = - 6 = 15 - 6 = 9 Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 3 www.InyaTrust.com 19) Solve by using the formula. x2 + 12 = 7x a = 1, b = -7 , c = 12 −(−7) ± (−7) − 4x1x12 = 2x1 7 ± √49 − 48 = 2 7 ± √1 = 2 7±1 = 2 = or = = or = or 20) If cot A = = = and sinA = , Find cos A. cotA = cosA = cotA.sinA cosA = = 21) Calculate the slope of a line joining the points (3,-2) and (4, 5). m= 5−(−2) 4−3 5+2 m= 1 m= 7 22) Verify Euler’s formula for the given graph N = 6, R = 5, A = 9 N+R = 6+ 5 = 11 A+2 = 9 + 2 = 11 ∴ N+R = A+2 22) Sketch out the field to the following notes from the field book (1 cm = 50m.) To D 100 To C 50To B 350 300 250 150 50 150 To E 100To F From A Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 4 www.InyaTrust.com 1cm = 50m 50m =1cm, 150m = 3cm, 250m = 5cm, 300m = 6cm, 350m = 7cm, 100m = 2cm IV. Answer the following 23) Calculate the standard deviation of the following data X 0-10 10-20 20-30 f 7 10 15 3 x 2= 6 30-40 8 40-50 10 CI X f d=x-25 fd d2 fd2 0-10 10-20 20-30 30-40 40-50 5 15 25 35 45 7 10 15 8 10 -20 -10 0 10 20 -140 -100 0 80 200 400 100 0 100 400 2800 1000 0 800 4000 50 = ∑ − = − = – . = √ . = 40 8600 ∑ . Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 5 www.InyaTrust.com 23) prove that “If two circles touch each other externally, the centers and the point of contact is collinear” If two circles touch each other externally, thecentres and the point of contact are collinear. Given:A and B are the centres of touching circles. P is the point of contact. To prove : A,P,and B are collinear. Construction: Draw the tangent XPY. Proof:In the figure ∠APX = 900……………..(1) ∵Radius drawn at the point of contact is ∠BPX = 900 ………… ..(2) perpendicular to the tangent ∠APX + ∠BPX = 900 +900 [ by adding (1) and (2) ∠APB = 1800 [ APB is a straight line ∴ APB is a straight line ∴ A, P andB are collinear. V. Answer the following 4 x 3= 12 24) Draw transverse common tangents to two circles of radii 4.5cm and 2.5cm having Their Centers 10cm apart and measure their lengths. Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 6 www.InyaTrust.com 25) Draw a graph of y = x2 and find the value of√5. 5 = ±2.2 Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 7 www.InyaTrust.com 27) Prove that “If two triangles are equiangular, then their corresponding sides are Proportional” Theorem: “ If two triangles are equiangular,then their corresponding sides are proportional”. Given: In ∆ABC and ∆DEF, ( i). ∠BAC = ∠EDF (ii). ∠ABC = ∠DEF To prove: AB DE BC = EF = CA FD Construction: i) Mark points G’ and H’ on AB and AC such that. Proof:In ∆AGH and ∆DEF, [ ∵ Construction AG = DE ∠BAC = ∠EDF [ ∵ Given [ ∵ Construdtion AH = DF ∴ ∆AGH ≡ ∆DEF [ ∵ S.A.S. postulates ∴ ∠AGH = ∠DEF [∵ Corresponding angles] ಆದ ೆ∠ABC = ∠DEF [ ∵ Given ⇒ ∴ ∴ ∴ ∠AGH = ∠ABC [ ∵ Axioms GH ॥ BC AB AG = = BC GH = = CA HA [∵ converse of thales Theorem [∵∆AGH ≡ ∆DEF Typed By: Yakub S.,GHS Nada,Belthangady for MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 8

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