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 = 2n - 1 , then the value of S2 ---- (A) 1 (B) 2 (C) 3 (D) 2) The value of n+1P2 is --( (A) n(n+1) (B) n(n-1) (C) (n+1)(n-1) (D) 3) The two coins are tossed at a time , the total number of outcomes n (S) ---(A) 2 (B) (C) 6 (D) 8 4) The formula to find coefficient of variation ------(A) 5) If sin (B) = x100 (C) 10 ) (D) , then = ----- (A) cos (B) (C) 6) The distance between the points (6, 5) and (4, 4). sec (A) √ (B) 1 7) If f(x) = 4x + 5, then f( 1 ) = (A) 9 (B) -9 (C) 1 2 (C) (D) tan (D) (D) −1 -1 II. Answer the following 8) Write 144 as product of prime factors. 1x5=5 2 144 2 72 2 36 2 18 3 9 3 144 = 2x2x2x2x3x3 9) Draw Venn diagram of A ∩ (B\C) Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 1 www.InyaTrust.com 10) State Thales Theorem. Thales theorem :If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionally 11) Write the formula to find the total surface area of a Sphere. A = 4 r2 12) What are concentric circles? Circles having the same centre but different radii are called concentric circles. III. Answer the following . 2x 10 = 20 12) Draw a pair of tangents to a circle of radius 4cm from an external point 7cm apart from the centre. 13) Rationalize the denominator and simplify √ √ √ = √ = √ √ √ √ √ √ √ = √ x √ √ 14) Find the product :√3 x √5 √3 = 3 = 3 = √3 √5 = 5 = 5 = √5 √3 x5 √27x25 √675 Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 2 www.InyaTrust.com 15) If U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 2, 4, 6, 8 }, B= { 1, 3, 5, 7 } ,then Prove that (AUB)1 = A1 ∩B1 . U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8 }, B= {1, 3, 5, 7 } , LHS (AUB)1 = {1,2, 3,4, 5,6, 7,8 }1 = {0, 9 } RHS = A1∩B1 ={ 2, 4, 6, 8 }1∩{ 1, 3, 5, 7 }1 = { 0, 1,3, 5, 7,9 }∩{0, 2, 4, 6, 8,9 } = {0, 9 } LHS = RHS ∴(AUB)1 = A1 ∩B1 . 16) 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 17. Solve by using the formula. x2 – 2x + 4 = 0 a = 1, b = -2 , c = 4 −(−2) ± (−2) − 4x1x4 = 2x1 2 ± √4 − 16 = 2 2 ± √−12 = 2 2 ± 2√−3 = 2 = 1 ± √−3 17) Find the value of 60 + 2 60 + 2 45 . 45 . = √3 +2x1 = 3 +2 = 5 18) Find the coordinates of point P which divides the line joining A (4,-5) and B (6, 3) in the ratio 2:5. P (x,y) = , P (x,y) = P (x,y) = , , Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 3 www.InyaTrust.com 19) Verify Euler’s formula for the given graph N = 3, R = 5, A = 6 N+R = 3+ 5 = 8 A+2 = 6 + 2 = 8 ∴ N+R = A+2 22) Sketch out the field to the following notes from the field book (1 cm = 20m.) To C 120To D 210 200 120 80 200To B From A 1cm = 20m ⇒ 80m = 4cm, 120m = 6cm, 210m = 10.5cm, 200m = 10cm, Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 4 www.InyaTrust.com IV. Answer the following 23) Calculate the standard deviation of the following data X 0-4 5-9 10-14 f 1 4 3 CI f 0-4 5-9 10-14 15-19 1 4 3 2 Assumed Mean Methdo d=x-12 fd X 2 7 12 17 -10 -5 0 5 10 = ∑ = = 15-19 2 d2 fd2 100 25 0 25 100 100 0 50 -20 250 ∑ − − -10 -20 0 10 3 x 2= 6 − – = √ = . 24) prove that “If two circles touch each other internally, the centers and the point of Contact is collinear” If two circles touch each other internally the centres and the point of contact are collinear. Given:A and B are centres of touching circles. P is point of contact. To prove : A,P,and B are collinear Construction: Draw the common tangent XPY . Join AP and BP. Proof:In the figure ∠APX = 900……………..(1) ∵Radius drawn at the point of contact ∠BPX = 900 ………… ..(2) is perpendicular to the tangent. ∠APX = ∠BPX = 900 [ From (1) and (2) AP and BP lie on the same line ∴ APB is a straight line ∴ A, P and B are collinear. Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 5 www.InyaTrust.com V. Answer the following 4 x 3= 12 25) Draw transverse common tangents to two circles of radii 6cm and 2cm having their Centers 8 cm 26) Solve graphically: x2 + 4x – 5 = 0. x -6 -5 -3 -2 y 7 0 -8 -9 -1 -8 0 -5 1 0 2 7 -- Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 6 www.InyaTrust.com 27) State and Prove Pythagoras Theorem. Theorem:Phythagoras Therem In a right angled triangle,the square of the hypotenuse is equal to the sum of the square of the other two sides. Given: ∆ABC In which ∠ABC = 900 To Prove : AB2 + BC2 = CA2 Construction: Draw BD ⟘ AC . Proof: In ∆ABC and ∆ADB , ∠ABC = ∠ADB = 900 [ ∵ Given and Construction ∠BAD =∠BAD [∵ Common angle ∴ ∆ABC ~ ∆ADB [∵ AA criteria ⇒ AB AD = AC AB ⇒ AB2 = AC.AD……..(1) In ∆ABC and ∆BDC , ∠ABC = ∠BDC = 900 [ ∵ Given and construction ∠ACB = ∠ACB [∵ Common angle ∴ ∆ABC ~ ∆BDC [∵ AA criteria ⇒ BC DC = AC BC ⇒ BC2 = AC.DC……..(2) (1) + (2) AB2+ BC2 = (AC.AD) + (AC.DC) AB2+ BC2 = AC.(AD + DC) AB2+ BC2 = AC.AC AB2+ BC2 = AC2 [ ∵AD + DC = AC] Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 7 www.InyaTrust.com Typed By: Yakub S, GHS Nada, Belthangady for MSTF Mangalore (Belthangady wing) www.InyaTrust.com Page 8

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