www.InyaTrust.com BELTHANGADY TALUK MATHS TEACHERS WORKSHOP MINIMUM STUDY LEVEL QUESTION PAPER Time: 2hour I. SUBJECT: MATHEMATICS Choose the best alternative from following options TOTAL: 50 1x7=7 1) If Tn = 5-4n , then T2 = (A) 3 (B) −1 (C) − (D) 8 2) The value of nP0 is--(A) n! (B) 0 (C) 1 (D) n 3) An unbiased dice is thrown, what is the probability that a perfect square number occurs (A) (B) (C) (D) 1 4) Mean =70 and coefficient of variation is 6 ,Find standard deviation (A) 4 (B) . (C)0.42 (D) 0.4 5) The distance between the points (2,3) and (6,6) is (A) 5 (B) 4 (C) 6 (D) 3 6) If cos = , then the value equal to sec is (A) (B) (C) (D) 2 7) If f(x) = x + x - 6 , the value of f(2) is (A) 2 (B) 4 (C) 0 (D) 1 II. Answer the following 1x5=5 8) The Venn diagram shows the students who can speak English and Hindi. If the total number of student in a class is 70 then, find the number of students speaks either English or Hindi. =60 9) Write the prime factors of 3825. 3x3x5x5x17 10) In ∆ABC If DE॥BC, AD = 7cm, CD = 5cm, BC = 18cm find CE. Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 1 www.InyaTrust.com ∆ABC, DE॥BC, ∴ = = ⇒ AE = ∴ CE = 18-10.5 = 10.5 ∴ CE = 7.5cm 11) What is the name of a straight line which intersects a circle at two distinct points? secant 12) Write a formula to find the circumference of the base of the cylindrical vessel. C=2 r III. Answer the following 2x 10 = 20 13) In a medical examination of 150 people, it was found that 90 had eye problem, 50 had heart problem and 30 had both complaints. Draw a Venn diagram to show how many people had either eye problem or heart problem. A-{The people had eye problem} B-{The people had Heart problem} n(A) = 90 ,n(B) = 50, n(A∩B) = 30 n(AUB) = n(A) + n(B) –n(A∩B) = 90 + 50 - 30 = 110 14) 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 15) Find the product : √2 x √3 √2 = 2 = 2 = √2 √3 = 3 = 3 = √3 √2 x3 √16x27 √432 16) In a circle of radius 3.5cm draw two radii such that the angle between them is700 Construct tangents at the non-centre ends of the radii. 17) How many diagonals can be drawn in a pentagon Formula - nC2 - n 5 C2 – 5 ! = ( )! - 5 ! = ! ( )! ! - 5 = - 5 = 10 - 5 = 5 Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 3 www.InyaTrust.com 18) Solve by using the formula x2 - 4x + 2 =0 a = 1, b = -4 , c = 2 −(−4) ± (−4) − 4x1x2 = 2x1 4 ± √16 − 8 = 2 4 ± √8 = 2 4 ± 2√2 = 2 = 2 ± √2 19) If cot = then find cos and cosec cos . = cosec = 20) Find the slop of a line joining the points (4,-8) and (5,-2). m= m= m= −2− (−8) 5−4 −2+8 6 1 1 m= 21). Verify Euler’s formula for Pentahedron. F = 5, E = 9, V = 6 F+V = 5+ 6 = 11 E+2 = 9 + 2 = 11 ∴ F+V = E+2 Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 4 www.InyaTrust.com 22) Sketch out the field to the following notes from the field book (1 cm = 20m.) To C 220 120 To D 200 120 80 To D 80 200 To B From A 1cm = 20m ⇒80m=4cm, 120m=6cm, 200m=10cm, 220m=11cm, IV. Answer the following 23) Calculate the standard deviation of the following data X f 10 4 20 3 = ∑ 40 5 X f d=x-30 fd d2 fd2 10 20 30 40 50 4 3 6 5 2 -20 -10 0 10 20 -80 -30 0 50 40 400 100 0 100 400 1600 300 0 500 800 20 = 30 6 3 x 2= 6 − − -20 50 2 3200 ∑ − Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 5 www.InyaTrust.com = – = √ = . 24) prove that “If two circles touch each other, the centers and the point of contact Collinear” If two circles touch each other, the centres and the point of contact are collinear. Case-1). 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. Case-2 ). 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. Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 6 www.InyaTrust.com 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. V) Answer the following 4 x 3= 12 25) Draw transverse common tangents to two circles of radii 4cm and 2cm having their Centers 8cm apart and measure their lengths. Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 7 www.InyaTrust.com 26) Draw the graph of y = x2 – 8x + 7 x y 0 7 8 7 1 0 7 0 3 -8 5 -8 4 -9 Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 8 www.InyaTrust.com 27) Prove that “A straight line is drawn parallel to one side of the triangle, and then it divides other two sides proportionally”. ∆ABC ಯ , DE॥BC Given: AD To prove: = DB AE EC Construction: 1. Join D,E and E,B. 2.Draw EL ⟘ AB and DN⟘ AC . ∆ABC Proof: ∆BDE = ∆ABC ∆BDE ∆ADE ∆CDE ∆ADE ∆CDE ∴ = = = 1 2 1 2 xADxEL xDBxEL 1 [∵ A = 2 xbxh AD DB 1 2 1 2 xAExDN xDBxDN 1 [∵ A = xbxh 2 AE EC = [∵∆BDE ≡ ∆ Typed By:Yakub S, GHS Nada, Belthangady. For MSTF Mangalore(Belthangady wing) www.InyaTrust.com Page 9
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