Page 1 PRE – SA 1 (2016) Class – X SUB : MATHEMATICS Time Allowed : 3 Hrs. Maximum Marks : 90 Section – A (1 Marks) Q.1 If 9 2 2 sin 5cos 6. ? ? + = Find tan ? Q.2 In ABC ?  DF BC Find the value of x Q.3 If mean of 1,2, 3 ……. n is 16 , 11 n then find the value of n. Q.4 State whether the following statement is true or false. Justify your answer. ( ) Sin Sin Sin A B A B + = + Section – B ( 2 Marks Each) Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your answer. Q.6 In the given fig  DE AC and  . DF AE Prove that EF EC BF BE  Page 2 PRE – SA 1 (2016) Class – X SUB : MATHEMATICS Time Allowed : 3 Hrs. Maximum Marks : 90 Section – A (1 Marks) Q.1 If 9 2 2 sin 5cos 6. ? ? + = Find tan ? Q.2 In ABC ?  DF BC Find the value of x Q.3 If mean of 1,2, 3 ……. n is 16 , 11 n then find the value of n. Q.4 State whether the following statement is true or false. Justify your answer. ( ) Sin Sin Sin A B A B + = + Section – B ( 2 Marks Each) Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your answer. Q.6 In the given fig  DE AC and  . DF AE Prove that EF EC BF BE  Q.7 The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg. and that of B and C be 43 kg. Find the weight of B. Q. 8 Find the value of tan 60 geometrically. Q. 9 Find HCF of 3.5 , and 6.5 and 8.5 Q.10 If 2 23 4 19 x y and x y + =  = Find the value of 2 y x  SectionC (Three Marks Each) Q.11 Check whether 4 n can end with the digit 0 for any natural number n. Q.12 Draw the graph of the equation 5 7 50 7 5 46 x y and x y + = + = and shade the triangular region formed by the lines and xaxis also find the area of triangle. Q.13 Two candles of equal height but different thickness are lighted. The first burns off in 6 hours and the second in 8 hours. How long, after lighting both, will be first candle be half the height of the second? Q.14 If and a ß are the zeroes of the polynomial 2 2 15 x x   then form a quadratic polynomial whose zeroes are ( ) ( ) 2 2 and a ß Q.15 If Cos sin 2cos ? ? ? + = Show that os sin 2sin C ? ? ?  = Q.16 Evaluate 2 2 2 2 2 tan 60 4sin 45 3Sec 30 5Cos 90 Cos 30 Sec60 30 ec Cot + + + +  Q.17 ABC ? and DBC ? are on the same box BC and on opposite sides of BC. O is the point of intersection of AD and BC. Prove that: area ABC AO areaof DBC DO ? = ? Q.18 In ABC ? , A is obtuse angle PB AC ? and QC AB ? . Prove that AB AQ AC AP × = × Page 3 PRE – SA 1 (2016) Class – X SUB : MATHEMATICS Time Allowed : 3 Hrs. Maximum Marks : 90 Section – A (1 Marks) Q.1 If 9 2 2 sin 5cos 6. ? ? + = Find tan ? Q.2 In ABC ?  DF BC Find the value of x Q.3 If mean of 1,2, 3 ……. n is 16 , 11 n then find the value of n. Q.4 State whether the following statement is true or false. Justify your answer. ( ) Sin Sin Sin A B A B + = + Section – B ( 2 Marks Each) Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your answer. Q.6 In the given fig  DE AC and  . DF AE Prove that EF EC BF BE  Q.7 The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg. and that of B and C be 43 kg. Find the weight of B. Q. 8 Find the value of tan 60 geometrically. Q. 9 Find HCF of 3.5 , and 6.5 and 8.5 Q.10 If 2 23 4 19 x y and x y + =  = Find the value of 2 y x  SectionC (Three Marks Each) Q.11 Check whether 4 n can end with the digit 0 for any natural number n. Q.12 Draw the graph of the equation 5 7 50 7 5 46 x y and x y + = + = and shade the triangular region formed by the lines and xaxis also find the area of triangle. Q.13 Two candles of equal height but different thickness are lighted. The first burns off in 6 hours and the second in 8 hours. How long, after lighting both, will be first candle be half the height of the second? Q.14 If and a ß are the zeroes of the polynomial 2 2 15 x x   then form a quadratic polynomial whose zeroes are ( ) ( ) 2 2 and a ß Q.15 If Cos sin 2cos ? ? ? + = Show that os sin 2sin C ? ? ?  = Q.16 Evaluate 2 2 2 2 2 tan 60 4sin 45 3Sec 30 5Cos 90 Cos 30 Sec60 30 ec Cot + + + +  Q.17 ABC ? and DBC ? are on the same box BC and on opposite sides of BC. O is the point of intersection of AD and BC. Prove that: area ABC AO areaof DBC DO ? = ? Q.18 In ABC ? , A is obtuse angle PB AC ? and QC AB ? . Prove that AB AQ AC AP × = × Q. 19 Find mean : CLASS 010 1020 2030 3040 4050 FREQUENCY 7 12 13 10 8 Q.20 Find the median of the data: Marks 010 1020 2030 3040 4050 5060 6070 7080 8090 90100 No. of students 5 3 4 3 3 4 7 9 7 8 Section – D (Four Marks Each) Q. 21 Find other zeroes of the polynomial ( ) 4 3 2 2 7 19 14 30 p x x x x x = +   + if two of its zeroes are 2 2 and  . Q.22 In a triangle, if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the first side is a right angle. Q.23 Evaluate: ( ) ( ) 2 2 Sec Cos 90 tan cot 90 Sin 55 Sin 35 tan10tan20tan60tan70tan80 ec ? ? ? ?    + + Q.24 If 1 tan , tan 1 2 1 m A B m m = = + + Using the formula ( ) tan tan tan 1 tan tan A B A B A B + + =  Find A and B where A+B is an acute angle and 3A+B= 105. Q.25 p(x) is a polynomial of degree more than 2, when p(x) is divided by 2 x + it leaves a remainder 2 and when it is divided by ( ) 3 x  it leaves a remainder 3. If p(x) when divided by 2 6 x x   leaves a remainder ax+b. Find the value of ab. Q.26 The following table gives the production yield per hectare of wheat of 100 farms of a village: Production yield in kg/Hectare 5055 5560 6065 6570 7075 7580 No. of Farms 2 8 12 24 38 16 Change the above distribution to more than type distribution and draw its again. Page 4 PRE – SA 1 (2016) Class – X SUB : MATHEMATICS Time Allowed : 3 Hrs. Maximum Marks : 90 Section – A (1 Marks) Q.1 If 9 2 2 sin 5cos 6. ? ? + = Find tan ? Q.2 In ABC ?  DF BC Find the value of x Q.3 If mean of 1,2, 3 ……. n is 16 , 11 n then find the value of n. Q.4 State whether the following statement is true or false. Justify your answer. ( ) Sin Sin Sin A B A B + = + Section – B ( 2 Marks Each) Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your answer. Q.6 In the given fig  DE AC and  . DF AE Prove that EF EC BF BE  Q.7 The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg. and that of B and C be 43 kg. Find the weight of B. Q. 8 Find the value of tan 60 geometrically. Q. 9 Find HCF of 3.5 , and 6.5 and 8.5 Q.10 If 2 23 4 19 x y and x y + =  = Find the value of 2 y x  SectionC (Three Marks Each) Q.11 Check whether 4 n can end with the digit 0 for any natural number n. Q.12 Draw the graph of the equation 5 7 50 7 5 46 x y and x y + = + = and shade the triangular region formed by the lines and xaxis also find the area of triangle. Q.13 Two candles of equal height but different thickness are lighted. The first burns off in 6 hours and the second in 8 hours. How long, after lighting both, will be first candle be half the height of the second? Q.14 If and a ß are the zeroes of the polynomial 2 2 15 x x   then form a quadratic polynomial whose zeroes are ( ) ( ) 2 2 and a ß Q.15 If Cos sin 2cos ? ? ? + = Show that os sin 2sin C ? ? ?  = Q.16 Evaluate 2 2 2 2 2 tan 60 4sin 45 3Sec 30 5Cos 90 Cos 30 Sec60 30 ec Cot + + + +  Q.17 ABC ? and DBC ? are on the same box BC and on opposite sides of BC. O is the point of intersection of AD and BC. Prove that: area ABC AO areaof DBC DO ? = ? Q.18 In ABC ? , A is obtuse angle PB AC ? and QC AB ? . Prove that AB AQ AC AP × = × Q. 19 Find mean : CLASS 010 1020 2030 3040 4050 FREQUENCY 7 12 13 10 8 Q.20 Find the median of the data: Marks 010 1020 2030 3040 4050 5060 6070 7080 8090 90100 No. of students 5 3 4 3 3 4 7 9 7 8 Section – D (Four Marks Each) Q. 21 Find other zeroes of the polynomial ( ) 4 3 2 2 7 19 14 30 p x x x x x = +   + if two of its zeroes are 2 2 and  . Q.22 In a triangle, if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the first side is a right angle. Q.23 Evaluate: ( ) ( ) 2 2 Sec Cos 90 tan cot 90 Sin 55 Sin 35 tan10tan20tan60tan70tan80 ec ? ? ? ?    + + Q.24 If 1 tan , tan 1 2 1 m A B m m = = + + Using the formula ( ) tan tan tan 1 tan tan A B A B A B + + =  Find A and B where A+B is an acute angle and 3A+B= 105. Q.25 p(x) is a polynomial of degree more than 2, when p(x) is divided by 2 x + it leaves a remainder 2 and when it is divided by ( ) 3 x  it leaves a remainder 3. If p(x) when divided by 2 6 x x   leaves a remainder ax+b. Find the value of ab. Q.26 The following table gives the production yield per hectare of wheat of 100 farms of a village: Production yield in kg/Hectare 5055 5560 6065 6570 7075 7580 No. of Farms 2 8 12 24 38 16 Change the above distribution to more than type distribution and draw its again. Q.27 Prove that: in os 1 ec tan 1 os cot 1 s A c A s A A c ecA A + = +  +  Q.28 If the mean of the following frequency distribution is 65.6. Find the missing frequencies x & y. Class 1030 3050 5070 7090 90110 110130 Frequency 5 8 x 20 y 2 =50 Q.29 A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs. 216 and full and one half reserved first class tickets costs Rs. 327. What is the basic first class full fare and what is the reservation charge? Q.30 In ABC ? is triangle. PQ is a line segment intersecting AB in P and AC in Q. Such that PQ/BC and divides ABC ? into two parts equal in area. Find BP/AB. Q.31 Show that 2 p will leave a remainder 1 when divided by 8 if p is an odd positive integer.Read More
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