Maths Past Year Paper SA-1(Set -4) - 2016, Class 10, CBSE Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Maths Past Year Paper SA-1(Set -4) - 2016, Class 10, CBSE Class 10 Notes | EduRev

 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
-  
 
Section-C (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 x-axis 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
-  
 
Section-C (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 x-axis 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 0-10 10-20 20-30 30-40 40-50 
FREQUENCY 7 12 13 10 8 
  
Q.20 Find the median of the data: 
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 
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 a-b. 
 
Q.26 The following table gives the production yield per hectare of wheat of 100 farms of a village: 
Production yield in kg/Hectare 50-55 55-60 60-65 65-70 70-75 75-80 
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
-  
 
Section-C (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 x-axis 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 0-10 10-20 20-30 30-40 40-50 
FREQUENCY 7 12 13 10 8 
  
Q.20 Find the median of the data: 
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 
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 a-b. 
 
Q.26 The following table gives the production yield per hectare of wheat of 100 farms of a village: 
Production yield in kg/Hectare 50-55 55-60 60-65 65-70 70-75 75-80 
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 10-30 30-50 50-70 70-90 90-110 110-130  
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
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 10

Dynamic Test

Content Category

Related Searches

Important questions

,

Objective type Questions

,

Class 10

,

shortcuts and tricks

,

Summary

,

Sample Paper

,

Class 10

,

CBSE Class 10 Notes | EduRev

,

ppt

,

CBSE Class 10 Notes | EduRev

,

Exam

,

Maths Past Year Paper SA-1(Set -4) - 2016

,

Viva Questions

,

Maths Past Year Paper SA-1(Set -4) - 2016

,

study material

,

MCQs

,

video lectures

,

CBSE Class 10 Notes | EduRev

,

mock tests for examination

,

practice quizzes

,

Free

,

pdf

,

Class 10

,

Semester Notes

,

Previous Year Questions with Solutions

,

Maths Past Year Paper SA-1(Set -4) - 2016

,

past year papers

,

Extra Questions

;