CBSE Class 10 Maths HOTs Pair Of Linear Equations In Two Variables

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Like the crest of a peacock so is mathematics at the head of all knowledge.

1. At a certain time in a deer park, the number of heads and the number of legs of deer

and human visitors were counted and it was found there were 39 heads & 132 legs.

Find the number of deer and human visitors in the park.

(Ans:27,12)

Ans: Let the no. of deers be x

And no. of humans be y

ASQ :

x + y = 39 ---- (1)

4 x + 2 y = 132 ----- (2)

Multiply (1) and (2)

On solving, we get …

x = 27 and y= 12

 No. of deers = 27 and No. of humans = 12

Please refer to link below to download pdf file ofCBSE Class 10 Pair Of Linear Equations In Two Variables HOTs

ADDITIONAL QUESTION

Find the values of a and b for which the following system of linear equations has infinite solutions:

2x - (a - 4) y = 2b + 1

4x – (a - 1)y = 5b–1

Solve : 41x + 53y = 135 ; 53x + 41y = 147

Solve the pair of linear equations

(a – b) x + (a + b) y = a² – 2ab – b²

(a + b) (x + y) = a² + b²

Cars are parked in a parking place at a particular point of time in rows. If 3 cars are extra in a row, there would be one row less. If 3 cars are less in a row, there would be 2 rows more. Find the number of cars in the parking place at that particular point of time.

Solve for x and y:

1/7x + 1/6y = 3

1/2x - 1/3y = 5

Solve for u and v:

2(3u-v) = 5uv; 2(u+3v) = 5uv.

A train covered a certain distance at uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. Also if the train were slower by 6 km/h, it would have taken 6 hours more than the scheduled time. Find the length of the journey.

On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery seller gains Rs 7. If sell the tea set at 5% gain and the lemon set at 10% gain, he gains Rs 13. Find the actual price of the tea set and the lemon set.

More MCQs for NCERT Class 10 Mathematics Linear Equations in Two Variables....

Question. Two numbers are in the ratio 3: 4. If 5 is subtracted from each .then the ratio will be 2:3. What is the smallest number?

(A) 15 (B) 18

(C) 20 (D) 24

Answer : (A)

Question. The present age difference between father and son is 14 years. The ratio of their age will be 4:3 after 11 years. How old is son now?

(A) 25 years (B) 31 years

(C) 28 years (D) 30 years

Answer :(B)

Question. The value of K if the linear equations x + 2y = 3 and 5x + ky + 7 = 0 has unique solution is

(A) K ≠ 1 (B) K ≠ 10

(C) K ≠ 5 (D) K ≠ 15

Answer : (B)

Question. 3-years ago, the sum of ages of a father and his son were 40 years. After 2-year, the sum of ages of the father and his son will be__________

(A) 40 (B) 46

(C) 50 (D) 56

Answer : (C)

Question. A boat goes 16 km upstream and 24 km downstream in 6 hours. Also it covers 12 km up stream and 36 km downstream in the same time. Find the speed of the boat in still water?

(A) 8 km/h (B) 4 km/h

(C) 2*1/2 km/h

(D) None of these

Answer : (A)

Question. Sum of the digits of two digit number is 9. The number obtained by interchanging the digit is 18 more than twice the original number. The original number is:

(A) 72 (B) 27

(C) 36 (D) 63

Answer : (B)

Question. In the equations 3x + 2y =13xy and 4x -5y = 2xy , the value of xand y satisfy that the equations are:

(A) (2,3) (B) (3,2)

(C)(1/2 , 1/3)

(D) (1/3 / 1/2)

Answer : (C)

Question. A father is 7 times as old as his son. Two year ago, the father was 13 times as old as his son.

Father’s present age is:

(A) 24 years (B) 28 years

(C) 30 years (D) 32 years

 Answer : (B)

Question. If x + y + 7and3x -2y =11. Then the value of x will be:

(A) 5 (B) 6

(C) 7 (D) 8

Answer : (A)

Question. If 3y -2x = 4and4y - px = 2perpendicular to each other the value of ‘p’ will be:

(A) 3/2

(B) 8/3

(C) 6 (D) -6

Answer : (D)

Question. In a two digit number, the number of ten’s place is double of the number of unit’s place. If we exchange the numbers mutually then the number decrease b 18, then the number is:-

(A) 24 (B) 36

(C) 39 (D) 42

Answer : (D)

Question. The system of equation- x + 2y = 6,3x + 6y =18

(A) Is inconsistent (B) Has an infinite number of solution

(C) Has a unique solution (D) None of these

Answer : (B)

Question. 

Please refer to link below for CBSE Class 10 Mathematics HOTs Pair of Linear Equations in Two Variables Set A

Please refer to attached file for CBSE Class 10 Mathematics HOTs Pair Of Linear Equations In Two Variables

Q1. Does the point(1,-2) lie on the line whose equation is 3x-y-5=0?

Question. A man can row three quarters of a km against the stream in 11 1/4 minutes and return in 7 1/2 minutes. The speed of man in still water is:

(A) 2 km/h

(B) 3 km/h

(C) 4 km/h

(D) 5 km/h

Answer : D

Question. If the system 𝑘𝑥 − 5𝑦 = 2,6𝑥 + 2𝑦 = 7 has no solution, then 𝑘 =
a) -10
b) -5
c) -6
d) -15
Answer : D

Question. If 2𝑥 + 3𝑦 = 0 𝑎𝑛𝑑 4𝑥 – 3𝑦 = 0 then 𝑥 + 𝑦 =
a) 0
b) -1
c) 1
d) 2
Answer : A

Question. If 3𝑥 + 2𝑦 = 13 and 3𝑥 − 2𝑦 = 5 then 𝑥 + 𝑦 =
a) 5
b)3
c) 7
d) 11
Answer : A

Question. The equation 𝑥 − 𝑦 = 0.9 and 11/𝑥 + 𝑦 = 2 have the solution
a) 𝑥 = 5 ,𝑦 = 1
b) 𝑥 = 2.3 ,𝑦 = 3.2
c) 𝑥 = 3,𝑦 = 2
d) 𝑥 = 3.2,𝑦 = 2.3
Answer : D

Question. If (6, k) is a solution of the equation 3𝑥 + 𝑦 = 22 𝑡ℎ𝑒𝑛 𝑘 =
a) - 4
b) 4
c) 3
d) -3
Answer : B

Question. 

 

 

 

Question. If the system of equation3x + y =1,(2k +1) x +(k -1) y = (2k +1) , has no solution, then the value of k is:

(A) 2

(B) 3

(C) - 2

(D) 1

Answer : A

 

Question. If x - y = 3and x + y > 9the least value of ' x ' is:

(A) 6 

(B) 3

(C) 2 

(D) 1

Answer : A

 

Question. A boat whose speed is 18km/hr in still water takes 1 hr more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream.

(A) 8 km/hr 

(B) 6 km/hr

(C) 10 km/hr 

(D) 5.5 km/hr

Answer : B

 

Question. Five years ago the sum of ages of the father and the son was 40 years. In present it's ratio is 4:1, then the present age of father is………..

(A) 30 years 

(B) 40 years

(C) 45 years 

(D) 42 years

Answer : B

 

Question. The sum of two numbers is 100 and one number is two less than twice the other number. Then the numbers are

(A) 34, 66 

(B) 24, 76

(C) 44, 56 

(D) 46, 54

Answer : A

 

Question. It is given that there is no solution to the system x + 2y = 3,ax +by = 4 . Which one of the following is true?

(A) a has a unique value 

(B) b has a unique value

(C) a can have more than one value 

(D) a has exactly two different values

Answer : C

Question. If x=a, y=b is the solution of the equations x-y=2 and x+y=4, then the values of a and b are, respectively
(A) 3 and 5
(B) 5 and 3
(C) 3 and 1
(D) -1 and 3
Answer : C

Question. The larger of the two supplementary angles exceed the smaller by 18°, then the angles are:
(A) 99°, 81°
(B) 98°, 82°
(C) 97°, 83°
(D) None of these.
Answer : A

Question. A pair of linear equation which has a unique solution x=2, y=-3 is
(A) x+y=-1 and 2x-3y=-5
(B) 2x+5y=-11 and 4x+10y=-22
(C) 2x-y=1 and 3x+2y=0
(D) X-4y-14=0 and x-y-13=0
Answer : B AND D

Question. Graphically, the pair of equation
6x-3y+10=0
2x-y+9=0
Represents two lines which are
(A) Intersecting at exactly one point
(B) Intersecting at exactly two point
(C) Coincident
(D) Parallel
Answer : D

Question. In a number of two digits, unit’s digit is twice the tens digit. If 36 be added to the number, the digits are reversed. The number is
(a) 36
(b) 63
(c) 48
(d) 84
Answer : C

Question. If the pair of linear equations a₁x+b₁y+c₁ =0 0and a₂x+b₂y+c₂ =0 has infinite number of solutions then the correct condition is:

(A) a₁/a₂ = b₁/b₂ =c₁/c₂

(B) a₁/a₂ = b₁/b₂ c₁/c₂

(C) a₁/a₂ = b₁/b₂

(D) a₁/a₂ = c₁/c₂

Answer : A