## RS Aggarwal Class 10 Solutions Chapter 3 Linear equations in two variables MCQS

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables MCQS.

### RS Aggarwal Solutions Class 10 Chapter 3

- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3A
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3B
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3C
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3D
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3E
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3F
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables MCQS
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Test Yourself

**Choose the correct answer in each of the following questions.**

**Question 1.**

**If 2x + 3y = 12 and 3x – 2y = 5 then**

**(a) x = 2, y = 3**

**(b) x = 2, y = -3**

**(c) x = 3, y = 2**

**(d) x = 3, y = -2**

**Solution:**

**(c)**

**Question 2.**

**If x – y = 2 and then**

**(a) x = 4, y = 2**

**(b) x = 5, y = 3**

**(c) x = 6, y = 4**

**(d) x = 7, y = 5**

**Solution:**

**(c)**

**Question 3.**

**Solution:**

**(a)**

**Question 4.**

**Solution:**

**(d)**

**Question 5.**

**Solution:**

**(a)**

**Question 6.**

**Solution:**

**(b)**

**Question 7.**

**If 4x + 6y = 3xy and 8x + 9y = 5xy then**

**(a) x = 2, y = 3**

**(b) x = 1, y = 2**

**(c) x = 3, y = 4**

**(d) x = 1, y = -1**

**Solution:**

**(c)** 4x + 6y = 3xy, 8x + 9y = 5xy

Dividing each term by xy,

**Question 8.**

**If 29x + 37y = 103 and 37x + 29y = 95 then**

**(a) x = 1, y = 2**

**(b) x = 2, y = 1**

**(c) x = 3, y = 2**

**(d) x = 2, y = 3**

**Solution:**

**(a)**

**Question 9.**

**(c) 0**

**(d) none of these**

**Solution:**

**(c)**

**Question 10.**

**Solution:**

**(b)**

**Question 11.**

**The system kx – y = 2 and 6x – 2y = 3 has a unique solution only when**

**(a) k = 0**

**(b) k ≠ 0**

**(c) k = 3**

**(d) k ≠ 3**

**Solution:**

**(d)**

**Question 12.**

**The system x – 2y = 3 and 3x + ky = 1 has a unique solution only when**

**(a) k = -6**

**(b) k ≠ -6**

**(c) k = 0**

**(d) k ≠ 0**

**Solution:**

**(b)**

**Question 13.**

**The system x + 2y = 3 and 5x + ky + 7 = 0 has no solution, when**

**(a) k =10**

**(b) k ≠ 10**

**(c) k = **

**(d) k = -21**

**Solution:**

**(a)**

**Question 14.**

**If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel then the value of k is**

**(a) **

**(b) **

**(c) **

**(d) **

**Solution:**

**(d)**

**Question 15.**

**For what value of k do the equations kx – 2y = 3 and 3x + y = 5 represent two lines intersecting at a unique point?**

**(a) k = 3**

**(b) k = -3**

**(c) k = 6**

**(d) all real values except -6**

**Solution:**

**(d)**

**Question 16.**

**The pair of equations x + 2y + 5 = 0 and -3x – 6y + 1 = 0 has**

**(a) a unique solution**

**(b) exactly two solutions**

**(c) infinitely many solutions**

**(d) no solution**

**Solution:**

**(d)**

**Question 17.**

**The pair of equations 2x + 3y = 5 and 4x + 6y = 15 has**

**(a) a unique solution**

**(b) exactly two solutions**

**(c) infinitely many solutions**

**(d) no solution**

**Solution:**

**(d)**

**Question 18.**

**If a pair of linear equations is consistent then their graph lines will be**

**(a) parallel**

**(b) always coincident**

**(c) always intersecting**

**(d) intersecting or coincident**

**Solution:**

**(d)** The system of equations is consistent then their graph lines will be either intersecting or coincident.

**Question 19.**

**If a pair of linear equations is inconsistent then their graph lines will be**

**(a) parallel**

**(b) always coincident**

**(c) always intersecting**

**(d) intersecting or coincident**

**Solution:**

**(a)** The pair of lines of equation is inconsistent then the system will not have no solution i.e., their lines will be parallel.

**Question 20.**

**In a ∆ABC, ∠C = 3∠B = 2 (∠A + ∠B), then ∠B = ?**

**(a) 20°**

**(b) 40°**

**(c) 60°**

**(d) 80°**

**Solution:**

**(b)**

**Question 21.**

**In a cyclic quadrilateral ABCD, it is being given that ∠A = (x + y + 10)°, ∠B = (y + 20)°, ∠C = (x + y – 30)° and ∠D = (x + y)°. Then, ∠B = ?**

**(a) 70°**

**(b) 80°**

**(c) 100°**

**(d) 110°**

**Solution:**

**(b)** ABCD is a cyclic quadrilateral

∠A = (x + y + 10)°, ∠B = (y + 20)°, ∠C = (x + y – 30)° and ∠D = (x + y)°

∠A + ∠C = 180°

Now, x + y + 10°+ x + y – 30° = 180°

⇒ 2x + 2y – 20 = 180°

⇒ 2x + 2y = 180° + 20° = 200°

⇒ x + y = 100° …(i)

and ∠B + ∠D = 180°

⇒ y + 20° + x + y = 180°

⇒ x + 2y = 180° – 20° = 160° …(ii)

Subtracting,

-y = -60° ⇒ y = 60°

and x + 60° = 100°

⇒ x = 100° – 60° = 40°

Now, ∠B = y + 20° = 60° + 20° = 80°

**Question 22.**

**The sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. The number is**

**(a) 96**

**(b) 69**

**(c) 87**

**(d) 78**

**Solution:**

**(d)** Let one’s digit of a two digit number = x

and ten’s digit = y

Number = x + 10y

By interchanging the digits,

One’s digit = y

and ten’s digit = x

Number = y + 10x

According to the conditions,

x + y = 15 …(i)

y + 10x = x + 10y + 9

⇒ y + 10x – x – 10y = 9

⇒ 9x – 9y = 9

⇒ x – y = 1 …(ii)

Adding (i) and (ii),

2x = 16 ⇒ x = 8

and x + y = 15

⇒ 8 + y = 15

⇒ y = 15 – 8 = 7

Number = x + 10y = 8 + 10 x 7 = 8 + 70 = 78

**Question 23.**

**In the given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator, it becomes . If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes . The fraction is**

**(a) **

**(b) **

**(c) **

**(d) **

**Solution:**

**(b)** Let the numerator of a fractions = x

and denominator = y

**Question 24.**

**5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is**

**(a) 45 years**

**(b) 50 years**

**(c) 47 years**

**(d) 40 years**

**Solution:**

**(d)** Let present age of man = x years

and age of his son = y years

5 years hence,

Age of man = (x + 5) years

and age of son = y + 5 years

(x + 5) = 3 (y + 5)

⇒ x + 5 = 3y + 15

x = 3y + 15 – 5

x = 3y + 10 ……(i)

and 5 years earlier

Age of man = x – 5 years

and age of son = y – 5 years

x – 5 = 7 (y – 5)

x – 5 = 7y – 35

⇒ x = 7y – 35 + 5

x = 7y – 30 ……….(ii)

From (i) and (ii),

7y – 30 = 3y + 10

⇒ 7y – 3y = 10 + 30

⇒ 4y = 40

y = 10

x = 3y + 10 = 3 x 10 + 10 = 30 + 10 = 40

Present age of father = 40 years

**Question 25.**

**The graphs of the equations 6x – 27 + 9 = 0 and 3x – 7 + 12 = 0 are two lines which are**

**(a) coincident**

**(b) parallel**

**(c) intersecting exactly at one point**

**(d) perpendicular to each other**

**Solution:**

**(b)**

**Question 26.**

**The graphs of the equations 2x + 3y – 2 = 0 and x – 27 – 8 = 0 are two lines which are**

**(a) coincident**

**(b) parallel**

**(c) intersecting exactly at one point**

**(d) perpendicular to each other**

**Solution:**

**(c)**

**Question 27.**

**The graphs of the equations 5x – 15y = 8 and 3x – 9y = are two lines which are**

**(a) coincident**

**(b) parallel**

**(c) intersecting exactly at one point**

**(d) perpendicular to each other**

**Solution:**

**(a)**

The system has infinitely many solutions.

The lines are coincident.

Hope given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables MCQS are helpful to complete your math homework.

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