Linear Equations Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

The equations kx – y = 2 and 6x – 2y = 3 have a unique solution. Then,

∴ $k/6 ≠ 1/2$ ⇒ k ≠ 3

Answer: (c)

Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.

Let the number of spades be x. Then, number of clubs = (7 – x).

Number of diamonds = 2 x number of spades = 2x;

Number of hearts = 2 x number of diamonds = 4x.

Total number of cards = x + 2x + 4x + 7 – x – 6x + 7.

Therefore 6x + 7 = 13⇔6x = 6⇔x – 1.

Hence, number of clubs = (7 – x) = 6.

Answer: (c)

Given that x + $1/x$ = 2 ... (i)

Squaring both sides, we get

$(x + 1/x)^2$ = 4

⇒ $x^2 + 1/{x^2}$ + 2 = 4

⇒ $x^2 + 1/{x^2}$ = 2 ... (ii)

Now, $(x - 1/x)^2 = (x^2 + 1/{x^2})$ – 2

= 2 – 2 = 0 [from equation (ii)]

∴ x – $1/x$ = 0

Answer: (c)

Given that,

2x – 3y = 5 ... (i)

and –4x + 6y = 11 ... (ii)

Also, ${a_1}/{a_2} = 2/{-4} = {-1}/2$

${b_1}/{b_2} = {-3}/6 = {-1}/2$

⇒${a_1}/{a_2} ={b_1}/{b_2} = {-1}/2 ≠ {c_1}/{c_2}$

So, both equations are in parallel. So, it is not solved graphically.

Hence, A and R are individually true and R is correct explanation of A.

Answer: (c)

Let there be (x + 1) members. Then,

Father's share = $1/4$ , share of each other member = $3/{4x}$.

∴ 3 $(3/{4x}) = 1/4$⇔4x = 36⇔x=9

Hence, total number of family member = 10.

Answer: (b)

Let the two-digit number be 10y + x.

According to question,

x + y = 10 ... (i)

and 10y + x – 18 = 10x + y

⇒9x – 9y = –18

⇒x – y = –2 ... (ii)

On solving equations (i) and (ii), we get

x = 4 and y = 6

∴ Required product = xy = 4 × 6 = 24.