Question

If a pair of linear equations in two variables is consistent, then the lines represented by two

equations are

(a) intersecting (b) parallel

(c) always coincident (d) intersecting or coincident

Q.2 If the system of equations 2x + 3y =5, 4x + ky =10 has infinitely many solutions, then k =

(a) 1 (b)

2

1

(c) 3 (d) 6

Q.3 The pair of equations ax + 2y =7 and 3x + by =16 represent parallel lines if

(a) a = b (b) 3a =2b (c) 2a = 3b (d) ab =6

Q.4 The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the number

get reversed. The number is

(a) 25 (b) 72 (c) 63 (d) 36

Q.5 In a  ABC, C = 3 B =2 (A + B) then A, B and C are

(a) 200

, 400

, 1200

(b) 400

, 400

, 1000

(c) 600

, 900

, 400

(d) None of these

Q.6 In the given figure ABCD is a rectangle. The value of x and y is

(a) x = 22 cm & y = 14 cm (b) x = 14 cm & y = 22 cm

(c) x = 24 cm & y = 10 cm (d) None of these

Q.7 For what value of k, do the equation 3x – y +8 = 0 and 6x – ky = -16 represent coincident

lines?

(a)

2

1

(b)

2

1

(c) 2 (d) None of these

Q.8 Which of the pair of linear equations have no solution?

(a) x+y = 6 ; 2x + 2y = 12 (b) 2x + y = 3; 3x + 4y =9

(c) 2x + 3y = 6 ; 4x + 6y = 9 (d) None of these​

Answer 1

1.If a pair of linear equations in two variables is consistent, then the lines represented by two

equations are

(a) intersecting (b) parallel

(c) always coincident (d) intersecting or coincident

$Option \: \green { (d) } \: is \: correct$

Q.2 If the system of equations 2x + 3y =5, 4x + ky =10 has infinitely many solutions, then k =

(a) 1 (b)

2

1

(c) 3 (d) 6

$Compare \: 2x + 3y - 5 = 0 \:and \\4x+ky-10 = 0 \:with \: a_{1}x + b_{1}y + c_{1} = 0 \: and \\a_{2}x + b_{2}y + c_{2} = 0,we \: get$

$a_{1} = 2 , \: b_{1} = 3 \: and \: c_{1} = -5$

$a_{2} = 4 , \: b_{2} = k \: and \: c_{2} = -10$

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \\\blue { Given \:( Coincident \: lines )}$

$\implies \frac{2}{4} = \frac{3}{k}$

$\implies k = \frac{3 \times 4 }{2}$

$\implies k = 6$

Therefore.,

$Option \: pink { ( d) } \:is \: correct.$

•••♪

Answer 2

Answer:

Find the sum of 7+ 10\frac{1}{2}10

2

1

+ 14 + ... + 84