Here you will find NCERT MCQ Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables with Answers PDF Free Download based on the important concepts and topics given in the textbook as per CBSE new exam pattern. This may assist you to understand and check your knowledge about the Chapter 3 Pair of Linear Equations in Two Variables. Students also can take a free test of the Multiple Choice Questions of Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables. Each question has four options followed by the right answer. These MCQ Questions are selected supported by the newest exam pattern as announced by CBSE.

## Q1. 10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys who took part in the quiz.

(a) 3

(b) 7

(c) 2

(d) 8

(a) 3 No. of boys = x and No. of girls = y x + y =10 y = x + 4 x = 3 y = 7 => Number of boys = 3

## Q2. Area of figure OABC is (in square units):

(a) 1

(b) 2

(c) 3

(d) 4

(d) 4 Area of figure OABC = 4 square units => Correct option is (d).

## Q3. If x + 5y = 34 and x – 5y = – 6, find the value of 5y – 2x.

(a) – 8

(b) 14

(c) 8

(d) 20

(a) – 8 x + 5y = 34 x – 5y = – 6 x=14 Solving these, x = 14; y = 4 => Correct option is (a).

## Q4. 5 pencils and 7 pens together cost Rs. 50 whereas 7 pencils and 5 pens cost Rs. 46. Find the cost of 2 pencils and 3 pens.

(a) Rs. 42

(b) Rs. 39

(c) Rs. 21

(d) Rs. 16

(c) Rs. 21 Let, cost of 1 pencil = x and cost of 1 pen = y – 2 Cost of 2 pencil and 3 pens = 6 +15 = Rs. 21 => Correct option is (c)

## Q5. An equation ax + by + c = 0 is a linear equation in 2 variables, where a, b, c are :

(a) natural numbers

(b) whole numbers

(c) integers

(d) real numbers

(d) real numbers

## Q6. A linear equation in two variables has:

(a) 1 solution

(b) 2 solutions

(c) no solution

(d) infinitely many

(d) infinitely many A linear equation in two variables has infinite number of solutions. => Correct option is (d)

## Q7. In a AABC, ?A = x°, ?B = (3a – 2)° and ?C = y°. Also, ?C – ?B = 9°. Find the value of ?B.

(a) 73°

(b) 82°

(c) 25°

(d) 49°

(a) 73° ?A + ?B + ?C = 180° => x + (3x – 2) + y = 180 4x + y = 182 …(1) y – 3x + 2 = 9 …(2) Solving (1) & (2), y = 82, x = 25° => ?B = 73°

## Q8. The perimeter of a rectangle is 44 cm. Its length exceeds twice its breadth by 4 cm. Find the area of the rectangle.

(a) 46 cm²

(b) 49 cm²

(c) 96 cm²

(d) 69 cm²

(c) 96 cm² Let, Length = x cm Breadth = y cm => 2(x + y) = 44 => x + y =221, y = 6 cm ,x = 16 cm x = 2y+4 => Area = 16 x 6 = 96 cm²

## Q9. For what value of k, will the equations, x + 2y + (11 – k) = 0 and 2x + ky + (10 + k) = 0 represent the coincident lines :

(a) k = 12

(b) k = 4

(c) k = 36

(d) k = 2

(b) k = 4

## Q10. A pair of linear equations is not consistent if:

(a) if has one solution

(b) it has many solutions

(c) graph intersect or coincide

(d) graph is parallel

(d) graph is parallel 37. Correct option is (d)

## Q11. The pair of equations y = 9 and y = – 7 has:

(a) one solution

(b) two solutions

(c) infinitely many

(d) no solution solutions

(d) no solution solutions y = 9 and y = – 7 are lines parallel to X-axis, thus these are parallel lines and hence no solution

## Q12. In a triangle, the sum of two angles is equal to the third angle. If the difference between two angles is 30°, find the angles.

(a) 15°, 45°, 75°

(b) 20°, 50°, 80°

(c) 30°, 60°, 90°

(d) 45°, 45°, 90°

(c) 30°, 60°, 90° (x) + (y) + (x + y) 180° x + y = 90° x – y = 30° => x = 60°, y = 30° => Angles are 30°, 60° and 90°

## Q13. The line x – y + 1 = 0 meets Y-axis at:

(a) (0,1)

(b) (4,0)

(c) (2,3)

(d) (0,6)

(a) (0,1) Correct option is (a).

## Q14. The solutions of the system of equations, x – y + 1 = 0, 3x + 2y -12 = 0 is :

(a) (0,1)

(b) (4,0)

(c) (2,3)

(d) (0,6)

(c) (2,3) Since the two lines meet at (2, 3) Correct option is (c).

## Q15. The sum of a two digit number is 8. The number obtained by reversing the digits exceeds the number by 18. Then the given number is :

(a) 53

(b) 35

(c) 26

(d) 62

(b) 35 Let, the digit at units’ place = x and digit at ten’s place = y => x + y = 8 and lOx + y = 18 + (10y + x) No. = 35.

## Q16. Equation of line m is :

(a) x = – 2

(b) x = 2

(c) y = 2

(d) y = – 2

(c) y = 2 y = 2 => Correct option is (c).

## Q17. The figure obtained by lines l, m, X-axis and Y-axis, can not be the :

(a) square

(b) rectangle

(c) trapezium

(d) triangle

(d) triangle The figure obtained is square. Since every square is a rectangle and is a trapezium also. Thus, the wrong name is triangle => Correct option is (d).

## Q18. Coordinates of A, B, C (in order) are:

(a) (2,0), (2,-2) (0,-2)

(b) (0,2), (-2,2), (-2,0)

(c) (-2,0), (2,2), (0,-2)

(d) (0,2), (2,2), (0,-2)

(b) (0,2), (-2,2), (-2,0) A(0,2), B(-2,2), C(-2,0). => Correct option is (b).

## Q19. Find the values of x and y if ABCD is a cyclic quadrilateral, ?A = 6x + 10°, ?B = (5x)°, ?C = (x + y)° (?D)=(3y-10)°.

(a) x = 30°, y = 20°

(b) x = 20°, y = 30°

(c) x = 40°, y = 10°

(d) x = 10°, y = 40°

(b) x = 20°, y = 30° ABCD is cyclic => ?A + ?C = 180° and ?B + ?D = 180° => 6x + 10 + x + y = 180° => 7x + y = 170° 5x + 3y – 10 = 180° => 5x + 3y = 190° x = 20°, y = 30° => Correct option is (b)

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