Q 1 – The pair of equations x = a and y = b graphically represents lines which are
(A) parallel
(B) intersecting at (b, a)
(C) coincident
(D) intersecting at (a, b)
Ans. Option (D) is Correct.
Q 2 –The pair of equations y = 0 and y = -7 has :
(A) one solution
(B) two solutions
(C) infinitely many solutions
(D) no solution
Ans. Option (D) is correct
Q 3 – One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be :
(A) 10x + 14y + 4 = 0
(B) -10x-14y+4 = 0
(C) -10x + 14y + 4 = 0
(D) 10x -14y = – 4
Ans. Option (D) is correct.
Q 4 – For what value of k, do the equations 3x – y + 8 =0 and 6x – ky = – 16 represent coincident lines ?
(A) 
(B) 
(C) 2
(D) -2
Ans. Option (C) is correct,
Q 5 – The Given Problem is based on which mathematical concept?
(A) Pair of line equations
(B) Quadratic equations
(C) Polynomials
(D) None of the above
Ans. Option (A) is Correct.
Q 6 – A pair of linear equations which has a unique solution x = 2, y = -3 is:
(A) x + y = -1
2x – 3y = -5
(B) 2x + 5y = -11
4x + 10y = -22
(C) 2x – y = 1 x – 4y -14 = 0
3x + 2y = 0
(D) x-4y-14= 0
x – y – 13 =0
Ans. Option (B) & (D) is correct
Q 7 – Aruna has only 1 and 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is 75, then the number of 1 and 2 coins are, respectively.
(A) 35 and 15
(B) 35 and 20
(C) 15 and 35
(D) 25 and 25
Ans. Option (D) is correct
Q 8 – The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively:
(A) 4 and 24
(B) 5 and 3q
(C) 6 and 36
(D) 3 and 24
Ans. Option (C) is correct.
Q 9 – 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
Ans. Option (C) is correct.
Q 10 – The larger of 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.
Ans. Option (A) is correct.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of
Reason (R). Mark the correct choice as.
(A) Both A and R are true and R is the correct explanation of A
(B) Both A and R are true but R is NOT the correct explanation of A
(C) A is true but R is false
(D) A is false and R is True
Q 11 – Assertion (A): If the pair of linear equations 3x + y = 3 and 6x + ky = 8 does not have a solution, then the value of k = 2.
Reason (R): If the pair of linear equations x + y – 4 = 0 and 2x + ky = 3 does not have a solution, then the value of k = 2.
Ans. Option (B) is correct.
Q 12 – Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.
Reason (R): Two lines are given to he parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.
Ans. Option (D) is correct.
Q 13 – Assertion (A): If the equation 3x – y + 8 = 0 and 6x -ky = -16 represent coincident lines, then the value of k = 2.
Reason (R): If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is 15.
Ans. Option (C) is correct
Q 14 – Assertion (A): If 4 chairs and 3 tables cost 2100 and 5 chairs and 2 tables cost 1750, then the cost of 1 chair is 150.
Reason (R): Sum of the ages of a father and the son is 40 years. It father’s age is 3 times that of his son, then the son’s age is 12 years.
Ans. Option (C) is correct
Q 15 – Assertion (A): The solution of the pair of linear equations x + y = 5 and 2x – 3y = 4 is x = 
and y= {latex}\frac{6}{5}[/latex].
Reason (R): The solution of the pair of linear equations 3x + 4y = 10 and 2x – 2y = 2 is x = 2 and y = 1.
Ans. Option (B) is correct.
Q 16 – Assertion (A): In a .∆ABC, ∠c= 3LB = 2(∠A + ∠B), then ∠A = 20°.
Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.
Ans. Option (B) is correct
Attempt any four sub-parts from each question. Each sub-part carries 1 mark.
Read the following text and answer the following questions on the basis of the same:
It is common that Governments revise travel fares from time to time based on various factors such as inflation ( a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations.
| Name of the city | Distance travelled (kin) | Amount paid (Z) |
| City A | 10 | 75 |
| 15 | 110 | |
| City B | 8 | 9 |
| 14 | 145 |
Situation 1: In city A, for a journey of 10 km, the charge paid is ? 75 and for a journey of 15 kin, the charge paid is Z 110.Situation 2: In a city B, for a journey of 8 km, the charge paid is Z 91 and for a journey of 14 km, the charge paid is Z 145.
Refer situation 1
Q 17 – If the fixed charges of auto rickshaw be x and the running charges be Z y kmihr, the pair of linear equations representing the situation is
(A) x + 10y = 110, x + 15y = 75
(B) x+ 10y =75, x + 15y= 110
(C) 10x + y =110, 15x + y =75
(D) 10x + y = 75, 15x + y =110
Ans. Option (B) is correct
Q 18 – A person travels a distance of 50 km. The amount he has to pay is
(A) Z 155
(B) Z 255
(C) Z 355
(D) Z 455
Ans. Option (C) is correct.
Q 19 – What will a person have to pay for travelling a distance of 30 km ?
(A) Z 185
(B) Z 289
(C) Z 275
(D) Z 305
Ans. Option (B) is correct.
Q 20 – The graph of lines representing the conditions are:
(situation 2)
Ans. Option (C) is correct
Q 21 – What is the relative speed of both cars while they are travelling in the same direction ?
(A) (u + v) km/hr
(B) (u — v) km/hr
(C) (u/v) km/hr
(D) (uv) km/hr
Ans. Option (B) is correct.
Q 22 – What is the relative speed of both cars while they are travelling towards each other ?
(A) (u + v) km/hr
(B) (u — v) km/hr
(C) (u/v) km/hr
(D) (uv) km/hr
Ans. Option (A) is correct
Q 23 – What is the actual speed of one car?
(A) 60 km/hr
(B) 40 km/hr
(C) 100 km/hr
(D) 20 km/hr
Ans. Option (A) is correct
Q 24 – What is the actual speed of other car?
(A) 60 km/hr
(B) 40 km/hr
(C) 100 lun/hr
(D) 20 km/hr
Ans. Option (B) is correct
Q 25 – The given problem is based on which mathematical concept
(A) Pair of linear equations
(B) Quadratic equations
(C) Polynomials
(D) none of the above
Ans. Option (A) is correct
Q 26 – The number of marbles Jivanti had:
(A) 15
(8) 30
(C) 40
(D) 5
Ans. Option (A) is Correct.
Q 27 – The number of marbles John had:
(A) 40
(B) 30
(C) 15
(D) 20
Ans. Option (B) is Correct.
Q 28 – If 45 is replaced by 55 in the above case discussed in the question, then the number of marbles Jivanti have
(A) 15
(B) 30
(C) 20
(D) 35
Ans. Option (C) is correct
Q 29– According to the question 3, the number of marbles John have:
(A) 30
(B) 40
(C) 45
(D) 35
Ans. option (D) is Correct.