2

Q1. Solve 3x + (-1 + 2) = x + 3? 

• 1) -1
• 2) 1
• 3) 2
• 4) -2

Solution

3x +1 = x +3 ∴2x=2 ∴x=1 

Q2. A theater charges Rs.70 for each evening show and Rs.50 for matinees. On one particular day, 1200 tickets were sold. Also, the number of people who watched evening shows on that day was 30 more than twice the number of people who watched matinee show. How many of each type of ticket did they sell and what is the money incurred from the evening shows?

Solution

Let the number of matinee tickets = x Number of tickets for evening show = 30 + 2x Total number of tickets = x + (30 + 2x) Given that the total number of tickets = 1200 x + (30 + 2x) = 1200 3x + 30 = 1200 3x = 1200 - 30 3x = 1170 x = 390 So number of tickets for the matinee show = 390 Number of tickets for the evening show = 30 + (2 × 390) = 30 + 780 = 810 Money incurred from the evening show = 810 × 70 = Rs.56700

Q3. The perimeter of a rectangle is 30cm. If its breadth is 3cm, then its length is 

• 1) 6
• 2) 9
• 3) 12
• 4) 3

Solution

Perimeter = 2l+2b ∴ 30=2l+ 2 × 3, since b=3 cm ∴ 2l = 30 - 6  ∴ Length = 12 cm 

Q4. The sum of the numbers is 25.One of the numbers is twice the other. Which of the following expressions is true?

• 1) y = x + 25
• 2) x + 2x = 25
• 3) 2x = 25
• 4) x + x = 25

Solution

Let one number be x, then other will be 2x. According to the condition: x+ 2x=25

Q5. 4p - 11 - p = 2 + 2p - 20.So, the value of p is 

• 1) None of the above
• 2) -7
• 3) 0
• 4) 7

Solution

4p - 11 - p = 2 + 2p - 20 ∴ 4p - p - 2p = 2 - 20 + 11 ∴ p = -7

Q6. A linear equation in one variable has

• 1) More than two solutions
• 2) Two solutions
• 3) Only one solution
• 4) No solution

Solution

A linear equation in one variable has only one solution. 

Q7. Rakesh is 5 years younger than Suresh. What is the age of Suresh?

• 1) 5x
• 2) 5 - x
• 3) None of the above
• 4) X + 5

Solution

Let Rakesh’s age be x, then Suresh’s age will be x + 5.

Q8. Which of the following is a linear equation?  

• 1)
• 2)
• 3) None of the above
• 4)

Solution

A linear equation has the maximum power of variable as ‘one’. 

Q9. In 2x - 4 = 6, x=?

• 1) 6
• 2) 1
• 3) 2
• 4) 5

Solution

2x - 4 =6, ∴x=5 

Q10. In x = 0, comparing with ax + b=c, we get a, b, c =? 

• 1) 1, 1, 0
• 2) 0, 1, 1
• 3) 0, 1,0
• 4) 1, 0, 0

Solution

We have x = 0. Comparing with ax + b = c, we get a=1, b=0 and c=0.

Q11. In an election, 25025 villagers voted for one of two candidates for Panchayat President. If the winner received 14 votes more than three fourth votes that loser got, how many votes were received by the winner?

• 1) 10733
• 2) 3573
• 3) 6242
• 4) 14292

Solution

Q12.    

• 1) 1  
• 2) 16  
• 3)  
• 4) 2  

Solution

 

Q13. Two sisters bought 20 pens together. One bought 8 pens. How many pens did the other sister buy?

• 1) 20
• 2) 12
• 3) 8
• 4) None of the above

Solution

One bought 8 pens, so let the second sister buy x pens. ∴ According to the condition, ∴ 8 + x = 20 ∴ x = 12

Q14. The sum of two consecutive natural numbers is 45.Find the numbers. (Use y to represent ‘the numbers’.)

• 1) None of the above
• 2) 21,22
• 3) 19,20
• 4) 23,22

Solution

The consecutive natural numbers are y and y + 1. ∴ y+y+1=45  ∴ 2y=44 ∴ y = 22 and y+1 =23

Q15. Which of the following is not a linear equation of the for max + b = c,

• 1) 3x-5=0
• 2)
• 3) X = 2
• 4) 4x=8

Solution

A linear equation in one variable is an equation of the form ax + b = c, .

Q16.

• 1)
• 2) 2
• 3) 4
• 4)

Solution

Q17. When 10 is added to six times a number, the result is 22. Find the number.

• 1) 1
• 2) 4
• 3) 3
• 4) 2

Solution

Let the number be x. ∴10+6x=22 ∴ 6x= 12 ∴ x = 2 

Q18. Solve for z:    

• 1) 16  
• 2)  
• 3) 2  
• 4) 1  

Solution

   

Q19. What is the value of x, if −1 - (2 - x) = 2 - (3x + 1)?

• 1) -1
• 2) 0
• 3) 1
• 4) None of the above

Solution

−1−2+x=2−3x−1 ∴ x + 3x = 3+ 1 ∴ 4x = 4 ∴ x = 1

Q20. A linear equation in one variable is an equation of the form

• 1) ax + b = c,
• 2) ax + b = c,
• 3) ax + b = c,
• 4) ax + b = c,

Solution

A linear equation in one variable is an equation of the for max + b = c, .

Q21. Sarita's parents give her pocket money according to her grades. For each grade "A", they add Rs 12 to her monthly pocket money and for each grade "C", they subtract Rs 5. In her recent examination, she got only "A's" and "C's" in her 6 subjects. If she got a total of Rs 21 as her pocket money, then find in how many subjects she got grade "A" and grade "C"?

Solution

Let the number of subjects in which Sarita got A grades be x. Then, the number of subjects in which she got grade C would be (6-x) Total money that Sarita got on securing grade A = 12x Total money that Sarita got on securing grade C = -5(6-x) Now, total pocket money that Sarita got after her recent exams = Rs 21 Therefore, we hae: 12x + [-5(6-x)] = 21 12x - 30 + 5x = 21 17x = 30 + 21 17x = 51 x = 3 Number of subjects in which Sarita got grade A is 3 and number of subjects in which she got grade C is (6 - 3) = 3.

Q22. In a linear equation, the maximum power of the variable appearing in the equation is one 

• 1) Always
• 2) None of the above
• 3) Most of the time
• 4) Never

Solution

In a linear equation, the maximum power of the variable appearing in the equation is one always. 

Q23. If 8x - 3 = 25 + 17x, then x is 

• 1) 28
• 2) Cannot be solved
• 3)
• 4) 3

Solution

8x - 3 = 25 + 17x  ∴−9x = 28 ∴ x =

Q24. In 20 - 7x = 6x - 6, x =?

• 1) 2
• 2) 1
• 3) -2
• 4) -2

Solution

20 - 7x = 6x - 6 ∴ -7x -6x = -6 -20 ∴ -13x = -26 ∴ x = 2

Q25. Solve 3(2x - 1) + x - 9 = 11x.

• 1) 1
• 2) -1
• 3) 3
• 4) -3

Solution

3(2x - 1) + x - 9 = 11x ∴ 6x-3+x - 9=11x ∴ 7x - 11x = 12 ∴ -4x = 12 ∴ x = -3

Q26. Which of the following is a linear equation in one variable?

• 1) X = 2
• 2)
• 3) =0
• 4)

Solution

A linear equation in one variable is an equation of the form ax + b = c, ; maximum power of x is one. 

Q27.

• 1) 2
• 2) 3
• 3) -2
• 4) 1

Solution

Q28. Which of the following is not a linear equation in one variable?

• 1) 7x + 5 = 0
• 2) 8 = 9y
• 3)
• 4) 4x = 8

Solution

A linear equation has maximum power of variable as ‘one’.

Q29. The smallest side of a triangle is 5 cm less than one-third of the biggest side. The smallest side is also 3 cm less than half of the third side. If the perimeter of the triangle is 39 cm, then find the three sides of the triangle.

Solution

Let the smallest side of the triangle be x cm. From the given information, x = Biggest side = 3x+15 Also, x = Third side = 2x+6 Perimeter of triangle = Smallest side + biggest side + third side Perimeter = x+ (3x+15) + (2x+6) = 39 6x +21 = 39 6x = 39-21 6x = 18 x = 3 Smallest side = 3 cm Biggest side = 3x+15 = (3×3)+15 = 24 cm Third side = 2x+6 = (2×3) + 6 = 12 cm

Q30. Find the value of x satisfying the equation. Also, verify the solution.

Solution

  Verification: L.H.S=R.H.S Hence, Verified

Q31. Solve for x:

Solution

(Transposing ½ to RHS) (Transposing x to LHS) (L.C.M of 8 and 2 = 8) Dividing both sides by 2, we get

Q32. Solve for x: 2x + 3x - 3 =

Solution

2x + 3x - 3 = 2x + 3x = ……... (Transposing 3 to RHS) Dividing both sides by 5,