RD Sharma solution class 7 chapter 8 Linear Equations In One Variables Objective Type Question

Objective Type Question

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Question 1:

Mark the correct alternative in the following question:

The zero of 3x + 2 is

(a) 23                                     (b) 32                                     (c) -23                                     (d) -32

Answer 1:

If 3x+2=0, then3x=-2          (Transposing +2 to RHS)x=-23

So, the zero of 3x + 2 is -23.

Note: A zero is that number, when put in place of the variable, makes the expression equal to zero.

Hence, the correct alternative is option (c).

Question 2:

Mark the correct alternative in the following question:

If 2x-32=5x+34, then x=(a) 34                                     (b) -34                                     (c) 43                                     (d) -43

Answer 2:

As, 2x-32=5x+342x-5x=32+34           (By transposing -32 to RHS and 5x to LHS)-3x=64+34-3x=6+34x=94×(-3)                 (By transposing -3 to RHS)x=34×(-1)x=3-4 x=-34

Hence, the correct alternative is option (b).

Question 3:

Mark the correct alternative in the following question:

If x2-4=x3-1, then x=(a) 3                                     (b) 6                                     (c) 18                                     (d) 2

Answer 3:

As, x2-4=x3-1x2-x3=4-1             (By transposing x3 to LHS and -4 to RHS)3x6-2x6=33x-2x6=3x6=3x=3×6                    (By transposing 6 to RHS) x=18

Hence, the correct alternative is option (c).

Question 4:

Mark the correct alternative in the following question:

If x+2x-2=23, then x=(a) -10                                     (b) 10                                     (c) 43                                     (d) -43

Answer 4:

As, x+2x-2=233(x+2)=2(x-2)              (By cross multiplication)3x+6=2x-43x-2x=-6+4               (By transposing 2x to LHS and 6 to RHS) x=-10

Hence, the correct alternative is option (a).

Question 5:

Mark the correct alternative in the following question:

If x6+x4=x2+34, then x=(a) 9                                     (b) 6                                     (c) -9                                     (d) 4

Answer 5:

As, x6+x4=x2+34x6+x4-x2=34           (By transposing x2 to LHS)2x12+3x12-6x12=342x+3x-6x12=34-x12=34-x×4=3×12              (By cross multiplication)-4x=36x=36-4 x=-9

Hence, the correct alternative is option (c).

Question 6:

Mark the correct alternative in the following question:

If 2x+53=14x+4, then x=(a) 3                                     (b) 4                                     (c) 34                                     (d) 43

Answer 6:

As, 2x+53=14x+42x-14x=4-53                (By transposing 53 to RHS and 14x to LHS)2x1-x4=41-538x4-x4=123-538x-x4=12-537x4=737x×3=4×7                          (By cross multiplication)21x=28x=2821 x=43

Hence, the correct alternative is option (d).

Question 7:

Mark the correct alternative in the following question:

If x2-x3=5, then x=(a) 8                                     (b) 16                                     (c) 24                                     (d) 30

Answer 7:

As, x2-x3=53x6-2x6=53x-2x6=5x6=5x=5×6         (By transposing 6 to RHS) x=30

Hence, the correct alternative is option (d).

Question 8:

Mark the correct alternative in the following question:

If x-23=2x-13-1, then x=(a) 2                                     (b) 4                                     (c) 6                                     (d) 8

Answer 8:

As, x-23=2x-13-1x-23-2x-13=-1          (By transposing 2x-13 to LHS)(x-2)-(2x-1)3=-1x-2-2x+13=-1-x-13=-1-x-1=-1×3                 (By transposing 3 to RHS)-x-1=-3-x=-3+1                       (By transposing -1 to RHS)-x=-2 x=2

Hence, the correct alternative is option (a).

Question 9:

Mark the correct alternative in the following question:

The sum of two consecutive whole numbers is 43. The smaller number is

(a) 21                                 (b) 22                                 (c) 23                                 (d) 24

Answer 9:

Let the two consecutive whole numbers be x and x+1.As, the sum of the two consecutive whole numbers is 43.x+(x+1)=432x+1=432x=43-1              (By transposing 1 to RHS)2x=42x=422                    (By transposing 2 to RHS) x=21

So, the smaller number is 21.

Hence, the correct alternative is option (a).

Question 10:

Mark the correct alternative in the following question:

The sum of two consecutive odd numbers is 36. The larger number is

(a) 17                                  (b) 15                                  (c) 19                                  (d) 21

Answer 10:

Let the two consecutive odd numbers be x and x+2.As, the sum of the two consecutive odd numbers is 36.x+(x+2)=362x+2=362x=36-22x=34x=342x=17 x+2=17+2=19

So, the larger number is 19.

Hence, the correct alternative is option (c).

Question 11:

Mark the correct alternative in the following question:

Twice a number when increased by 7 gives 25. The number is

(a) 7                                   (b) 9                                   (c) 10                                   (d) 8

Answer 11:

Let the number be x.As, twice the number when increased by 7 gives 25.2x+7=252x=25-7          (By transposing 7 to RHS)2x=18x=182               (By transposing 2 to RHS) x=9

So, the number is 9.

Hence, the correct alternative is option (b).

Question 12:

Mark the correct alternative in the following question:

The length of a rectangle is three times its width and its perimeter 56 m. The length is

(a) 7 m                               (b) 14 m                               (c) 21 m                               (d) 28 m

Answer 12:

Let the width of the rectangle be x. Then,the length of the rectangle=3xAs, perimeter of the rectangle=56 m2×(Length+Breadth)=562×(3x+x)=562×4x=568x=56x=568 x=7So, the length of the rectangle=3x=3×7=21 m

Hence, the correct alternative is option (c).

Question 13:

Mark the correct alternative in the following question:

Two-third of a number is greater than one-third of the number by 5. The number is

(a) 10                                (b) 5                                (c) 15                                (d) 12

Answer 13:

Let the number be x.As, two-third of a number is greater than one-third of the number by 5.23x-13x=52x-x3=5x3=5x=5×3 x=15

So, the number is 15.

Hence, the correct alternative is option (c).

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Question 14:

Mark the correct alternative in the following question:

If the sum of a number and its two-fifth is 70. The number is

(a) 70                                 (b) 50                                 (c) 60                                 (d) 90

Answer 14:

Let the number be x.As, the sum of a number and its two-fifth is 70.x+25x=70x1+2x5=705x5+2x5=705x+2x5=707x5=707x=70×5            (By transposing 5 to RHS)7x=350x=3507               (By transposing 7 to RHS) x=50

So, the number is 50.

Hence, the correct alternative is option (b).

Question 15:

Mark the correct alternative in the following question:

23 of a number is less than the original number by 20. The number is

(a) 30                                  (b) 40                                  (c) 50                                  (d) 60

Answer 15:

Let the number be x.As, 23 of the number is less than the original number by 20.x-23x=20x1-2x3=203x3-2x3=203x-2x3=20x3=20x=20×3            (By transposing 3 to RHS) x=60

So, the number is 60.

Hence, the correct alternative is option (d).

Question 16:

Mark the correct alternative in the following question:

A number is as much greater than 31 as it is less than 81. The number is

(a) 46                                   (b) 56                                   (c) 66                                   (d) 76

Answer 16:

Let the number be x.As, the number is as much greater than 31 as it is less than 81.x-31=81-xx+x=81+31            (By transposing -x to LHS and -31 to RHS)2x=112x=1122                     (By transposing 2 to RHS) x=56

So, the number is 56.

Hence, the correct alternative is option (b).

Question 17:

Mark the correct alternative in the following question:

Two complementary angles differ by 20°. The smaller angle is

(a) 55°                                    (b) 25°                                    (c) 65°                                    (d) 35°

Answer 17:

Let the smaller angle be x. Then,The larger angle=(x+20°)As, the sum of the two complementary angles is always 90°.x+(x+20°)=90°2x+20°=90°2x=90°-20°2x=70°x=70°2                     (By transposing 2 to RHS) x=35°

So, the smaller angle is 35°.

Hence, the correct alternative is option (d).

Question 18:

Mark the correct alternative in the following question:

Two supplementary angles differ by 40°. The measure of the larger angle is

(a) 70°                                     (b) 80°                                     (c) 110°                                     (d) 100°

Answer 18:

Let the larger angle be x. Then,The smaller angle=(x-40°)As, the sum of the two supplementary angles is always 180°.x+(x-40°)=180°2x-40°=180°2x=180°+40°2x=220°x=220°2                     (By transposing 2 to RHS) x=110°

So, the measure of the larger angle is 110°.

Hence, the correct alternative is option (c).

Question 19:

Mark the correct alternative in the following question:

The sum of three consecutive odd numbers is 81. The middle number is

(a) 25                                     (b) 27                                     (c) 31                                     (d) 29

Answer 19:

Let the three consecutive odd numbers be x, x+2 and x+4.As, the sum of the three consecutive numbers is 81.x+(x+2)+(x+4)=813x+6=813x=81-6               (By transposing 6 to RHS)3x=75x=753                     (By transposing 3 to RHS)x=25 x+2=25+2=27

So, the middle number is 27.

Hence, the correct alternative is option (b).

Question 20:

If 2(2n + 5) = 3(3n - 10), then n =

(a) 5                                       (b) 3                                      (c) 7                                      (d) 8

Answer 20:

As, 2(2n+5)=3(3n-10)4n+10=9n-304n-9n=-10-30             (By transposing 10 to RHS and 9n to LHS)-5n=-40n=-40-5                             (By transposing -5 to RHS) n=8

Hence, the correct alternative is option (d).

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