 # SSC Linear Equations Questions with Answers

#### Linear Equations

An excellent collection of SSC Linear equations questions and answers with detailed explanations for competitive exams. Given below are some of the most repeated practice questions on Linear equations for SSC CGL, CHSL, JE, GD constable, Stenographer, MTS, and CPO exams. Go through this very important online quiz based on model and previous year asked questions from SSC Linear equations with solutions to ace the exam.

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Instructions

For the following questions answer them individually

Question 1

The graphs of x = a and y = b intersect at

Question 2

If the sum of two numbers, one of which is $$\frac{2}{5}$$ times the other, is 50, then the numbers are

Question 3

The total cost of 8 buckets and 5 mugs is 92 and the total cost of 5 buckets and 8 mugs is 77. Find the cost of 2 mugs and 3 buckets.

Question 4

The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is

Question 5

If x + (1/x) = 2, then what is the value of $$x^{64}+x^{121}$$ ?

Question 6

The area of the triangle formed by the graphs of the equations x= 0, 2x+ 3y= 6 and x+ y= 3 is :

Question 7

If a+b+c=27, then what is the value of $$(a-7)^{3}+(b - 9)^{3}+(c - 11)^{3}-3(a - 7)(b - 9)(c - 11)$$ ?

Question 8

The straight line 2x + 3y = 12 passes through :

Question 9

If x = 332, y = 332, z = 332, then the value of $$x^3 + y^3 + z^3 - 3xyz$$ is

Question 10

2x- ky + 7 = 0 and 6x- 12y+ 15 = 0 has no solution for

Question 11

A point in the 4th quadrant is 6 unit away from x-axis and 7 unit away from y-axis. The point is at

Question 12

A number exceeds its two fifth by 75. The number is

Question 13

If $$x,y,z \neq 0$$ and $$\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{1}{z^{2}}$$ = $$\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}$$ then the relation among x, y, z is

Question 14

If a* b= a+ b+ a/b, then the value of 12 * 4 is :

Question 15

If $$x^{2}+y^{2}+z^{2}=2(x-y-z)-3$$, then the value of $$2x-3y+4z$$ is [Assume that x, y, z are all real numbers) :

Question 16

If a + b+c= 0, then the value $$(\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b})$$ $$(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b})$$ is:

Question 17

If a, b, c are non-zero, $$a+\frac{1}{b}=1$$ and $$b+\frac{1}{c}=1$$ then the value of abc is :

Question 18

The equations 3x+ 4y = 10 -x+ 2y = 0 have the solution (a, b). The value of a + b is

Question 19

Find the maximum number of trees which can be planted, 20 metres apart, on the two sides of a straight road 1760 metres long

Question 20

The mean of 20 items is 55. If two items 45 and 30 are removed, the new mean of the remaining items is

Question 21

If $$\frac{3}{4}$$ of a number is 7 more then $$\frac{1}{6}$$ of the number, then $$\frac{5}{3}$$ of the number is

Question 22

If $$\frac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b} - \sqrt{a-2b}}=\frac{\sqrt{3}}{1}$$, find the value of $$\frac{a}{b}$$

Question 23

The area in sq. unit. of the triangle formed by the graphs ofx= 4, y= 3 and 3x+ 4y= 12 is

Question 24

Mohan gets 3 marks for each correct sum and loses 2 marks for each wrong sum. He attempts 30 sums and obtains 40 marks. The number of sums solved correctly is

Question 25

Find the roots of the quadratic equation : $$27x^2 + 57x - 14 = 0$$

Question 26

If $$x = k^{3} - 3k^{2}$$ and $$y= 1 - 3k,$$ then for what value of $$k$$. will be $$x= y$$?

Question 27

The sum of four numbers is 48. When 5 and 1 are added to the first two; and 3 and 7 are subtracted from the 3rd and 4th, all the four numbers will be equal. The numbers are

Question 28

A three­ digit number 4a3 is added to another three ­digit number 984 to give the four digit­ number 13b7 which is divisible by 11. Then the value of (a+b) is:

Question 29

A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes 5/6 . What is the fraction ?

Question 30

If $$x^{3}+\frac{3}{x}=4(a^{3}+b^{3})$$ and $$3x+\frac{1}{x^3}=4(a^{3}-b^{3})$$, then $$a^{2}-b^{2}$$ is equal to

Question 31

If $$x=3t, y=\frac{1}{2} (t+1)$$ then the value of t for which $$x=2y$$ is

Question 32

The value of a machine depreciates every year at the rate of 10% on its value at the beginning of that year. If the current value of the machine is r 729, its worth 3years ago was:

Question 33

If $$x^{2} - y^{2} = 80$$ and x- y= 8, then the average of x and y is

Question 34

The total cost of 8 buckets and 5 mugs is 92 and the total cost of 5 buckets and 8 mugs is 77. Find the cost of 2 mugs and 3 buckets.

Question 35

If $$\frac{4x}{3}+2p=12$$ for what value of $$p, x=6$$ ?

Question 36

The mean of 50 numbers is 30. Later it was discoverd that two entries were wrongly entered as 82 and 13 instead of 28 and 31. Find the correct mean.

Question 37

What will be the roots of the quadratic equation $$x^2 - 25x + 156 = 0$$?

Question 38

The graphs of 2x + 1 = 0 and 3y- 9 = 0 intersect at the point

Question 39

Given that $$x^{3} + y^{3} = 72$$ and $$xy = 8$$ with $$x > y$$. Then the value of $$(x - y)$$ is

Question 40

When 7 is subtracted from thrice a number, the result is 14. What is the number ?

Question 41

If (a + b + c) = 0, then $$(\frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab})$$ is

Question 42

If 50% of (x - y) = 30% of (x + y), then what per cent of x is y?

Question 43

If $$a^{2} + b^{2} + c^{2} + 3 = 2 (a- b - c)$$, then the value of $$2 a - b + c$$ is :

Question 44

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Litres of liquid A contained by the can initially was

Question 45

If 4x/3 + 2P = 12, for what value of P, x = 6?

Question 46

Which of the following is not a quadratic equation?

Question 47

If x and y are positive real numbers and xy = 8, then the minimum value of 2x + y is

Question 48

If sum of the roots of a quadratic equation is ­7 and product of the roots is 12. Find the quadratic equation.

Question 49

If $$\dfrac{x^{2}}{yz}+\dfrac{y^{2}}{zx}+\dfrac{z^{2}}{xy}=3$$, then what is the value of $$(x+y+z)^{3}$$ ?

Question 50

If $$2x+3y=\frac{11}{2}$$ and $$xy=\frac{5}{6}$$ then the value of $$8x^{3}+27y^{3}$$ is