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

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 2

Which of the following is not a quadratic equation?

Question 3

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 4

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

Question 5

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 6

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 7

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 8

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 9

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 10

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

Question 11

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 12

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

Question 13

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

Question 14

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 15

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 16

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

Question 17

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

Question 18

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

Question 19

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 20

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

Question 21

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

Question 22

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 23

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 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

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 26

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

Question 27

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 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

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 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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 47

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

Question 48

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

Question 49

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 50

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

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