{"id":40984,"date":"2020-03-04T17:04:16","date_gmt":"2020-03-04T11:34:16","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=40984"},"modified":"2020-03-04T17:04:16","modified_gmt":"2020-03-04T11:34:16","slug":"linear-equations-questions-for-ssc-cgl-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/linear-equations-questions-for-ssc-cgl-pdf\/","title":{"rendered":"Linear Equations Questions for SSC CGL PDF"},"content":{"rendered":"

Linear Equations Questions for SSC CGL PDF<\/strong><\/span><\/h1>\n

Download SSC CGL Questions on Linear Equations\u00a0 PDF based on previous papers very useful for SSC CGL Exams. Top-15 Very Important Linear Equations Questions for SSC CGL Exam.<\/p>\n

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Question 1:\u00a0<\/b>If $\\frac{\\sqrt{a+2b}+\\sqrt{a-2b}}{\\sqrt{a+2b} – \\sqrt{a-2b}}=\\frac{\\sqrt{3}}{1}$, find the value of $\\frac{a}{b}$<\/p>\n

a)\u00a0$2:\\sqrt{3}$<\/p>\n

b)\u00a0$\\sqrt{3}:4$<\/p>\n

c)\u00a0$\\sqrt{3}:2$<\/p>\n

d)\u00a0$4:\\sqrt{3}$<\/p>\n

Question 2:\u00a0<\/b>A point in the 4th quadrant is 6 unit away from x-axis and 7 unit away from y-axis. The point is at<\/p>\n

a)\u00a0(7, -6)<\/p>\n

b)\u00a0(-7, 6)<\/p>\n

c)\u00a0(-6, -7)<\/p>\n

d)\u00a0(-6, 7)<\/p>\n

Question 3:\u00a0<\/b>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<\/p>\n

a)\u00a09, 7, 15, 17<\/p>\n

b)\u00a04, 12, 12, 20<\/p>\n

c)\u00a05, 11, 13, 19<\/p>\n

d)\u00a06, 10, 14, 18<\/p>\n

Question 4:\u00a0<\/b>The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is<\/p>\n

a)\u00a05<\/p>\n

b)\u00a03<\/p>\n

c)\u00a04<\/p>\n

d)\u00a07<\/p>\n

Question 5:\u00a0<\/b>If x = 332, y = 332, z = 332, then the value of $x^3 + y^3 + z^3 – 3xyz$ is<\/p>\n

a)\u00a010000<\/p>\n

b)\u00a00<\/p>\n

c)\u00a08000<\/p>\n

d)\u00a09000<\/p>\n

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Question 6:\u00a0<\/b>2x- ky + 7 = 0 and 6x- 12y+ 15 = 0 has no solution for<\/p>\n

a)\u00a0k=- 1<\/p>\n

b)\u00a0k=- 4<\/p>\n

c)\u00a0k = 4<\/p>\n

d)\u00a0k = 1<\/p>\n

Question 7:\u00a0<\/b>A number exceeds its two fifth by 75. The number is<\/p>\n

a)\u00a0125<\/p>\n

b)\u00a0112<\/p>\n

c)\u00a0100<\/p>\n

d)\u00a0150<\/p>\n

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Question 8:\u00a0<\/b>Given that $x^{3} + y^{3} = 72$ and $xy = 8$ with $x > y$. Then the value of $(x – y)$ is<\/p>\n

a)\u00a04<\/p>\n

b)\u00a0-4<\/p>\n

c)\u00a02<\/p>\n

d)\u00a0-2<\/p>\n

Question 9:\u00a0<\/b>If the sum of two numbers, one of which is $\\frac{2}{5}$ times the other, is 50, then the numbers are<\/p>\n

a)\u00a0$\\frac{115}{7}$ and $\\frac{235}{7}$<\/p>\n

b)\u00a0$\\frac{150}{7}$ and $\\frac{200}{7}$<\/p>\n

c)\u00a0$\\frac{240}{7}$ and $\\frac{110}{7}$<\/p>\n

d)\u00a0$\\frac{250}{7}$ and $\\frac{100}{7}$<\/p>\n

Question 10:\u00a0<\/b>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<\/p>\n

a)\u00a012<\/p>\n

b)\u00a020<\/p>\n

c)\u00a015<\/p>\n

d)\u00a018<\/p>\n

Question 11:\u00a0<\/b>The area of the triangle formed by the graphs of the equations x= 0, 2x+ 3y= 6 and x+ y= 3 is :<\/p>\n

a)\u00a03 sq. unit<\/p>\n

b)\u00a0$4\\frac{1}{2}$ sq. unit<\/p>\n

c)\u00a0$1\\frac{1}{2}$ sq. unit<\/p>\n

d)\u00a01 sq. unit<\/p>\n

Question 12:\u00a0<\/b>The graphs of x = a and y = b intersect at<\/p>\n

a)\u00a0(a, b)<\/p>\n

b)\u00a0(b, a)<\/p>\n

c)\u00a0(-a, b)<\/p>\n

d)\u00a0(a, -b)<\/p>\n

Question 13:\u00a0<\/b>The area in sq. unit. of the triangle formed by the graphs ofx= 4, y= 3 and 3x+ 4y= 12 is<\/p>\n

a)\u00a012<\/p>\n

b)\u00a08<\/p>\n

c)\u00a010<\/p>\n

d)\u00a06<\/p>\n

Question 14:\u00a0<\/b>The equations 3x+ 4y = 10 -x+ 2y = 0 have the solution (a, b). The value of a + b is<\/p>\n

a)\u00a01<\/p>\n

b)\u00a02<\/p>\n

c)\u00a03<\/p>\n

d)\u00a04<\/p>\n

Question 15:\u00a0<\/b>If $2x+3y=\\frac{5}{6} and $xy=\\frac{5}{6}$ then the value of $8x^{3}+27y^{3}$ is<\/p>\n

a)\u00a0$583$<\/p>\n

b)\u00a0$\\frac{583}{4}$<\/p>\n

c)\u00a0$187$<\/p>\n

d)\u00a0$\\frac{671}{8}$<\/p>\n

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Answers & Solutions:<\/strong><\/span><\/p>\n

1)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

here in this question $\\frac{\\sqrt{a+2b}+\\sqrt{a-2b}}{\\sqrt{a+2b-}\\sqrt{a-2b}}=\\frac{\\sqrt{3}}{1}$<\/p>\n

using componendo and dividendo, we will get<\/p>\n

$\\frac{\\sqrt(a+2b)}{\\sqrt(a-2b)} = \\frac{\\sqrt3 + 1 }{\\sqrt3 – 1}$<\/p>\n

now on squaring both side and solving, we will get<\/p>\n

16 b = 4a$\\surd3$<\/p>\n

$\\frac{a}{b}$ = $\\frac{4}{\\surd3}$<\/p>\n

2)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

A point in the 4th quadrant will be in the form of $(x,-y)$<\/p>\n

Since, the point is 6 units away from x axis, => y coordinate = 6<\/p>\n

and the point is 7 units away from y axis, => x coordinate = 7<\/p>\n

=> Point = (7,-6)<\/p>\n

3)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

Let the numbers be $a,b,c,d$<\/p>\n

=> $a+b+c+d$ = 48 ——–Eqn(1)<\/p>\n

When 5 & 1 are added to first two, => $(a+5) and (b+1)$<\/p>\n

and when 3 & 7 are subtracted from last two, => $(c-3) and (d-7)$<\/p>\n

According to question :<\/p>\n

=> $a+5 = b+1 = c-3 = d-7 = k$ (let)<\/p>\n

Now, in eqn(1)<\/p>\n

$(a+5) + (b+1) + (c-3) + (d-7)$ = 48 + (5+1-3-7)<\/p>\n

=> $k+k+k+k$ = 48-4<\/p>\n

=> $k$ = 11<\/p>\n

=> Numbers are : $a = k-5 = 11-5 = 6$<\/p>\n

Similarly, $b$ = 10<\/p>\n

$c$ = 14<\/p>\n

$d$ = 18<\/p>\n

4)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

Equation : $3x + 4y = 12$<\/p>\n

To find $x$-intercept, put $y$=0<\/p>\n

=> $3x + 0 = 12$<\/p>\n

=> $x$ = 4<\/p>\n

Similarly to find $y$-intercept, we need to put $x$ = 0<\/p>\n

=> $0 + 4y = 12$<\/p>\n

=> $y$ = 3<\/p>\n

Thus, the line passes through (4,0) in x-axis and (0,3) in y-axis<\/p>\n

Using, $d = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$<\/p>\n

=> $x_1 = 0 , x_2 = 4 , y_1 = 0 , y_2 = 3$<\/p>\n

=> $d = \\sqrt{4^2 + 3^2}$<\/p>\n

=> $d = \\sqrt{25} = 5$<\/p>\n

5)\u00a0Answer\u00a0(B)<\/strong><\/p>\n

when x = y = z= 332 , then $(x^2 + y^2 + z^2 – xy – yz – xz)$ = 0<\/p>\n

and hence $x^3 + y^3 + z^3 – 3xyz$ = 0 as $x^3 + y^3 + z^3 – 3xyz$ = (x+y+z) $(x^2 + y^2 + z^2 – xy – yz – xz)$<\/span><\/p>\n

and hence the answer for this question is = 0<\/p>\n

6)\u00a0Answer\u00a0(C)<\/strong><\/p>\n

NOTE : – For the pair of equations : $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$<\/p>\n

The equations have no solution only if : $\\frac{a_1}{a_2} = \\frac{b_1}{b_2} \\neq \\frac{c_1}{c_2}$<\/p>\n

Equations : $2x- ky + 7 = 0$ and $6x- 12y+ 15 = 0$<\/p>\n

Comparing with above formula, we get :<\/p>\n

=> $\\frac{2}{6} = \\frac{-k}{-12}$<\/p>\n

=> $\\frac{k}{12} = \\frac{1}{3}$<\/p>\n

=> $k = 4$<\/p>\n

7)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

Let the number be $x$<\/p>\n

Acc to ques :<\/p>\n

=> $x – \\frac{2}{5}x = 75$<\/p>\n

=> $\\frac{3x}{5} = 75$<\/p>\n

=> $x = 125$<\/p>\n

8)\u00a0Answer\u00a0(C)<\/strong><\/p>\n

Given : $x^{3} + y^{3} = 72$ and $xy = 8$<\/p>\n

Solution : $(x+y)^3 = x^3 + y^3 + 3xy(x+y)$<\/p>\n

=> $(x+y)^3 = 72 + 3.8(x+y)$<\/p>\n

=> $(x+y)^3 – 24(x+y) – 72 = 0$<\/p>\n

This is a cubic equation in terms of $(x+y)$ which has one real root = 6<\/p>\n

=> $x+y = 6$<\/p>\n

Now, $(x-y)^2 = (x+y)^2 – 4xy$<\/p>\n

=> $(x-y) = \\sqrt{6^2 – 4*8} = \\sqrt{4}$<\/p>\n

=> $(x-y) = 2$<\/p>\n

9)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

Let the number be $x$<\/p>\n

=> Other number will be $\\frac{2x}{5}$<\/p>\n

Acc to ques :<\/p>\n

=> $x$ + $\\frac{2x}{5}$ = 50<\/p>\n

=> $7x$ = 250<\/p>\n

=> $x$ = $\\frac{250}{7}$<\/p>\n

and second number = $\\frac{2}{5} * \\frac{250}{7} = \\frac{100}{7}$<\/p>\n

10)\u00a0Answer\u00a0(B)<\/strong><\/p>\n

Let the number be $x$<\/p>\n

Acc to ques :<\/p>\n

=> $\\frac{3x}{4} = \\frac{x}{6} + 7$<\/p>\n

=> $\\frac{14x}{24} = 7$<\/p>\n

=> $x = 12$<\/p>\n

=> $\\frac{5}{3}$ of the number = $\\frac{5}{3}$ * 12 = 20<\/p>\n

11)\u00a0Answer\u00a0(C)<\/strong><\/p>\n

<\/p>\n

AC represents $x+y=3$<\/p>\n

BC represents $2x+3y=6$<\/p>\n

AB represents $x=0$<\/p>\n

=> ABC is the required triangle.<\/p>\n

Base AB = 1 unit and height OC = 3 units<\/p>\n

=> Area of $\\triangle$ABC = $\\frac{1}{2}$ * AB * OC<\/p>\n

= $\\frac{1}{2}$ * 1 * 3 = 1$\\frac{1}{2}$ sq. unit<\/p>\n

12)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

<\/p>\n

Clearly, the lines x = a and y = b meets at a point (a,b)<\/p>\n

13)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

Clearly, x=4 is a vertical line passing through (4,0) and y=3 is a horizontal line passing through the point (0,3)
\nThe line 3x+ 4y= 12 also passes through (4,0) and (0,3) .
\nHence, it is a right angled triangle with base=4 units and height=3 units.
\nThe area of the triangle is = $\\frac{1}{2}bh$
\n= $\\frac{1}{2}\\times4\\times3$
\n=6 units<\/p>\n

14)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

3x + 4y = 0 —> (1)
\nx – 2y = 10
\n$(x – 2y = 10)\\times2$
\n2x – 4y = 20 —> (2)
\n5x = 20
\nx = 4
\ny = -3
\nx + y = 1<\/p>\n

15)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

$2x+3y=\\frac{11}{2}$<\/p>\n

cubing on both sides<\/p>\n

$(2x+3y)^{3}=(\\frac{11}{2})^{3}$<\/p>\n

$8x^{3}+27y^{3}+3(2x)(8y)(2x+3y)=\\frac{1331}{8}$<\/p>\n

$8x^{3}+27y^{3}+3(16xy)(2x+3y)=\\frac{1331}{8}$<\/p>\n

$8x^{3}+27y^{3}+3(16(\\frac{5}{6})(\\frac{5}{6})=\\frac{1331}{8}$<\/p>\n

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We hope this Linear Equations Questions for SSC CGL Exams will be highly useful for your preparation.<\/p>\n","protected":false},"excerpt":{"rendered":"

Linear Equations Questions for SSC CGL PDF Download SSC CGL Questions on Linear Equations\u00a0 PDF based on previous papers very useful for SSC CGL Exams. Top-15 Very Important Linear Equations Questions for SSC CGL Exam. Question 1:\u00a0If $\\frac{\\sqrt{a+2b}+\\sqrt{a-2b}}{\\sqrt{a+2b} – \\sqrt{a-2b}}=\\frac{\\sqrt{3}}{1}$, find the value of $\\frac{a}{b}$ a)\u00a0$2:\\sqrt{3}$ b)\u00a0$\\sqrt{3}:4$ c)\u00a0$\\sqrt{3}:2$ d)\u00a0$4:\\sqrt{3}$ Question 2:\u00a0A point in the 4th […]<\/p>\n","protected":false},"author":49,"featured_media":40989,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3167,125,9,504,378,1493,1459,1611,1741,1441],"tags":[3687,462],"class_list":{"0":"post-40984","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-downloads-en","8":"category-featured","9":"category-ssc","10":"category-ssc-cgl","11":"category-ssc-chsl","12":"category-ssc-cpo","13":"category-ssc-gd","14":"category-ssc-je","15":"category-ssc-mts","16":"category-stenographer","17":"tag-linear-equation-questions","18":"tag-ssc-cgl"},"better_featured_image":{"id":40989,"alt_text":"Linear Equations Questions for SSC CGL PDF","caption":"Linear Equations Questions for SSC CGL PDF","description":"Linear Equations Questions for SSC CGL 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