{"id":170781,"date":"2021-10-26T15:06:24","date_gmt":"2021-10-26T09:36:24","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=170781"},"modified":"2021-10-26T15:17:16","modified_gmt":"2021-10-26T09:47:16","slug":"line-graphs-questions-for-nmat-download-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/line-graphs-questions-for-nmat-download-pdf\/","title":{"rendered":"Line Graphs Questions For NMAT – Download [PDF]"},"content":{"rendered":"

Line Graphs Questions for NMAT – Download [PDF]<\/h1>\n

Download Line Graphs Questions for NMAT PDF. Top 10 very important Line Graphs Questions for NMAT based on asked questions in previous exam papers.<\/p>\n

Download Line Graphs Questions for NMAT<\/a><\/p>\n

Get 5 NMAT Mocks for Rs. 499<\/a><\/p>\n

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Question 1:\u00a0<\/b>The area, in sq. units, enclosed by the lines $x=2,y=\\mid x-2\\mid+4$, the X-axis and the Y-axis is equal to<\/p>\n

a)\u00a010<\/p>\n

b)\u00a06<\/p>\n

c)\u00a08<\/p>\n

d)\u00a012<\/p>\n

Question 2:\u00a0<\/b>Determine the value(s) of \u201ca\u201d for which the point $(a, a^{2})$ lies inside the triangle formed by the lines: 2x+ 3y= 1, x+ 2y=3 and 5x-6y= 1<\/p>\n

a)\u00a0(-3,-1) \u22c3 (1\/2, 1)<\/p>\n

b)\u00a0(-\u221e, 1\/3) \u22c3 (1\/2, \u221e)<\/p>\n

c)\u00a0(-3\/2,-1) \u22c3 (1\/2, 1)<\/p>\n

d)\u00a0(-\u221e, 1) \u22c3 (1\/3, 6)<\/p>\n

e)\u00a0None of the above<\/p>\n

Question 3:\u00a0<\/b>When the curves $y = log_{10}x$ and $y = x^{-1}$ are drawn in the x-y plane, how many times do they intersect for values $x \\geq 1$ ?<\/p>\n

a)\u00a0Never<\/p>\n

b)\u00a0Once<\/p>\n

c)\u00a0Twice<\/p>\n

d)\u00a0More than twice<\/p>\n

Question 4:\u00a0<\/b>In the X-Y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 4 is<\/p>\n

a)\u00a08<\/p>\n

b)\u00a012<\/p>\n

c)\u00a016<\/p>\n

d)\u00a020<\/p>\n

Question 5:\u00a0<\/b>The graph of y – x (on the y axis) against y + x (on the x axis) is as shown below. (All graphs in this question are drawn to scale and the same scale and the same scale has been used on each axis.)<\/p>\n

<\/figure>\n

Which of the following shows the graph of y against x?<\/p>\n

a)<\/p>\n

<\/figure>\n

b)<\/p>\n

<\/figure>\n

c)<\/p>\n

<\/figure>\n

d)<\/p>\n

<\/figure>\n
<\/a><\/div>\n

Question 6:\u00a0<\/b>The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is:<\/p>\n

a)\u00a01<\/p>\n

b)\u00a02<\/p>\n

c)\u00a0infinite<\/p>\n

d)\u00a00<\/p>\n

Question 7:\u00a0<\/b>The figure below shows the graph of a function f(x). How many solutions does the equation f(f(x)) = 15 have?<\/p>\n

<\/figure>\n

a)\u00a05<\/p>\n

b)\u00a06<\/p>\n

c)\u00a07<\/p>\n

d)\u00a08<\/p>\n

e)\u00a0cannot be determined from the given graph<\/p>\n

Question 8:\u00a0<\/b>Find the equation of the graph shown below.<\/p>\n

<\/figure>\n

a)\u00a0y = 3x – 4<\/p>\n

b)\u00a0y = $2x^{2}$ – 40<\/p>\n

c)\u00a0x = $2y^{2}$ – 40<\/p>\n

d)\u00a0y = $2x^{2}$ + 3x – 19<\/p>\n

e)\u00a0x = $2y^{2}$ + 3x – 19<\/p>\n

Question 9:\u00a0<\/b>Let g(x) = max(5 – x, x + 2). The smallest possible value of g(x) is<\/p>\n

a)\u00a04.0<\/p>\n

b)\u00a04.5<\/p>\n

c)\u00a01.5<\/p>\n

d)\u00a0None of the above<\/p>\n

Question 10:\u00a0<\/b>The area bounded by the three curves |x+y| = 1, |x| = 1, and |y| = 1, is equal to:<\/p>\n

a)\u00a04<\/p>\n

b)\u00a03<\/p>\n

c)\u00a02<\/p>\n

d)\u00a01<\/p>\n

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

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

<\/figure>\n

The required figure is a trapezium with vertices A(0,0), B(2,0), C(2,4) and D(0,6)<\/p>\n

AB = 2 BC = 4 and AD = 6<\/p>\n

Area of trapezium =\u00a0$\\frac{1}{2}\\left(sum\\ of\\ the\\ opposite\\ sides\\right)\\cdot height$ =\u00a0$\\frac{1}{2}\\left(4+6\\right)\\cdot2\\ =\\ 10$<\/p>\n

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

Let us draw the diagram first,<\/p>\n

Let L$_{1}$:\u00a02x+ 3y -1 = 0<\/p>\n

L$_{2}$: x+ 2y -3 = 0<\/p>\n

L$_{3}$: 5x-6y- 1 = 0<\/p>\n

<\/figure>\n

With respect to\u00a0L$_{1}$, we can see that the point\u00a0$(a, a^{2})$ lies within the triangle and (0, 0) are opposite side. Therefore,<\/p>\n

L$_{(a, a^2)}$*\u00a0L$_{(0, 0)}$ < 0<\/p>\n

$\\Rightarrow$ $(2a+ 3a^2-1)(-1)<0$<\/p>\n

$\\Rightarrow$ $(3a^2+2a-1)>0$<\/p>\n

$\\Rightarrow$ a < -1 or a > $\\frac{1}{3}$\u00a0 \u00a0… (1)<\/p>\n

With respect to\u00a0L$_{2}$, we can see that the point\u00a0$(a, a^{2})$ lies within the triangle and (0, 0) are on the same side. Therefore,<\/p>\n

L$_{(a, a^2)}$*\u00a0L$_{(0, 0)}$ > 0<\/p>\n

$\\Rightarrow$ $(a+ 2a^2-3)(-3)>0$<\/p>\n

$\\Rightarrow$ $(2a^2+a-3)<0$<\/p>\n

$\\Rightarrow$ $\\frac{-3}{2}$ < a < 1\u00a0 … (2)<\/p>\n

With respect to\u00a0L$_{3}$, we can see that the point\u00a0$(a, a^{2})$ lies within the triangle and (0, 0) are on the same side. Therefore,<\/p>\n

L$_{(a, a^2)}$*\u00a0L$_{(0, 0)}$ > 0<\/p>\n

$\\Rightarrow$ $(5a- 6a^2-1)(-1)>0$<\/p>\n

$\\Rightarrow$ $(6a^2-5a+1)>0$<\/p>\n

$\\Rightarrow$ a < $\\frac{1}{3}$ or a > $\\frac{1}{2}$\u00a0 \u00a0… (3)<\/p>\n

From equation (1), (2) and (3) we can say that<\/p>\n

a $\\epsilon$ (-3\/2,-1) \u22c3 (1\/2, 1). Hence, option C is the correct answer.<\/p>\n

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

Graph of logx goes on increasing in 1st quadrant and graph of 1\/x goes no decreasing with both intersecting only once<\/p>\n

\"\"<\/p>\n

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

If the moduli are removed, the equations formed are<\/p>\n

x+y+x-y = 4 => x=2<\/p>\n

x+y-x+y = 4 => y =2<\/p>\n

-x-y+x-y = 4 => y=-2<\/p>\n

-x-y-x+y = 4 => x=-2<\/p>\n

The area enclosed by these equations is a square with vertices at (2,2), (-2,2), (-2,-2), (2,-2) as shown in figure.<\/p>\n

<\/p>\n

The required area = 4*4 = 16<\/p>\n

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

For a normal graph with y and x-axis, the equation of the line passing through the origin is y =mx where m is the slope of the line.<\/p>\n

m is +ve if the angle made by the line with the x-axis is <\u00a0$90^{\\circ\\ }$<\/p>\n

$\\therefore\\ $ The equation of the line in the given graph would be y-x = k( y+\u00a0x) since the axes are y-x and y+x and the line is passing through the origin.<\/p>\n

k > 1 because the angle is greater than 45$^{\\circ\\ }$<\/p>\n

$y=\\frac{k\\left(x+1\\right)}{1-k}$<\/p>\n

Since k>1<\/p>\n

Therefore y<0 for x>-1 and y>0 for x<-1<\/p>\n

Option d correctly satisfy this condition<\/p>\n

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

<\/figure>\n

The graphs of\u00a0$2^{x}+2^{-x} and 2-(x-2)^{2}$ never intersect. So, number of solutions=0.<\/p>\n

Alternate method:<\/strong><\/p>\n

We notice that the minimum value of the term in the LHS will be greater than or equal to\u00a02 {at x=0;\u00a0LHS = 2}. However, the term in the RHS is less than or equal to 2 {at x=2; RHS = 2}. The values of x\u00a0at which both the sides become 2 are distinct; hence, there are zero real-valued solutions to the above equation.<\/p>\n

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

It has been given that f(f(x)) = 15.
\nFrom the graph, we can see that the value of f(4) = 15 and f(12) = 15
\nTherefore, f(x) can be 4 or 12.<\/p>\n

<\/figure>\n

When f(x) = 4, x can take 4 values
\nWhen f(x) = 12, x can take 3 values.
\nTherefore, there are 4+3 = 7 solutions in total.
\nTherefore, option\u00a0C is the right answer.<\/p>\n

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

When x\u00a0 = -3, y = -10
\nThis is satisfied only in option D.<\/p>\n

Hence, option D is the correct answer.<\/p>\n

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

Smallest possible value would be at 5-x = x+2 i.e. x= 1.5 as shown\"\"<\/p>\n

Substituting we get smallest value as 3.5.<\/p>\n

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

|x| = 1 and |y| = 1 form a square of area = 2*2 = 4 sq units<\/p>\n

|x+y| = 1 forms a set of parallel lines cutting the axes at (1,0), (0,1), (-1,0) and (0,-1). The graph is as shown:<\/p>\n

<\/p>\n

The area bounded by the three curves is 2*2 – 1\/2*1*1*2 = 4 – 1 = 3 sq units<\/p>\n

Get 5 NMAT Mocks for Rs. 499<\/a><\/p>\n

<\/a><\/div>\n

We hope this Line Graphs Questions for NMAT pdf for NMAT exam will be highly useful for your Preparation.<\/p>\n","protected":false},"excerpt":{"rendered":"

Line Graphs Questions for NMAT – Download [PDF] Download Line Graphs Questions for NMAT PDF. Top 10 very important Line Graphs Questions for NMAT based on asked questions in previous exam papers. Take NMAT mock test Question 1:\u00a0The area, in sq. units, enclosed by the lines $x=2,y=\\mid x-2\\mid+4$, the X-axis and the Y-axis is equal […]<\/p>\n","protected":false},"author":32,"featured_media":172693,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,3167,4977],"tags":[5115,4979],"class_list":{"0":"post-170781","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-downloads-en","10":"category-nmat","11":"tag-line-graphs","12":"tag-nmat-2021"},"better_featured_image":{"id":172693,"alt_text":"NMAT Line Graphs Questions PDF","caption":"NMAT Line Graphs Questions PDF","description":"NMAT Line Graphs Questions 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