{"id":148580,"date":"2021-09-15T17:21:06","date_gmt":"2021-09-15T11:51:06","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=148580"},"modified":"2021-09-15T17:21:06","modified_gmt":"2021-09-15T11:51:06","slug":"quadratic-equation-questions-for-nmat-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/quadratic-equation-questions-for-nmat-pdf\/","title":{"rendered":"Quadratic Equation Questions for NMAT – Download [PDF]"},"content":{"rendered":"

Quadratic Equation Questions for NMAT PDF:<\/strong><\/span><\/h1>\n

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

Download Quadratic Equation Questions for NMAT<\/a><\/p>\n

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

Take NMAT mock test<\/a><\/p>\n

Question 1:\u00a0<\/b>The number of integers that satisfy the equality $(x^{2}-5x+7)^{x+1}=1$ is<\/p>\n

a)\u00a03<\/p>\n

b)\u00a02<\/p>\n

c)\u00a04<\/p>\n

d)\u00a05<\/p>\n

Question 2:\u00a0<\/b>The number of distinct real roots of the equation $(x+\\frac{1}{x})^{2}-3(x+\\frac{1}{x})+2=0$ equals<\/p>\n

Question 3:\u00a0<\/b>How many disticnt positive integer-valued solutions exist to the equation $(X^{2}-7x+11)^{(X^{2}-13x+42)}=1$ ?<\/p>\n

a)\u00a08<\/p>\n

b)\u00a04<\/p>\n

c)\u00a02<\/p>\n

d)\u00a06<\/p>\n

Question 4:\u00a0<\/b>If $x^2 + x + 1 = 0$, then $x^{2018} + x^{2019}$ equals which of the following:<\/p>\n

a)\u00a0$x+1$<\/p>\n

b)\u00a0$x$<\/p>\n

c)\u00a0$-x$<\/p>\n

d)\u00a0$x-1$<\/p>\n

Question 5:\u00a0<\/b>If $U^{2}+(U-2V-1)^{2}$= \u2212$4V(U+V)$ , then what is the value of $U+3V$ ?<\/p>\n

a)\u00a0$0$<\/p>\n

b)\u00a0$\\dfrac{1}{2}$<\/p>\n

c)\u00a0$\\dfrac{-1}{4}$<\/p>\n

d)\u00a0$\\dfrac{1}{4}$<\/p>\n

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

Question 6:\u00a0<\/b>If $x+1=x^{2}$ and $x>0$, then $2x^{4}$\u00a0 is<\/p>\n

a)\u00a0$6+4\\sqrt{5}$<\/p>\n

b)\u00a0$3+3\\sqrt{5}$<\/p>\n

c)\u00a0$5+3\\sqrt{5}$<\/p>\n

d)\u00a0$7+3\\sqrt{5}$<\/p>\n

Question 7:\u00a0<\/b>If $x^{2}$+3x-10is a factor of $3x^{4}+2x^{3}-ax^{2}+bx-a+b-4$ then the closest approximate values of a and b are<\/p>\n

a)\u00a025, 43<\/p>\n

b)\u00a052, 43<\/p>\n

c)\u00a052, 67<\/p>\n

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

Question 8:\u00a0<\/b>If $xy + yz + zx = 0$, then $(x + y + z)^2$ equals<\/p>\n

a)\u00a0$(x + y)^2 + xz$<\/p>\n

b)\u00a0$(x + z)^2 + xy$<\/p>\n

c)\u00a0$x^2 + y^2 + z^2$<\/p>\n

d)\u00a0$2(xy + yz + xz)$<\/p>\n

Question 9:\u00a0<\/b>If the equation $x^3 – ax^2 + bx – a = 0$ has three real roots, then it must be the case that,<\/p>\n

a)\u00a0b=1<\/p>\n

b)\u00a0b $\\neq$ 1<\/p>\n

c)\u00a0a=1<\/p>\n

d)\u00a0a $\\neq$ 1<\/p>\n

Question 10:\u00a0<\/b>If the roots of the equation $x^3 – ax^2 + bx – c = 0$ are three consecutive integers, then what is the smallest possible value of b?[CAT 2008]<\/p>\n

a)\u00a0$\\frac{-1}{\\sqrt 3}$<\/p>\n

b)\u00a0$-1$<\/p>\n

c)\u00a0$0$<\/p>\n

d)\u00a0$1$<\/p>\n

e)\u00a0$\\frac{1}{\\sqrt 3}$<\/p>\n

Join 7K MBA Aspirants Telegram Group<\/a><\/p>\n

Download Highly Rated CAT preparation App<\/a><\/p>\n

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

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

$\\left(x^2-5x+7\\right)^{x+1}=1$<\/p>\n

There can be a solution when\u00a0$\\left(x^2-5x+7\\right)=1$ or $x^2-5x\\ +6=0$<\/p>\n

or x=3 and x=2<\/p>\n

There can also be a solution when x+1 = 0 or x=-1<\/p>\n

Hence three possible solutions exist.<\/p>\n

2)\u00a0Answer:\u00a01<\/b><\/p>\n

Let $a=x+\\frac{1}{x}$
\nSo, the given equation is $a^2-3a+2=0$
\nSo, $a$ can be either 2 or 1.<\/p>\n

If $a=1$, $x+\\frac{1}{x}=1$ and it has no real roots.
\nIf $a=2$, $x+\\frac{1}{x}=2$ and it has exactly one real root which is $x=1$<\/p>\n

So, the total number of distinct real roots of the given equation is 1<\/p>\n

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

$(X^{2}-7x+11)^{(X^{2}-13x+42)}=1$<\/p>\n

if\u00a0$(X^{2}-13x+42)$=0 or\u00a0$(X^{2}-7x+11)$=1 or\u00a0$(X^{2}-7x+11)$=-1 and\u00a0$(X^{2}-13x+42)$ is even number<\/p>\n

For\u00a0X=6,7 the value $(X^{2}-13x+42)$=0<\/p>\n

$(X^{2}-7x+11)$=1 for X=5,2.<\/p>\n

$(X^{2}-7x+11)$=-1 for X=3,4 and for X=3 or 4,\u00a0$(X^{2}-13x+42)$ is even number.<\/p>\n

.’. {2,3,4,5,6,7} is the solution set of X.<\/p>\n

.’. X can take six values.<\/p>\n

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

We know that,<\/p>\n

$x^{3} – 1 = (x – 1)(x^{2} + x + 1)$<\/p>\n

Since,\u00a0$x^2 + x + 1 = 0$<\/p>\n

$\\therefore $\u00a0$x^{3} – 1$ = 0<\/p>\n

=>\u00a0$x^{3}$ = 1<\/p>\n

Now,\u00a0$x^{2018} + x^{2019}$<\/p>\n

=\u00a0$(x^{3})^{672} * x^{2}$ +\u00a0$(x^{3})^{673}$<\/p>\n

=\u00a0$1^{672} * x^{2}$ +\u00a0$1^{673}$<\/p>\n

=\u00a0$x^{2}$ + 1<\/p>\n

= -x<\/p>\n

Hence, option C.<\/p>\n

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

Given that $U^{2}+(U-2V-1)^{2}$= \u2212$4V(U+V)$<\/p>\n

$\\Rightarrow$ $U^{2}+(U-2V-1)(U-2V-1)$= \u2212$4V(U+V)$<\/p>\n

$\\Rightarrow$ $U^{2}+(U^2-2UV-U-2UV+4V^2+2V-U+2V+1)$ =\u00a0\u2212$4V(U+V)$<\/p>\n

$\\Rightarrow$ $U^{2}+(U^2-4UV-2U+4V^2+4V+1)$ =\u00a0\u2212$4V(U+V)$<\/p>\n

$\\Rightarrow$ $2U^2-4UV-2U+4V^2+4V+1=\u22124UV-4V^2$<\/p>\n

$\\Rightarrow$ $2U^2-2U+8V^2+4V+1=0$<\/p>\n

$\\Rightarrow$ $2[U^2-U+\\dfrac{1}{4}]+8[V^2+\\dfrac{V}{2}+\\dfrac{1}{16}]=0$<\/p>\n

$\\Rightarrow$ $2(U-\\dfrac{1}{2})^2+8(V+\\dfrac{1}{4})^2=0$<\/p>\n

Sum of two square terms is zero i.e. individual square term is equal to zero.<\/p>\n

$U-\\dfrac{1}{2}$ = 0 and $V+\\dfrac{1}{4}$ = 0<\/p>\n

U = $\\dfrac{1}{2}$ and\u00a0V = $-\\dfrac{1}{4}$<\/p>\n

Therefore,\u00a0$U+3V$ =\u00a0$\\dfrac{1}{2}$+$\\dfrac{-1*3}{4}$ =\u00a0$\\dfrac{-1}{4}$. Hence, option C is the correct answer.<\/p>\n

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

We know that $x^2 – x – 1=0$
\nTherefore $x^4 = (x+1)^2 = x^2+2x+1 = x+1 + 2x+1 = 3x+2$
\nTherefore, $2x^4 = 6x+4$<\/p>\n

We know that $x>0$ therefore, we can calculate the value of $x$ to be $\\frac{1+\\sqrt{5}}{2}$
\nHence, $2x^4 = 6x+4 = 3+3\\sqrt{5}+4 = 3\\sqrt{5}+7$<\/p>\n

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

If $x^{2}$+3x-10is a factor of $3x^{4}+2x^{3}-ax^{2}+bx-a+b-4$
\nThen x = -5 and x = 2 will give $3x^{4}+2x^{3}-ax^{2}+bx-a+b-4$ = 0
\nSubstituting x = -5 we get,
\n$3(-5)^{4}+2(-5)^{3}-a(-5)^{2}+b(-5)-a+b-4 = 0$
\nSolving we get,
\n$26a+4b = 1621$…….(i)
\nSubstituting x = 2 we get,
\n$3(2)^{4}+2(2)^{3}-a(2)^{2}+b(2)-a+b-4 =0$
\n=> $5a-3b = 60$……..(ii)
\nSolving i and ii we get
\na and b $\\approx 52, 67$
\nHence, option C is the correct answer.<\/p>\n

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

$(x+y+z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + xz)$
\nas $xy+yz+xz = 0$
\nso equation will be resolved to $x^2 + y^2 + z^2$<\/p>\n

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

It can be clearly seen that if b=1 then $x^2(x – a) + (x – a) = 0$ an the equation gives only 1 real\u00a0value\u00a0of x<\/p>\n

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

b = sum of the roots taken 2 at a time.
\nLet the roots be n-1, n and n+1.
\nTherefore, $b = (n-1)n + n(n+1) + (n+1)(n-1) = n^2 – n + n^2 + n + n^2 – 1$
\n$b = 3n^2 – 1$. The smallest value is -1.<\/p>\n

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

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

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

Quadratic Equation Questions for NMAT PDF: Download Quadratic Equation Questions for NMAT PDF. Top 10 very important Quadratic Equation Questions for NMAT based on asked questions in previous exam papers. Take NMAT mock test Question 1:\u00a0The number of integers that satisfy the equality $(x^{2}-5x+7)^{x+1}=1$ is a)\u00a03 b)\u00a02 c)\u00a04 d)\u00a05 Question 2:\u00a0The number of distinct real […]<\/p>\n","protected":false},"author":42,"featured_media":148599,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,3167,125,4977],"tags":[3131,4979,4147],"class_list":{"0":"post-148580","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-featured","11":"category-nmat","12":"tag-nmat","13":"tag-nmat-2021","14":"tag-quadratic-equations"},"better_featured_image":{"id":148599,"alt_text":"NMAT Quadratic Equation Questions","caption":"NMAT Quadratic Equation Questions","description":"NMAT Quadratic Equation 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