{"id":36615,"date":"2019-10-24T19:04:54","date_gmt":"2019-10-24T13:34:54","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=36615"},"modified":"2019-10-24T19:04:54","modified_gmt":"2019-10-24T13:34:54","slug":"polynomial-questions-for-cat","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/polynomial-questions-for-cat\/","title":{"rendered":"Polynomial Questions for CAT"},"content":{"rendered":"

Polynomial Questions for CAT<\/strong><\/span><\/h2>\n

Download important Polynomial Questions for CAT PDF based on previously asked questions in CAT exam. Practice Polynomial Questions PDF for CAT exam.<\/p>\n

Download Polynomial Questions for CAT<\/a><\/p>\n

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Download CAT Quant Questions PDF<\/a><\/p>\n

Take Free Mock Test for CAT<\/a><\/p>\n

Question 1:\u00a0<\/b>If $f_{1}(x)=x^{2}+11x+n$ and $f_{2}(x)=x$, then the largest positive integer n for which the equation $f_{1}(x)=f_{2}(x)$ has two distinct real roots is<\/p>\n

Question 2:\u00a0<\/b>If $f(x^2 – 1) = x^4 – 7x^2 + k_1$ and $f(x^3 – 2) = x^6 – 9x^3 +k_2$ then the value of $(k_2 – k_1)$ is<\/p>\n

a)\u00a06<\/p>\n

b)\u00a07<\/p>\n

c)\u00a08<\/p>\n

d)\u00a09<\/p>\n

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

Question 3:\u00a0<\/b>Let $f(x) = ax^2 – b|x|$ , where a and b are constants. Then at x = 0, f(x) is
\n[CAT 2004]<\/p>\n

a)\u00a0maximized whenever a > 0, b > 0<\/p>\n

b)\u00a0maximized whenever a > 0, b < 0<\/p>\n

c)\u00a0minimized whenever a > 0, b > 0<\/p>\n

d)\u00a0minimized whenever a > 0, b< 0<\/p>\n

Take a free mock test for CAT<\/a><\/p>\n

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Question 4:\u00a0<\/b>If $f(x)=x^3-4x+p$ , and f(0) and f(1) are of opposite signs, then which of the following is necessarily true[CAT 2004]<\/p>\n

a)\u00a0-1 < p < 2<\/p>\n

b)\u00a00 < p < 3<\/p>\n

c)\u00a0-2 < p < 1<\/p>\n

d)\u00a0-3 < p < 0<\/p>\n

Question 5:\u00a0<\/b>Let $f(x) = ax^2 + bx + c$, where a, b and c are certain constants and $a \\neq 0$ ?It is known that $f(5) = – 3f(2)$. and that 3 is a root of $f(x) = 0$.What is the other root of f(x) = 0?[CAT 2008]<\/p>\n

a)\u00a0-7<\/p>\n

b)\u00a0– 4<\/p>\n

c)\u00a02<\/p>\n

d)\u00a06<\/p>\n

e)\u00a0cannot be determined<\/p>\n

Question 6:\u00a0<\/b>Let $f(x) = ax^2 + bx + c$, where a, b and c are certain constants and $a \\neq 0$ ?It is known that f(5) = – 3f(2). and that 3 is a root of f(x) = 0.What is the value of a + b + c?[CAT 2008]<\/p>\n

a)\u00a09<\/p>\n

b)\u00a014<\/p>\n

c)\u00a013<\/p>\n

d)\u00a037<\/p>\n

e)\u00a0cannot be determined<\/p>\n

Question 7:\u00a0<\/b>Let $f(x) = x^{2}$ and $g(x) = 2^{x}$, for all real x. Then the value of f[f(g(x)) + g(f(x))] at x = 1 is<\/p>\n

a)\u00a016<\/p>\n

b)\u00a018<\/p>\n

c)\u00a036<\/p>\n

d)\u00a040<\/p>\n

Download CAT Quant Questions PDF<\/a><\/p>\n

Crash course to Cracku CAT<\/a><\/p>\n

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

1)\u00a0Answer:\u00a024<\/b><\/p>\n

$f_{1}(x)=x^{2}+11x+n$ and\u00a0$f_{2}(x) = x$
\n$f_{1}(x)=f_{2}(x)$
\n=> $x^{2}+11x+n = x$
\n=> $ x^2 + 10x + n = 0 $
\n=> For this equation to have distinct real roots, b$^2$-4ac>0
\n$ 10^2 > 4n$
\n=> n < 100\/4
\n=> n < 25
\nThus, largest integral value that n can take is 24.<\/p>\n

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

$f(x^2 – 1) = x^4 – 7x^2 + k_1$<\/p>\n

Put $x^2 = 1$ to make it 0<\/p>\n

=> $f(0) = (1)^2 – 7(1) + k_1 = k_1 – 6$ ——–(i)<\/p>\n

Also,\u00a0$f(x^3 – 2) = x^6 – 9x^3 +k_2$<\/p>\n

Put $x^3 = 2$<\/p>\n

=> $f(0) = (2)^2 – 9(2) + k_2 = k_2 – 14$ ———–(ii)<\/p>\n

Equating (i) & (ii), we get\u00a0:<\/p>\n

=> $k_1 – 6 = k_2 – 14$<\/p>\n

=> $k_2 – k_1 = 14 – 6 = 8$<\/p>\n

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

$f(x) = ax^2 – b|x|$. When $x=0, f(x) = 0$
\nWhen $a > 0$ and $b < 0$,
\nFor x > 0, $f(x) = ax^2 – bx$, will be greater than 0 as $ax^2 > 0$ and $bx<0$ as $b$ is negative and $x$ is positive.
\nFor x < 0, $f(x) = ax^2 + bx$ will again be greater than 0 as $ax^2 >0$ and $bx>0$ as both $b$ and $x$ are negative.<\/p>\n

Therefore, the function $f(x)$ is positive when $x<0$ and when $x>0$ but becomes 0 when $x=0$.<\/p>\n

Therefore, for $a > 0$ and $b < 0$, f(x) will attain its minimum value at $x = 0$.<\/p>\n

Free CAT Practice – Study Material\u00a0<\/a><\/p>\n

Download CAT Quant Formulas PDF<\/a><\/p>\n

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

f(1) = 1-4+p = p-3
\nf(0) = p
\nSince they are of opposite signs, p(p-3) < 0
\n=> 0 < p < 3<\/p>\n

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

f(3) = 9a + 3b + c = 0 f(5) = 25a + 5b + c
\nf(2) = 4a + 2b + c
\nf(5) = -3f(2) => 25a + 5b + c = -12a -6b -3c
\n=> 37a + 11b + 4c = 0 –> (1)
\n4(9a + 3b + c) = 36a + 12b + 4c = 0 –> (2)
\nFrom (1) and (2), a – b = 0 => a = b
\n=> c = -12a
\nThe equation is, therefore, $ax^2 + ax – 12a = 0 => x^2 + x – 12 = 0$
\n=> -4 is a root of the equation.<\/p>\n

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

f(3) = 9a + 3b + c = 0 f(5) = 25a + 5b + c
\nf(2) = 4a + 2b + c
\nf(5) = -3f(2) => 25a + 5b + c = -12a -6b -3c
\n=> 37a + 11b + 4c = 0 –> (1)
\n4(9a + 3b + c) = 36a + 12b + 4c = 0 –> (2)
\nFrom (1) and (2), a – b = 0 => a = b
\n=> c = -12a
\nThe equation is, therefore, $ax^2 + ax – 12a = 0 => x^2 + x – 12 = 0$
\na + b + c = a + a – 12a = -10a.
\nBut the value of a is not given. Therefore, the value cannot be determined.<\/p>\n

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

$f[f(g(1)) + g(f(1))]$
\n= $f[f(2^1) + g(1^2)]$
\n= $f[f(2) + g(1)]$
\n= $f[2^2 + 2^1]$
\n= $f(6)$
\n= $6^2 = 36$<\/p>\n

Download CAT Previous Papers PDF<\/a><\/p>\n

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We hope this Polynomial Questions PDF for CAT with Solutions will be helpful to you.<\/p>\n","protected":false},"excerpt":{"rendered":"

Polynomial Questions for CAT Download important Polynomial Questions for CAT PDF based on previously asked questions in CAT exam. Practice Polynomial Questions PDF for CAT exam. Download CAT Quant Questions PDF Take Free Mock Test for CAT Question 1:\u00a0If $f_{1}(x)=x^{2}+11x+n$ and $f_{2}(x)=x$, then the largest positive integer n for which the equation $f_{1}(x)=f_{2}(x)$ has two […]<\/p>\n","protected":false},"author":42,"featured_media":36621,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125,350,362,366],"tags":[1713,2907],"class_list":{"0":"post-36615","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-featured","10":"category-iift","11":"category-snap","12":"category-xat","13":"tag-cat-2019","14":"tag-polynomial-questions-for-cat"},"better_featured_image":{"id":36621,"alt_text":"Polynomial Questions for CAT","caption":"Polynomial Questions for CAT\n","description":"Polynomial Questions for 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