{"id":36241,"date":"2019-10-17T13:09:58","date_gmt":"2019-10-17T07:39:58","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=36241"},"modified":"2019-10-17T13:09:58","modified_gmt":"2019-10-17T07:39:58","slug":"surds-indices-questions-for-rrb-ntpc-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/surds-indices-questions-for-rrb-ntpc-pdf\/","title":{"rendered":"Surds & Indices Questions for RRB NTPC PDF"},"content":{"rendered":"

Surds & Indices Questions for RRB NTPC PDF<\/strong><\/span><\/h2>\n

Download RRB NTPC Surds & Indices Questions PDF. Top 10 RRB NTPC questions based on asked questions in previous exam papers very important for the Railway NTPC exam.<\/p>\n

Download Surds & Indices Questions for RRB NTPC PDF<\/a><\/p>\n

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

Download RRB NTPC Previous Papers PDF<\/a><\/p>\n\n

Question 1:\u00a0<\/b>The two numbers $4^{30}$ and $25^{30}$ are written next to each other. What is the total number of digits written down?<\/p>\n

a)\u00a030<\/p>\n

b)\u00a059<\/p>\n

c)\u00a060<\/p>\n

d)\u00a0None of these<\/p>\n

Question 2:\u00a0<\/b>If $x = 9 + 4\\sqrt{5}$, what is $x + \\frac{1}{x}$<\/p>\n

a)\u00a017.83<\/p>\n

b)\u00a018.45<\/p>\n

c)\u00a018.00<\/p>\n

d)\u00a0None of these<\/p>\n

Question 3:\u00a0<\/b>What is the value of x for which $x^{2\/3}$ + $3x^{1\/3} – 4<0$?<\/p>\n

a)\u00a0-64 < x < 1<\/p>\n

b)\u00a0-1 < x < 64<\/p>\n

c)\u00a0-64 < x < 64<\/p>\n

d)\u00a01 < x < 64<\/p>\n

RRB NTPC Previous Papers [Download PDF]<\/a><\/p>\n

FREE RRB NTPC YOUTUBE VIDEOS<\/a><\/p>\n

Question 4:\u00a0<\/b>$ \\frac{1}{{3-2}\\sqrt{2}}$ – $ \\frac{1}{{3+2}\\sqrt{2}}$ = $2^x$. Find x?<\/p>\n

a)\u00a03\/2<\/p>\n

b)\u00a05\/2<\/p>\n

c)\u00a03<\/p>\n

d)\u00a07\/2<\/p>\n

Question 5:\u00a0<\/b>Which of the following surds is the greatest?<\/p>\n

a)\u00a0$ 4-\\sqrt{7}$<\/p>\n

b)\u00a0$ 5-\\sqrt{10}$<\/p>\n

c)\u00a0$ 8-\\sqrt{15}$<\/p>\n

d)\u00a0Cannot be determined<\/p>\n

Question 6:\u00a0<\/b>If $ x=\\sqrt{17}-\\sqrt{13}$, what is $ \\frac{30-\\sqrt{884}}{\\sqrt{17}+\\sqrt{13}}$?<\/p>\n

a)\u00a0$\\frac{x^2}{x-1}$<\/p>\n

b)\u00a0$\\frac{x^3}{x-1}$<\/p>\n

c)\u00a0$x^3$<\/p>\n

d)\u00a0$\\frac{x^3}{4}$<\/p>\n

RRB NTPC Free Mock Test<\/a><\/p>\n\n

Question 7:\u00a0<\/b>If $\\sqrt{28+5\\sqrt{12}} = a+\\sqrt{b}$, where a and b are positive rational numbers. Find a+b?<\/p>\n

a)\u00a02<\/p>\n

b)\u00a08<\/p>\n

c)\u00a013\/2<\/p>\n

d)\u00a0Cannot be determined<\/p>\n

Question 8:\u00a0<\/b>Which of the following surds is the greatest?<\/p>\n

a)\u00a0$\\sqrt{1}+\\sqrt{21}$<\/p>\n

b)\u00a0$\\sqrt{2}+\\sqrt{20}$<\/p>\n

c)\u00a0$\\sqrt{4}+\\sqrt{18}$<\/p>\n

d)\u00a0All of them are equal<\/p>\n

Question 9:\u00a0<\/b>Simplify: $\\sqrt{19+4\\sqrt{21}}$<\/p>\n

a)\u00a0$2+\\sqrt{26} $<\/p>\n

b)\u00a0$3-\\sqrt{15} $<\/p>\n

c)\u00a0$\\sqrt{5}+\\sqrt{26} $<\/p>\n

d)\u00a0$\\sqrt{12}+\\sqrt{7}$<\/p>\n

Question 10:\u00a0<\/b>Which of the following surds is the greatest?<\/p>\n

a)\u00a0$\\sqrt{2}+\\sqrt{14}$<\/p>\n

b)\u00a0$\\sqrt{3}+\\sqrt{13}$<\/p>\n

c)\u00a0$\\sqrt{5}+\\sqrt{11}$<\/p>\n

d)\u00a0$\\sqrt{7}+\\sqrt{8}$<\/p>\n

Download General Science Notes PDF<\/a><\/p>\n\n

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

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

Let $\\log_{10}{2}$ be x.
\nSo, the number of digits in $4^{30}$ is [60x] + 1.
\nSo, $\\log_{10}{5}$ is 1-x and the number of digits of $25^{30}$ is [60-60x]+1.
\nTotal number of digits is 2+[60x]+[60-60x] which is 62 + [60x]+[-60x].
\nAs 60x is not an integer, the value of [60x]+[-60x] = -1. So, value is 61<\/p>\n

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

$x = 9 + 4\\sqrt{5}$. So, $\\frac{1}{x}$ = $9 – 4\\sqrt{5}$. So, $x+ \\frac{1}{x}$ = 18<\/p>\n

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

-4 < $x^{1\/3}$ < 1 or -64 < x < 1<\/p>\n

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

$\\frac{1}{3-2\\sqrt{2}}-\\frac{1}{3+2\\sqrt{2}} = \\frac{3+2\\sqrt{2}-3+2\\sqrt{2}}{3^2-(2\\sqrt{2})^2} = 4\\sqrt{2}\/1 = 2^{5\/2}$. Hence x=5\/2.<\/p>\n

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

The value of $\\sqrt{7}$ is between 2 and 3. Hence, $4-\\sqrt{7}$ is between 1 and 2. Similarly, the value of b is between 1 and 2 and c is between 4 and 5. Hence, c) is the greatest.<\/p>\n

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

$\\frac{30-\\sqrt{884}}{\\sqrt{17}+\\sqrt{13}} = \\frac{(\\sqrt{17}-\\sqrt{13})^2}{\\sqrt{17}+\\sqrt{13}} = \\frac{(\\sqrt{17}-\\sqrt{13})^3}{(\\sqrt{17}+\\sqrt{13})(\\sqrt{17}-\\sqrt{13})}=\\frac{x^3}{17-13} = \\frac{x^3}{4}$.<\/p>\n

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

$\\sqrt{28+5\\sqrt{12}} = a+\\sqrt{b} \\rightarrow 28+5\\sqrt{12} = a^2+b+2a\\sqrt{b}$.<\/p>\n

Hence $a^2+b=28$ and $4 a^2 b =300$.<\/p>\n

Hence $a^2=25$ and b=3. As a is positive, a=5.<\/p>\n

Hence a+b=8.<\/p>\n

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

$(\\sqrt{a}+\\sqrt{b})^2 = a+b+2\\sqrt{ab}$.
\nAs a+b is equal for all three of them we need to compare which has the highest value for $\\sqrt{ab}$. So the term with highest value of ab will be the greatest.
\nab values for the three options are 21, 40 and 72.
\nHence c) is the greatest.<\/p>\n

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

Let $\\sqrt{19+4\\sqrt{21}} = \\sqrt{a}+\\sqrt{b}$
\n$\\rightarrow a+b+2\\sqrt{ab} = 19+4\\sqrt{21}$.
\nHence, a+b=19 and ab=84. Hence a=12, b=7.<\/p>\n

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

On squaring the four options we get $16+2\\sqrt{28}, 16+2\\sqrt{39}, 16+2\\sqrt{55}, 15+2\\sqrt{56}$.<\/p>\n

Out of a-c options, c is clearly the greatest.<\/p>\n

Similarly b is also rejected.<\/p>\n

Now between c and d, let d>c<\/p>\n

$15+2\\sqrt{56}>16+2\\sqrt{55}$
\n$2[\\sqrt{56}-\\sqrt{55}]>1$<\/p>\n

Multiply both sides of the equation by $[\\sqrt{56}+\\sqrt{55}]$<\/p>\n

$2[\\sqrt{56}-\\sqrt{55}][\\sqrt{56}+\\sqrt{55}]>[\\sqrt{56}+\\sqrt{55}]$<\/p>\n

2>$[\\sqrt{56}+\\sqrt{55}]$<\/p>\n

which is false as the value of each term of RHS lies between 7 and 8.<\/p>\n

This contradicts our assumption that d>c<\/p>\n

Hence c>d.<\/p>\n\n

DOWNLOAD APP FOR RRB FREE MOCKS<\/a><\/p>\n

We hope this Surds & Indices Questions pdf\u00a0 for RRB NTPC Exam will be highly useful for your Preparation.<\/p>\n","protected":false},"excerpt":{"rendered":"

Surds & Indices Questions for RRB NTPC PDF Download RRB NTPC Surds & Indices Questions PDF. Top 10 RRB NTPC questions based on asked questions in previous exam papers very important for the Railway NTPC exam. Take a free mock test for RRB NTPC Download RRB NTPC Previous Papers PDF Question 1:\u00a0The two numbers $4^{30}$ […]<\/p>\n","protected":false},"author":41,"featured_media":36244,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[169,125,31,1603],"tags":[491,1637,2052,2659],"class_list":{"0":"post-36241","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-downloads","8":"category-featured","9":"category-railways","10":"category-rrb-ntpc","11":"tag-rrb","12":"tag-rrb-exam","13":"tag-rrb-maths","14":"tag-rrb-ntpc-mocks"},"better_featured_image":{"id":36244,"alt_text":"Surds & Indices Questions for RRB NTPC PDF","caption":"Surds & Indices Questions for RRB NTPC PDF","description":"Surds & Indices Questions for RRB NTPC 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