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Hacker Rank

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data-testid="question-tab-item-unanswered">61</span></a></div></li><li
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class="question-tab__list-item" aria-label="Solve question 62"
href="https://www.hackerrank.com/test/e3o37mnmb4q/questions/9j51814oc5n" aria-
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data-testid="question-tab-item-unanswered">62</span></a></div></li><li
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href="https://www.hackerrank.com/test/e3o37mnmb4q/questions/co56fnjc89l" aria-
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data-testid="question-tab-item-unanswered">63</span></a></div></li><li
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href="https://www.hackerrank.com/test/e3o37mnmb4q/questions/b7ctn1aotrn" aria-
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data-testid="question-tab-item-unanswered">64</span></a></div></li><li
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href="https://www.hackerrank.com/test/e3o37mnmb4q/questions/8agke0tgh60" aria-
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data-testid="question-tab-item-unanswered">65</span></a></div></li><li
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data-testid="question-tab-item-unanswered">66</span></a></div></li><li
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data-testid="question-tab-item-unanswered">67</span></a></div></li><li
class="question-tab__list-item-wrapper"><div class="ui-tooltip-wrapper"><a
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data-testid="question-tab-item-unanswered">68</span></a></div></li><li
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data-testid="question-tab-item-unanswered">69</span></a></div></li><li
class="question-tab__list-item-wrapper"><div class="ui-tooltip-wrapper"><a
class="question-tab__list-item" aria-label="Solve question 70"
href="https://www.hackerrank.com/test/e3o37mnmb4q/questions/4h7o93kq7k7" aria-
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data-testid="question-tab-item-unanswered">70</span></a></div></li><li
class="question-tab__separator"></li></ul></div><div class="test-
container__content"><main id="main-content" class="question-view question-view--
mcq"><div class="grouped-mcq__scroll-window" data-testid="mcq-container"><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="44fer0brek-title">1. Numerical Computations</h2></section><section
class="question-view__instruction"><div class="candidate-rich-text disable-text-
selection"><div id="44fer0brek-instruction"><p class="Normal1">The arithmetic mean
of P, Q, R is 100 and that of P, Q, R, ‘m’ and ‘n’ is 90. Where<span style="font-
size:11pt;"><span style="line-height:115%;"><span style="font-family:Arial , sans-
serif;"><span lang="EN-IN" style="background:white;"><span style="font-
family:&quot;Calibri&quot; , sans-serif;">&nbsp;<img
src="./HackerRank_files/010701.png">&nbsp;</span></span><span lang="EN-IN"
style="background:white;"><span style="font-family:&quot;Calibri&quot; , sans-
serif;">&nbsp;</span></span></span></span></span>and&nbsp;<span style="font-
size:11pt;"><span style="line-height:115%;"><span style="font-family:Arial , sans-
serif;"><span lang="EN-IN" style="background:white;"><span style="font-
family:&quot;Calibri&quot; , sans-serif;"><img height="29"
src="./HackerRank_files/010702.png"
width="66">&nbsp;</span></span></span></span></span>. If P ≥ R. Find the minimum
possible value of P.</p>
</div></div></section><form data-gtm-form-interact-id="2"><div class="solution
solution--mcq"><section class="solution__heading"><div
class="solution__directive">Pick <strong>ONE</strong>
option</div></section><section class="solution__body"><div class="d-flex
solution__options-list" role="group" aria-labelledby="44fer0brek-title 44fer0brek-
instruction"><div class="radio-group" role="radiogroup"><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="44fer0brek" theme="theme-m" aria-setsize="4" aria-
posinset="1" value="1"><span class="custom-holder inset"></span></div><div
class="label">100</div></label></div><div class="ui-radio checked"><label
class="label-wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="44fer0brek" theme="theme-m" aria-setsize="4" aria-posinset="2" value="2"
data-gtm-form-interact-field-id="16"><span class="custom-holder
inset"></span></div><div class="label">120</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="44fer0brek" theme="theme-m" aria-setsize="4" aria-
posinset="3" value="3"><span class="custom-holder inset"></span></div><div
class="label">170</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="44fer0brek" theme="theme-m" aria-setsize="4" aria-posinset="4"
value="4"><span class="custom-holder inset"></span></div><div
class="label">150</div></label></div></div></div><button class="ui-btn ui-btn-
normal solution__clear-selection ui-btn-styled" type="button" aria-label="Clear
Selection for Question 1"><div class="ui-content align-icon-right"><span class="ui-
text" aria-hidden="false">Clear Selection</span></div></button><div
class="solution__status-message solution__status-message--success"
role="status"><span class="d-flex align-items-center"><svg viewBox="0 0 24 24"
width="1em" height="1em" class="status-icon ui-svg-icon" fill="currentColor"><path
d="M12 23C5.9 23 1 18.1 1 12c0-3 1.1-5.7 3.2-7.8C6.3 2.1 9.1 1 12 1c1.6 0 3.1.3 4.5
1 .5.2.7.8.5 1.3-.2.5-.8.7-1.3.5-1.2-.5-2.4-.8-3.7-.8-5 0-9 4-9 9s4 9 9 9 9-4 9-
9v-.9c0-.6.4-1 1-1s1 .4 1 1v.9c0 6.1-4.9 11-11 11z"></path><path d="M12 15c-.3
0-.5-.1-.7-.3l-3-3c-.4-.4-.4-1 0-1.4.4-.4 1-.4 1.4 0l2.3 2.3L22.3 2.3c.4-.4 1-.4
1.4 0s.4 1 0 1.4l-11 11c-.2.2-.4.3-.7.3z"></path></svg><span
class="solution__status-message__text"
aria-live="polite">Saved!</span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="etlbd6p1c0p-title">2. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="etlbd6p1c0p-
instruction"><p class="Normal1">In<strong>&nbsp;</strong>a quadratic equation
ax<sup>2</sup>&nbsp;+ bx + 4 = 0 (where x is a non-zero real number), find the
total number of ordered pairs (a, b) possible such that the roots of the quadratic
equation are equal. Also given that a and b are integers and a lie between -100 and
100 (both value inclusive).</p>
</div></div></section><form data-gtm-form-interact-id="3"><div class="solution
solution--mcq"><section class="solution__heading"><div
class="solution__directive">Pick <strong>ONE</strong>
option</div></section><section class="solution__body"><div class="d-flex
solution__options-list" role="group" aria-labelledby="etlbd6p1c0p-title
etlbd6p1c0p-instruction"><div class="radio-group" role="radiogroup"><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="etlbd6p1c0p" theme="theme-m" aria-setsize="4" aria-
posinset="1" value="1"><span class="custom-holder inset"></span></div><div
class="label">20</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="etlbd6p1c0p" theme="theme-m" aria-setsize="4" aria-posinset="2"
value="2"><span class="custom-holder inset"></span></div><div
class="label">18</div></label></div><div class="ui-radio checked"><label
class="label-wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="etlbd6p1c0p" theme="theme-m" aria-setsize="4" aria-posinset="3" value="3"
data-gtm-form-interact-field-id="17"><span class="custom-holder
inset"></span></div><div class="label">10</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="etlbd6p1c0p" theme="theme-m" aria-setsize="4" aria-
posinset="4" value="4"><span class="custom-holder inset"></span></div><div
class="label">21</div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" type="button" aria-label="Clear Selection
for Question 2"><div class="ui-content align-icon-right"><span class="ui-text"
aria-hidden="false">Clear Selection</span></div></button><div
class="solution__status-message solution__status-message--success"
role="status"><span class="d-flex align-items-center"><svg viewBox="0 0 24 24"
width="1em" height="1em" class="status-icon ui-svg-icon" fill="currentColor"><path
d="M12 23C5.9 23 1 18.1 1 12c0-3 1.1-5.7 3.2-7.8C6.3 2.1 9.1 1 12 1c1.6 0 3.1.3 4.5
1 .5.2.7.8.5 1.3-.2.5-.8.7-1.3.5-1.2-.5-2.4-.8-3.7-.8-5 0-9 4-9 9s4 9 9 9 9-4 9-
9v-.9c0-.6.4-1 1-1s1 .4 1 1v.9c0 6.1-4.9 11-11 11z"></path><path d="M12 15c-.3
0-.5-.1-.7-.3l-3-3c-.4-.4-.4-1 0-1.4.4-.4 1-.4 1.4 0l2.3 2.3L22.3 2.3c.4-.4 1-.4
1.4 0s.4 1 0 1.4l-11 11c-.2.2-.4.3-.7.3z"></path></svg><span
class="solution__status-message__text"
aria-live="polite">Saved!</span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="5517spmeosc-title">3. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="5517spmeosc-
instruction"><p class="Normal1">Each of P and Q takes not more than 10 chocolates
at random from a box containing an unlimited number of chocolates. What is the
probability that the difference between the numbers of chocolates taken by them is
not more than 7?</p>
</div></div></section><form data-gtm-form-interact-id="4"><div class="solution
solution--mcq"><section class="solution__heading"><div
class="solution__directive">Pick <strong>ONE</strong>
option</div></section><section class="solution__body"><div class="d-flex
solution__options-list" role="group" aria-labelledby="5517spmeosc-title
5517spmeosc-instruction"><div class="radio-group" role="radiogroup"><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="5517spmeosc" theme="theme-m" aria-setsize="4" aria-
posinset="1" value="1"><span class="custom-holder inset"></span></div><div
class="label"><div class="candidate-rich-text"><p class="Normal1"><span
style="font-size:11pt"><span style="background:white"><span style="line-
height:115%"><span style="font-family:Arial,sans-serif"><span
style="background:white"><span style="font-family:&quot;Calibri&quot;,sans-
serif"><span
style="color:black">94/100</span></span></span></span></span></span></span></p>
</div></div></label></div><div class="ui-radio checked"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="5517spmeosc" theme="theme-m" aria-setsize="4" aria-posinset="2" value="2"
data-gtm-form-interact-field-id="18"><span class="custom-holder
inset"></span></div><div class="label"><div class="candidate-rich-text"><p
class="Normal1"><span style="font-size:11pt"><span style="background:white"><span
style="line-height:115%"><span style="font-family:Arial,sans-serif"><span
style="background:white"><span style="font-family:&quot;Calibri&quot;,sans-
serif"><span
style="color:black">115/121</span></span></span></span></span></span></span></p>
</div></div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="5517spmeosc"
theme="theme-m" aria-setsize="4" aria-posinset="3" value="3"><span class="custom-
holder inset"></span></div><div class="label"><div class="candidate-rich-
text"><p>109/121</p>
</div></div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="5517spmeosc"
theme="theme-m" aria-setsize="4" aria-posinset="4" value="4"><span class="custom-
holder inset"></span></div><div class="label"><div class="candidate-rich-
text"><p>88/100</p>
</div></div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" type="button" aria-label="Clear Selection
for Question 3"><div class="ui-content align-icon-right"><span class="ui-text"
aria-hidden="false">Clear Selection</span></div></button><div
class="solution__status-message solution__status-message--success"
role="status"><span class="d-flex align-items-center"><svg viewBox="0 0 24 24"
width="1em" height="1em" class="status-icon ui-svg-icon" fill="currentColor"><path
d="M12 23C5.9 23 1 18.1 1 12c0-3 1.1-5.7 3.2-7.8C6.3 2.1 9.1 1 12 1c1.6 0 3.1.3 4.5
1 .5.2.7.8.5 1.3-.2.5-.8.7-1.3.5-1.2-.5-2.4-.8-3.7-.8-5 0-9 4-9 9s4 9 9 9 9-4 9-
9v-.9c0-.6.4-1 1-1s1 .4 1 1v.9c0 6.1-4.9 11-11 11z"></path><path d="M12 15c-.3
0-.5-.1-.7-.3l-3-3c-.4-.4-.4-1 0-1.4.4-.4 1-.4 1.4 0l2.3 2.3L22.3 2.3c.4-.4 1-.4
1.4 0s.4 1 0 1.4l-11 11c-.2.2-.4.3-.7.3z"></path></svg><span
class="solution__status-message__text"
aria-live="polite">Saved!</span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="8sa43qhgead-title">4. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="8sa43qhgead-
instruction"><p class="Normal1">Thirteen pipes are connected to a cistern. The
efficiency of the kth pipe is the sum of the efficiencies of the previous (k - 1)
pipes, where k = 2, 3, 4, …, 13. If the 9th pipe can fill the tank in 12 hours
working alone. In how many hours can the 13th pipe fill the tank working alone?</p>
</div></div></section><form data-gtm-form-interact-id="5"><div class="solution
solution--mcq"><section class="solution__heading"><div
class="solution__directive">Pick <strong>ONE</strong>
option</div></section><section class="solution__body"><div class="d-flex
solution__options-list" role="group" aria-labelledby="8sa43qhgead-title
8sa43qhgead-instruction"><div class="radio-group" role="radiogroup"><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="8sa43qhgead" theme="theme-m" aria-setsize="4" aria-
posinset="1" value="1"><span class="custom-holder inset"></span></div><div
class="label">3/7</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="8sa43qhgead" theme="theme-m" aria-setsize="4" aria-posinset="2"
value="2"><span class="custom-holder inset"></span></div><div
class="label">5/6</div></label></div><div class="ui-radio checked"><label
class="label-wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="8sa43qhgead" theme="theme-m" aria-setsize="4" aria-posinset="3" value="3"
data-gtm-form-interact-field-id="19"><span class="custom-holder
inset"></span></div><div class="label">3/4</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="8sa43qhgead" theme="theme-m" aria-setsize="4" aria-
posinset="4" value="4"><span class="custom-holder inset"></span></div><div
class="label">16</div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" type="button" aria-label="Clear Selection
for Question 4"><div class="ui-content align-icon-right"><span class="ui-text"
aria-hidden="false">Clear Selection</span></div></button><div
class="solution__status-message solution__status-message--success"
role="status"><span class="d-flex align-items-center"><svg viewBox="0 0 24 24"
width="1em" height="1em" class="status-icon ui-svg-icon" fill="currentColor"><path
d="M12 23C5.9 23 1 18.1 1 12c0-3 1.1-5.7 3.2-7.8C6.3 2.1 9.1 1 12 1c1.6 0 3.1.3 4.5
1 .5.2.7.8.5 1.3-.2.5-.8.7-1.3.5-1.2-.5-2.4-.8-3.7-.8-5 0-9 4-9 9s4 9 9 9 9-4 9-
9v-.9c0-.6.4-1 1-1s1 .4 1 1v.9c0 6.1-4.9 11-11 11z"></path><path d="M12 15c-.3
0-.5-.1-.7-.3l-3-3c-.4-.4-.4-1 0-1.4.4-.4 1-.4 1.4 0l2.3 2.3L22.3 2.3c.4-.4 1-.4
1.4 0s.4 1 0 1.4l-11 11c-.2.2-.4.3-.7.3z"></path></svg><span
class="solution__status-message__text"
aria-live="polite">Saved!</span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="apmd2e69ele-title">5. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="apmd2e69ele-
instruction"><p class="Normal1">9 people are sitting in a room. What is the
probability that exactly 3 of them have birthdays in the same month of the year and
no other two persons have birthdays in the same month of the year?</p>
</div></div></section><form data-gtm-form-interact-id="6"><div class="solution
solution--mcq"><section class="solution__heading"><div
class="solution__directive">Pick <strong>ONE</strong>
option</div></section><section class="solution__body"><div class="d-flex
solution__options-list" role="group" aria-labelledby="apmd2e69ele-title
apmd2e69ele-instruction"><div class="radio-group" role="radiogroup"><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="apmd2e69ele" theme="theme-m" aria-setsize="4" aria-
posinset="1" value="1"><span class="custom-holder inset"></span></div><div
class="label"><div class="candidate-rich-text"><p><span style="font-
size:11pt"><span style="background:white"><span style="line-height:115%"><span
style="font-family:Arial,sans-serif"><span lang="EN-IN"
style="background:white"><span style="font-family:&quot;Calibri&quot;,sans-
serif"><span
style="color:black">16170/12<sup>5</sup></span></span></span></span></span></
span></span></p>
</div></div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="apmd2e69ele"
theme="theme-m" aria-setsize="4" aria-posinset="2" value="2"><span class="custom-
holder inset"></span></div><div class="label"><div class="candidate-rich-
text"><p><span style="font-size:11pt"><span style="background:white"><span
style="line-height:115%"><span style="font-family:Arial,sans-serif"><span lang="EN-
IN" style="background:white"><span style="font-family:&quot;Calibri&quot;,sans-
serif"><span
style="color:black">16370/12<sup>2</sup></span></span></span></span></span></
span></span></p>
</div></div></label></div><div class="ui-radio checked"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="apmd2e69ele" theme="theme-m" aria-setsize="4" aria-posinset="3" value="3"
data-gtm-form-interact-field-id="20"><span class="custom-holder
inset"></span></div><div class="label"><div class="candidate-rich-text"><p
class="Normal1"><span style="font-size:11pt"><span style="background:white"><span
style="line-height:115%"><span style="font-family:Arial,sans-serif"><span lang="EN-
IN" style="background:white"><span style="font-family:&quot;Calibri&quot;,sans-
serif"><span
style="color:black">16270/12<sup>9</sup></span></span></span></span></span></
span></span></p>
</div></div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="apmd2e69ele"
theme="theme-m" aria-setsize="4" aria-posinset="4" value="4"><span class="custom-
holder inset"></span></div><div class="label"><div class="candidate-rich-text"><p
class="Normal1"><span style="font-size:11pt"><span style="background:white"><span
style="line-height:115%"><span style="font-family:Arial,sans-serif"><span lang="EN-
IN" style="background:white"><span style="font-family:&quot;Calibri&quot;,sans-
serif"><span style="color:black">None of
these</span></span></span></span></span></span></span></p>
</div></div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" type="button" aria-label="Clear Selection
for Question 5"><div class="ui-content align-icon-right"><span class="ui-text"
aria-hidden="false">Clear Selection</span></div></button><div
class="solution__status-message solution__status-message--success"
role="status"><span class="d-flex align-items-center"><svg viewBox="0 0 24 24"
width="1em" height="1em" class="status-icon ui-svg-icon" fill="currentColor"><path
d="M12 23C5.9 23 1 18.1 1 12c0-3 1.1-5.7 3.2-7.8C6.3 2.1 9.1 1 12 1c1.6 0 3.1.3 4.5
1 .5.2.7.8.5 1.3-.2.5-.8.7-1.3.5-1.2-.5-2.4-.8-3.7-.8-5 0-9 4-9 9s4 9 9 9 9-4 9-
9v-.9c0-.6.4-1 1-1s1 .4 1 1v.9c0 6.1-4.9 11-11 11z"></path><path d="M12 15c-.3
0-.5-.1-.7-.3l-3-3c-.4-.4-.4-1 0-1.4.4-.4 1-.4 1.4 0l2.3 2.3L22.3 2.3c.4-.4 1-.4
1.4 0s.4 1 0 1.4l-11 11c-.2.2-.4.3-.7.3z"></path></svg><span
class="solution__status-message__text"
aria-live="polite">Saved!</span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="7f4i2t5hb9i-title">6. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="7f4i2t5hb9i-
instruction"><p class="Normal1">Sayani forms a mixture of two compounds C1 and C2
by mixing them in the ratio 10:11. She labels the mixture as ‘X’. Compound C1
contains two elements E1 and E2 in the ratio of 5:2, while compound C2 contains two
elements E2 and E3 in the ratio of 7:11. How many units of element E2 are present
in 756 units of X (approximately)?</p>
</div></div></section><form data-gtm-form-interact-id="7"><div class="solution
solution--mcq"><section class="solution__heading"><div
class="solution__directive">Pick <strong>ONE</strong>
option</div></section><section class="solution__body"><div class="d-flex
solution__options-list" role="group" aria-labelledby="7f4i2t5hb9i-title
7f4i2t5hb9i-instruction"><div class="radio-group" role="radiogroup"><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="7f4i2t5hb9i" theme="theme-m" aria-setsize="4" aria-
posinset="1" value="1"><span class="custom-holder inset"></span></div><div
class="label">257</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="7f4i2t5hb9i" theme="theme-m" aria-setsize="4" aria-posinset="2"
value="2"><span class="custom-holder inset"></span></div><div
class="label">258</div></label></div><div class="ui-radio checked"><label
class="label-wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="7f4i2t5hb9i" theme="theme-m" aria-setsize="4" aria-posinset="3" value="3"
data-gtm-form-interact-field-id="21"><span class="custom-holder
inset"></span></div><div class="label">259</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="7f4i2t5hb9i" theme="theme-m" aria-setsize="4" aria-
posinset="4" value="4"><span class="custom-holder inset"></span></div><div
class="label">260</div></label></div></div></div><button class="ui-btn ui-btn-
normal solution__clear-selection ui-btn-styled" type="button" aria-label="Clear
Selection for Question 6"><div class="ui-content align-icon-right"><span class="ui-
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role="status"><span class="d-flex align-items-center"><svg viewBox="0 0 24 24"
width="1em" height="1em" class="status-icon ui-svg-icon" fill="currentColor"><path
d="M12 23C5.9 23 1 18.1 1 12c0-3 1.1-5.7 3.2-7.8C6.3 2.1 9.1 1 12 1c1.6 0 3.1.3 4.5
1 .5.2.7.8.5 1.3-.2.5-.8.7-1.3.5-1.2-.5-2.4-.8-3.7-.8-5 0-9 4-9 9s4 9 9 9 9-4 9-
9v-.9c0-.6.4-1 1-1s1 .4 1 1v.9c0 6.1-4.9 11-11 11z"></path><path d="M12 15c-.3
0-.5-.1-.7-.3l-3-3c-.4-.4-.4-1 0-1.4.4-.4 1-.4 1.4 0l2.3 2.3L22.3 2.3c.4-.4 1-.4
1.4 0s.4 1 0 1.4l-11 11c-.2.2-.4.3-.7.3z"></path></svg><span
class="solution__status-message__text"
aria-live="polite">Saved!</span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="2ockhd44ag0-title">7. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="2ockhd44ag0-
instruction"><p>If&nbsp;P = 1 – cos<sup>2</sup>θ + cos<sup>4</sup>θ. For all real
θ</p>
</div></div></section><form><div class="solution solution--mcq"><section
class="solution__heading"><div class="solution__directive">Pick
<strong>ONE</strong> option</div></section><section class="solution__body"><div
class="d-flex solution__options-list" role="group" aria-labelledby="2ockhd44ag0-
title 2ockhd44ag0-instruction"><div class="radio-group" role="radiogroup"><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="2ockhd44ag0" theme="theme-m" aria-
setsize="4" aria-posinset="1" value="1"><span class="custom-holder
inset"></span></div><div class="label">1/2 &lt; P ≤ 1</div></label></div><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="2ockhd44ag0" theme="theme-m" aria-
setsize="4" aria-posinset="2" value="2"><span class="custom-holder
inset"></span></div><div class="label">3/4 ≤ P ≤ 1</div></label></div><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="2ockhd44ag0" theme="theme-m" aria-
setsize="4" aria-posinset="3" value="3"><span class="custom-holder
inset"></span></div><div class="label">13/16 ≤ P ≤ 1</div></label></div><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="2ockhd44ag0" theme="theme-m" aria-
setsize="4" aria-posinset="4" value="4"><span class="custom-holder
inset"></span></div><div class="label">1/4 ≤ P ≤
1</div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" disabled="" type="button" aria-
label="Clear Selection for Question 7"><div class="ui-content align-icon-
right"><span class="ui-text" aria-hidden="false">Clear
Selection</span></div></button><div class="solution__status-message
solution__status-message--none solution__status-message--hidden"
role="status"><span class="d-flex align-items-center"><span
class="solution__status-message__text"
aria-live="polite"></span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="8q9542g8t3h-title">8. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="8q9542g8t3h-
instruction"><p class="Normal1">P and Q are bikes on a circular track with a radius
of 882 m. The speeds of P and Q are in the ratio 7:4 and P alone can complete one
round of the track in 49.5 seconds. P starts from point X in a clockwise direction,
Q starts from point Y in an anti-clockwise direction and they meet after 27.5
seconds at point Z. What is the length of the minor arc XY on the track?</p>
</div></div></section><form><div class="solution solution--mcq"><section
class="solution__heading"><div class="solution__directive">Pick
<strong>ONE</strong> option</div></section><section class="solution__body"><div
class="d-flex solution__options-list" role="group" aria-labelledby="8q9542g8t3h-
title 8q9542g8t3h-instruction"><div class="radio-group" role="radiogroup"><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="8q9542g8t3h" theme="theme-m" aria-
setsize="4" aria-posinset="1" value="1"><span class="custom-holder
inset"></span></div><div class="label">686 m</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="8q9542g8t3h" theme="theme-m" aria-setsize="4" aria-
posinset="2" value="2"><span class="custom-holder inset"></span></div><div
class="label">652 m</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="8q9542g8t3h" theme="theme-m" aria-setsize="4" aria-posinset="3"
value="3"><span class="custom-holder inset"></span></div><div class="label">704
m</div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="8q9542g8t3h"
theme="theme-m" aria-setsize="4" aria-posinset="4" value="4"><span class="custom-
holder inset"></span></div><div class="label">728
m</div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" disabled="" type="button" aria-
label="Clear Selection for Question 8"><div class="ui-content align-icon-
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Selection</span></div></button><div class="solution__status-message
solution__status-message--none solution__status-message--hidden"
role="status"><span class="d-flex align-items-center"><span
class="solution__status-message__text"
aria-live="polite"></span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="atob1p6r84q-title">9. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="atob1p6r84q-
instruction"><p class="Normal1">If ‘a4328b’ is divisible by 15, find the total
number of distinct possible values of (a +b).&nbsp;Here a and b are single-digit
whole numbers.</p>
</div></div></section><form><div class="solution solution--mcq"><section
class="solution__heading"><div class="solution__directive">Pick
<strong>ONE</strong> option</div></section><section class="solution__body"><div
class="d-flex solution__options-list" role="group" aria-labelledby="atob1p6r84q-
title atob1p6r84q-instruction"><div class="radio-group" role="radiogroup"><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="atob1p6r84q" theme="theme-m" aria-
setsize="4" aria-posinset="1" value="1"><span class="custom-holder
inset"></span></div><div class="label">5</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="atob1p6r84q" theme="theme-m" aria-setsize="4" aria-
posinset="2" value="2"><span class="custom-holder inset"></span></div><div
class="label">6</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="atob1p6r84q" theme="theme-m" aria-setsize="4" aria-posinset="3"
value="3"><span class="custom-holder inset"></span></div><div
class="label">3</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="atob1p6r84q" theme="theme-m" aria-setsize="4" aria-posinset="4"
value="4"><span class="custom-holder inset"></span></div><div
class="label">4</div></label></div></div></div><button class="ui-btn ui-btn-normal
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Selection</span></div></button><div class="solution__status-message
solution__status-message--none solution__status-message--hidden"
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class="solution__status-message__text"
aria-live="polite"></span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="84t0mbq85a4-title">10. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="84t0mbq85a4-
instruction"><p class="Normal1">Kasmira purchased a total of 38 products. She
purchased only three types of products i.e., N95 masks, hand sanitizers and
surgical gloves spending a total amount of $3540. Each N95 mask costs $80, each
hand sanitiser costs $150 and each surgical glove costs $30. If the number of hand
sanitizers that Kasmira bought were as minimum as it could be, then how many
surgical gloves did she buy?</p>
</div></div></section><form><div class="solution solution--mcq"><section
class="solution__heading"><div class="solution__directive">Pick
<strong>ONE</strong> option</div></section><section class="solution__body"><div
class="d-flex solution__options-list" role="group" aria-labelledby="84t0mbq85a4-
title 84t0mbq85a4-instruction"><div class="radio-group" role="radiogroup"><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="84t0mbq85a4" theme="theme-m" aria-
setsize="4" aria-posinset="1" value="1"><span class="custom-holder
inset"></span></div><div class="label">24</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="84t0mbq85a4" theme="theme-m" aria-setsize="4" aria-
posinset="2" value="2"><span class="custom-holder inset"></span></div><div
class="label">4</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="84t0mbq85a4" theme="theme-m" aria-setsize="4" aria-posinset="3"
value="3"><span class="custom-holder inset"></span></div><div
class="label">18</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="84t0mbq85a4" theme="theme-m" aria-setsize="4" aria-posinset="4"
value="4"><span class="custom-holder inset"></span></div><div
class="label">12</div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" disabled="" type="button" aria-
label="Clear Selection for Question 10"><div class="ui-content align-icon-
right"><span class="ui-text" aria-hidden="false">Clear
Selection</span></div></button><div class="solution__status-message
solution__status-message--none solution__status-message--hidden"
role="status"><span class="d-flex align-items-center"><span
class="solution__status-message__text"
aria-live="polite"></span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="1jb0f7qrfs8-title">11. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="1jb0f7qrfs8-
instruction"><p>In the year 2023, a new variant of the Omicron virus has led to a
dramatic loss of human lives worldwide and presented an unprecedented challenge to
public health and food distribution systems. A team of professors and virologists
at the World Health Organization were researching the number of variants of the new
mutant 'XE' variant of the Omicron virus. It was found that in the year 2020, it
was 10,000, then it increased by 60% in 2021 and then for 2022, it increased by 25%
over the previous year.</p>

<p>The number of variants of the new variant of the virus found in the present year
(Qc), the number of variants of the virus found in the previous year (Qp) and the
number of variants of the virus found in the previous-to-previous year (Qp − 1) are
associated to each other by the following equation (This association holds good for
any given year.)</p>

<p>&nbsp;</p>

<p>Qc = Qp + Z x log<sub>10</sub>Q<sub>p-1</sub>&nbsp;where Z is a constant.</p>

<p>log<sub>10</sub>2 = 0.3010</p>

<p>&nbsp;</p>

<p>Find the number of variants of the new mutant 'XE' variant of Omicron virus
which will be there in 2023 as well as find the value of Z.</p>
</div></div></section><form><div class="solution solution--mcq"><section
class="solution__heading"><div class="solution__directive">Pick
<strong>ONE</strong> option</div></section><section class="solution__body"><div
class="d-flex solution__options-list" role="group" aria-labelledby="1jb0f7qrfs8-
title 1jb0f7qrfs8-instruction"><div class="radio-group" role="radiogroup"><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="1jb0f7qrfs8" theme="theme-m" aria-
setsize="4" aria-posinset="1" value="1"><span class="custom-holder
inset"></span></div><div class="label">Z = 2,000, Q2023 =
24,204</div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="1jb0f7qrfs8"
theme="theme-m" aria-setsize="4" aria-posinset="2" value="2"><span class="custom-
holder inset"></span></div><div class="label">Z = 1,000, Q2023 =
24,204</div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="1jb0f7qrfs8"
theme="theme-m" aria-setsize="4" aria-posinset="3" value="3"><span class="custom-
holder inset"></span></div><div class="label">Z = 2,000, Q2023 =
22,402</div></label></div><div class="ui-radio"><label class="label-wrap"><div
class="radio-wrap"><input type="radio" class="radio-input" name="1jb0f7qrfs8"
theme="theme-m" aria-setsize="4" aria-posinset="4" value="4"><span class="custom-
holder inset"></span></div><div class="label">Z = 1,000, Q2023 =
22,204</div></label></div></div></div><button class="ui-btn ui-btn-normal
solution__clear-selection ui-btn-styled" disabled="" type="button" aria-
label="Clear Selection for Question 11"><div class="ui-content align-icon-
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Selection</span></div></button><div class="solution__status-message
solution__status-message--none solution__status-message--hidden"
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class="solution__status-message__text"
aria-live="polite"></span></span></div></section></div></form></div><div
class="grouped-mcq__question"><div class="grouped-mcq__hook"></div><section
class="question-view__title-wrapper"><h2 class="disable-text-selection question-
view__title" id="bo5ss1kpeqn-title">12. Numerical
Computations</h2></section><section class="question-view__instruction"><div
class="candidate-rich-text disable-text-selection"><div id="bo5ss1kpeqn-
instruction"><p>Consider the following two quantities P and Q, which are defined
as</p>

<p>P: The number of arrangements of all the letters of the word “QUESTION” such
that all the vowels are not together</p>

<p>Q: The number of arrangements of all the letters of the word “QUESTION” such
that no two vowels are together</p>

<p>Find the value of P/Q.</p>


</div></div></section><form><div class="solution solution--mcq"><section
class="solution__heading"><div class="solution__directive">Pick
<strong>ONE</strong> option</div></section><section class="solution__body"><div
class="d-flex solution__options-list" role="group" aria-labelledby="bo5ss1kpeqn-
title bo5ss1kpeqn-instruction"><div class="radio-group" role="radiogroup"><div
class="ui-radio"><label class="label-wrap"><div class="radio-wrap"><input
type="radio" class="radio-input" name="bo5ss1kpeqn" theme="theme-m" aria-
setsize="4" aria-posinset="1" value="1"><span class="custom-holder
inset"></span></div><div class="label">1</div></label></div><div class="ui-
radio"><label class="label-wrap"><div class="radio-wrap"><input type="radio"
class="radio-input" name="bo5ss1kpeqn" theme="theme-m" aria-setsize="4" aria-
posinset="2" value="2"><span class="custom-holder inset"></span></div><div
class="label">2</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="bo5ss1kpeqn" theme="theme-m" aria-setsize="4" aria-posinset="3"
value="3"><span class="custom-holder inset"></span></div><div
class="label">6</div></label></div><div class="ui-radio"><label class="label-
wrap"><div class="radio-wrap"><input type="radio" class="radio-input"
name="bo5ss1kpeqn" theme="theme-m" aria-setsize="4" aria-posinset="4"
value="4"><span class="custom-holder inset"></span></div><div class="label">None of
these</div></label></div></div></div><button class="ui-btn ui-btn-normal
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label="Clear Selection for Question 12"><div class="ui-content align-icon-
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Selection</span></div></button><div class="solution__status-message
solution__status-message--none solution__status-message--hidden"
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class="solution__status-message__text"
aria-live="polite"></span></span></div></section></div></form></div><section
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btn-styled" type="button"><div class="ui-content align-icon-right"><span class="ui-
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