question_answer 1) A matrix of certain characters is given. These characters follow a certain trend, row-wise or column-wise. Find out this trend and choose the missing character.
3 2 2 6 20 4 12 25 64 6 10 ?
A) 6 done
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B) 8 done
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C) 12 done
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D) 10 done
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question_answer 2) In a certain code language, (1) 'RILL PA' stands for 'My Dog'; (2) 'PA SEM TA' stands for 'Dog in Black'; (3) 'RILL HAK KOP' stands for 'My Dear Friend' and (4) 'TA KOP' stands for 'Black Friend'. Which of the following words signifies 'Dear' in the above code language?
A) SEM done
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B) PA done
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C) HAK done
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D) KOP done
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question_answer 3) The two terms in the given number series are missing. Find the correct alternative to complete the series. 13576, 17365, 75361, 63517,......, .........
A) 13576, 73381 done
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B) 75384, 57632 done
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C) 56713, 16537 done
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D) 16537, 35482 done
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question_answer 4) If L denotes \['\times '\], M denotes\['\div '\], P denotes \['+'\] and Q denotes \['-'\], then 16 P 24 M 8 Q 6 M 2 L 3=?
A) \[\frac{13}{6}\] done
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B) \[-\frac{1}{6}\] done
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C) \[\frac{1}{6}\] done
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D) \[10\] done
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question_answer 5) There are three poles X, Y and Z of different heights. Three spiders A, B and C start climbing up these poles at the same time. In each attempt, spider A climbs up the X pole 5 cms but slips back 1 cm, spider S climbs up the Y pole 6 cms but slips back 3 cms and spider C climbs up the Z pole 7 cms but slips back 2 cms. If each of the spiders make 50 attempts for reaching a top of the pole, then what is the height of the shortest pole?
A) 200 cms done
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B) 250 cms done
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C) 150 cms done
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D) 153 cms done
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question_answer 6) Choose the term from the options which will continue the following series. P 3 C, R 5 F, T 8 I, V 12 L,?
A) Y 17 O done
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B) X 17 M done
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C) X 17 O done
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D) X 16 O done
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question_answer 7) In a row of girls Alka and Kamini occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, Alka and Kamini occupy seventeenth place from the right and eighteenth place from the left, respectively. How many girls are there in the row?
A) 25 done
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B) 26 done
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C) 27 done
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D) Data inadequate done
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question_answer 8)
A, B, C, D, E, F and G are members of a family consisting of four adults and three children, two of them, F and G are girls. A and D are brothers and A is a doctor. E is an engineer married to one of the brothers and has two children. S is married to D and G is their child. Who is C?
A) A's son done
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B) E's daughter done
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C) F's father done
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D) G's brother done
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question_answer 9) In the given figure, circle stands for students, the square stands for laborious, triangle stands for intelligent and rectangle stands for lucky. Which of the following indicates those students who are laborious and lucky but not intelligent?
A) 3 done
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B) 4 done
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C) 2 done
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D) 6 done
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question_answer 10) On reaching in the conference hall 10 minutes before 11 : 40 A.M. for attending a meeting, the Director of a company knew that he had reached 20 minutes before the Joint Director who came 30 minutes late. What was the fixed time of the meeting?
A) 11 : 20 A.M. done
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B) 11 : 40 A.M. done
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C) 11 : 50 A.M. done
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D) 12 : 10 P.M. done
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question_answer 11) If Neha says, "Aarti's father Dhirendra is the only son of my father-in-law Vijendra", then how is Monika, who is sister of Aarti, related to Vijendra ?
A) Niece done
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B) Daughter done
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C) Wife done
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D) Grand-daughter done
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question_answer 12) One morning after sunrise, Shyam and Mohan were talking to each other face to face. If Mohan's shadow was exactly to the right of Shyam, which direction Mohan was facing?
A) East done
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B) South done
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C) North done
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D) Data inadequate done
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question_answer 13) How many squares are there in the given figure?
A) 16 done
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B) 20 done
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C) 18 done
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D) 21 done
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question_answer 14) Numbers on both sides of ?::? have same relationship. Choose the best alternative. 36 : 50 :: 64 : ?
A) 49 done
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B) 82 done
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C) 88 done
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D) 91 done
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question_answer 15) In the question, trace out the correct alternative such that Fig. (X) is embedded in one of them.
A) done
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B) done
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C) done
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D) done
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question_answer 16) If \[x=\left( \frac{1+i}{2} \right)\], \[(where\,i=\sqrt{-1})\]then the expression \[2{{x}^{4}}-2{{x}^{2}}+x+3\] equals
A) \[3-\left( \frac{i}{2} \right)\] done
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B) \[3+\left( \frac{i}{2} \right)\] done
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C) \[\left( \frac{3+i}{2} \right)\] done
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D) \[\left( \frac{3-i}{2} \right)\] done
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question_answer 17) In a college examination, a candidate is required to answer 6 out of 10 questions which are divided into two sections each containing 5 questions further the candidate is not permitted to attempt more than 4 questions from either of the section. The number of ways in which he can make up a choice of 6 questions is
A) 200 done
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B) 150 done
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C) 100 done
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D) 50 done
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question_answer 18) The range of the function \[f(x)\,={{6}^{x}}+{{3}^{x}}+{{6}^{-x}}+\]\[{{3}^{-x}}+2\] is
A) \[[-2,\infty )\] done
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B) \[(-2,\infty )\] done
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C) \[(6,\infty )\] done
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D) \[[6,\infty )\] done
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question_answer 19) Which of the following is not continuous for all x?
A) \[|x-1|+|x-2|\] done
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B) \[{{x}^{2}}-|x-{{x}^{2}}|\] done
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C) \[\sin \,|x|\,+|sin\,x|\] done
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D) \[\frac{\cos \,x}{|cos\,x|}\] done
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question_answer 20) If \[y=4x-5\]is a tangent to the curve \[{{y}^{2}}=p{{x}^{3}}+q\]at (2, 3), then
A) p = 2, q = - 7 done
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B) p = - 2, q = 7 done
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C) p = - 2, q = - 7 done
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D) p = 2, q = 7 done
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question_answer 21) The vectors \[\vec{a},\text{ }\vec{b}\]and \[\vec{c}\] are equal in length and taken pain wise, they make equal angles. \[\vec{a}=\hat{i}+\hat{j},\vec{b}=\hat{j}+\hat{k}\]and\[\vec{c}\]makes an obtuse angle with x-axis, then \[\vec{c}\] =
A) \[\hat{i}+\hat{k}\] done
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B) \[-\,\hat{i}+4\hat{j}-\hat{k}\] done
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C) \[\frac{1}{3}(-\,\hat{i}+4\hat{j}-\hat{k})\] done
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D) \[\frac{1}{3}(\,\hat{i}-4\hat{j}+\hat{k})\] done
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question_answer 22) A relation R on the set of complex numbers is defined by \[{{z}_{1}}R{{z}_{2}}\Leftrightarrow \frac{{{z}_{1}}-{{z}_{2}}}{{{z}_{1}}+{{z}_{2}}}\] real, then R is__.
A) An equivalence relation done
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B) Only reflexive done
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C) Only transitive done
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D) None of these done
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question_answer 23) If A is singular matrix, then adj is
A) Singular done
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B) Non-singular done
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C) Symmetric done
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D) Not defined done
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question_answer 24) If A and S are square matrices of the same order and A is non-singular, then for a positive integer n, is equal to
A) \[{{A}^{n}}{{B}^{n}}{{A}^{n}}\] done
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B) \[{{A}^{n}}{{B}^{n}}{{A}^{-n}}\] done
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C) \[{{A}^{-1}}{{B}^{n}}A\] done
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D) \[n({{A}^{-1}}BA)\] done
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question_answer 25) If\[4\text{ }si{{n}^{-1}}\,x+cos{{\,}^{-1}}x=\pi \], then x is equal to
A) \[0\] done
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B) \[\frac{1}{2}\] done
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C) \[-\frac{1}{2}\] done
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D) \[1\] done
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question_answer 26) The area bounded by the curve \[y=x,\text{ }\!\!|\!\!\text{ }x|\], axis and the ordinates \[x=-1,\text{ }x=1\]is given by
A) \[\frac{1}{3}\] done
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B) \[\frac{4}{3}\] done
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C) \[\frac{2}{3}\] done
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D) \[1\] done
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question_answer 27) Domain of the function \[f(x)\,=\sqrt{{{\log }_{0.5}}(3x-8)-lo{{g}_{0.5}}({{x}^{2}}+4)}\] is
A) \[(0,\infty )\] done
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B) \[(-\infty 8/3)\] done
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C) \[(-\,\infty ,\infty )\] done
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D) \[(8/3,\infty )\] done
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question_answer 28) If \[\vec{u}=\vec{a}-\vec{b},\,\,\vec{v}=\vec{a}+\vec{b}\] and \[|\vec{a}|\,=\,|\vec{b}|\,=2\], then \[|\vec{u}\times \vec{v}|\,\]is equal to
A) \[2\sqrt{16-{{(\vec{a}.\vec{b})}^{2}}}\] done
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B) \[\sqrt{16-{{(\vec{a}.\vec{b})}^{2}}}\] done
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C) \[2\sqrt{4-{{(\vec{a}.\vec{b})}^{2}}}\] done
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D) \[\sqrt{4-{{(\vec{a}.\vec{b})}^{2}}}\] done
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question_answer 29) The value of \[\underset{n\to \infty }{\mathop{lim}}\,\frac{\sqrt[n]{n!}}{n}\] is ____.
A) \[\frac{1}{e}\] done
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B) \[e\] done
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C) \[\frac{2}{e}\] done
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D) \[-\,e\] done
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question_answer 30) For k= 1, 2, 3 the box \[{{B}_{k}}\]contains k red balls and\[(k+1)\] white balls. Let \[P({{B}_{1}})=\,\frac{1}{2},P({{B}_{2}})=\frac{1}{3}\] and \[P({{B}_{3}})=\,\frac{1}{6}.A\] box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box \[{{B}_{2}}\] is
A) \[\frac{35}{78}\] done
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B) \[\frac{14}{39}\] done
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C) \[\frac{10}{13}\] done
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D) \[\frac{12}{13}\] done
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question_answer 31) \[co{{s}^{-1}}(cos(2\,{{\cot }^{-1}}(\sqrt{2}-1)))\]is equal to ___.
A) \[\sqrt{2}-1\] done
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B) \[\frac{\pi }{4}\] done
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C) \[\frac{3\pi }{4}\] done
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D) None of these done
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question_answer 32) The value of is
A) \[{{30}^{x}}\] done
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B) \[{{15}^{x}}\] done
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C) \[{{30}^{-x}}\] done
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D) \[0\] done
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question_answer 33) Let \[\{{{D}_{1}},{{D}_{2}},{{D}_{3}},......,{{D}_{n}}\}\]be the set of third order determinants that can be made with the distinct non-zero real numbers \[{{a}_{1}},{{a}_{2}},.....,{{a}_{9}}\], then
A) \[\sum\limits_{i=1}^{n}{{{D}_{i}}=1}\] done
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B) \[\sum\limits_{i=1}^{n}{{{D}_{i}}=0}\] done
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C) \[{{D}_{i}}={{D}_{j}}\forall i,j\] done
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D) None of these done
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question_answer 34) The area bounded by \[y={{x}^{2}}+2,\]x-axis, x=1 and x=2 is
A) \[\frac{16}{3}\]sq. units done
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B) \[\frac{17}{3}\]sq. units done
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C) \[\frac{13}{3}\]sq. units done
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D) \[\frac{20}{3}\]sq. units done
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question_answer 35) If for A X = B, and \[{{A}^{-1}}=\] , then X is equal to
A) done
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B) done
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C) done
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D) done
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question_answer 36) Tanya gives away to each of four girls \[\frac{1}{12},\frac{5}{18},\]\[\frac{7}{30},\frac{7}{48}\]of the apples in a basket and has only just enough apples to be able to do so without dividing an apple. Find the minimum number of apples she had.
A) 250 done
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B) 720 done
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C) 750 done
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D) None of these done
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question_answer 37) The length of a ladder is exactly equal to the height of the wall it is leaning against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then the height of the wall is
A) 12m done
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B) 15m done
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C) 18m done
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D) 11m done
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question_answer 38) The odds against a husband who is 50 years old, living till he is 70 are 7:5 and the odds against his wife who is now 40, living till she is 60 are 5 : 3. Find the probability that the couple will be alive 20 years hence.
A) \[\frac{21}{32}\] done
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B) \[\frac{5}{32}\] done
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C) \[\frac{15}{32}\] done
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D) \[\frac{12}{32}\] done
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question_answer 39) There are 5 blue socks, 4 red socks and 3 green socks in Debu's wardrobe. He has to select 4 socks from this set. In how many ways can he do so?
A) 245 done
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B) 120 done
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C) 495 done
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D) 60 done
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question_answer 40) S and is pouring from a pipe at the rate of \[12\,c{{m}^{3}}\]/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
A) \[\frac{1}{12\pi }\]cm/s done
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B) \[\frac{1}{24\pi }\]cm/s done
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C) \[\frac{1}{36\pi }\]cm/s done
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D) \[\frac{1}{48\pi }\]cm/s done
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question_answer 41) A man runs around a circular field of radius 50 m at the speed of 12 km/hr. What is the time taken by the man to take twenty rounds of the field?
A) 30 min done
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B) 32 min done
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C) 34 min done
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D) \[\frac{110}{7}\]min done
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question_answer 42) A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?
A) 0.9 done
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B) 0.75 done
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C) 0.6 done
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D) 0.45 done
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question_answer 43) A group of investigators took a fair sample of 1972 children from the general population and found that there are 1000 boys and 972 girls. If the investigators claims that their research is so accurate that the gender of a new born child can be predicted based on the ratio of the sample of the population, then what is the expectation in terms of the probability that a new child born will be a girl?
A) \[\frac{243}{250}\] done
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B) \[\frac{250}{257}\] done
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C) \[\frac{9}{10}\] done
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D) \[\frac{243}{493}\] done
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question_answer 44) The average weight of the 5 officers of a regiment is 42 kg. If a senior officer was replaced by a new officer and thus the average increased by 500 gm, the weight of the new officer is ___.
A) 44.5 kg done
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B) 45 kg done
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C) 42.5 kg done
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D) None of these done
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question_answer 45) The population of a certain species in the wild varies according to a sine curve over a period of 10 years. Using the diagram, determine at what time the population will be at a minimum in the 10 years period?
A) 9.5 yrs done
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B) 9 yrs done
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C) 7.5 yrs done
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D) 8 yrs done
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question_answer 46) If a, b, c are the roots of \[{{x}^{3}}-{{x}^{2}}-2004=0\], then the value of is equal to _____.
A) \[-\,2a{{c}^{3}}+2ac-4{{a}^{2}}c+2a{{b}^{3}}-2ab+4abc\] done
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B) \[2a{{c}^{3}}+2ac-4{{a}^{2}}c+2a{{b}^{3}}-2ab+4abc\] done
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C) \[-\,2a{{c}^{3}}-ac-4{{a}^{2}}c+2a{{b}^{3}}+2ab+4abc\] done
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D) None of these done
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question_answer 47) Which of the following is the value of \[\int\limits_{-\pi /2}^{\pi /2}{\left( \frac{\cos \,x}{1+{{e}^{x}}} \right)}\]dx?
A) 1 done
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B) 0 done
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C) - 1 done
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D) \[-\frac{1}{2}\] done
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question_answer 48) If\[si{{n}^{-1}}x+si{{n}^{-1}}\text{ }y=\frac{2\pi }{3}\text{ },\text{ }co{{s}^{-1}}\text{ }x\text{ }-\text{ }co{{s}^{-1}}\text{ }y=\frac{\pi }{3}\], then the number of values of (x, y) is_____.
A) 1 done
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B) 2 done
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C) 3 done
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D) 4 done
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question_answer 49) \[\int{\sqrt{x+a\sqrt{ax-{{a}^{2}}}}dx,0<a<2}=\frac{2}{{{a}^{3/2}}}\] \[{{\{ax+a\sqrt{ax-{{a}^{2}}}\}}^{3/2}}-\frac{\sqrt{2}}{2}[A+B]+c\]Then
A) \[A=\left[ \left\{ \left( \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2} \right)\sqrt{ax+{{a}^{2}}\sqrt{ax-{{a}^{2}}}} \right\} \right]\] done
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B) \[B=\log \left[ \left\{ \left( \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2} \right)\sqrt{ax+a\sqrt{ax-{{a}^{2}}}} \right\} \right]\] done
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C) \[A=\left\{ \left( \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2} \right)\sqrt{ax+a\sqrt{ax-{{a}^{2}}}} \right\}\] done
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D) \[B=\log \left\{ \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2}\sqrt{ax+a\sqrt{ax-{{a}^{2}}}} \right\}\] done
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question_answer 50) The vector \[\vec{c}\]directed along the internal bisector of the angle between the vectors \[\vec{a}=7\hat{i}-4\hat{j}-4\hat{k}\]and \[\vec{b}=-2\hat{i}-2\hat{j}+2\hat{k}\]with \[|\vec{c}|=5\sqrt{6}\]is
A) \[\pm \frac{5}{2}(\hat{i}-7\hat{j}+2\hat{k})\] done
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B) \[\frac{5}{2}(5\hat{i}+5\hat{j}+2\hat{k})\] done
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C) \[\frac{5}{2}(\hat{i}+7\hat{j}+2\hat{k})\] done
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D) \[\frac{5}{2}(-5\hat{i}+5\hat{j}+2\hat{k})\] done
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