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Question Number 157724 Answers: 1 Comments: 2

8. A number can be expressed as a terminating decimal,if the denominator has factors : (a) 2,3 or 5 (b) 2 or 3 (c) 3 or 5 (d) 2 or 5 9. Given that : HCF of 2520 and 6600= 120, LCM of 2520 and 6600= 252×k, then the value of k is : (a) 165 (b) 1625 (c) 550 (d) 600 10. The decimal expansion of the rational number ((47)/(2^4 ×5^(3 ) )) will terminate after : (a) 3 places (b) 4 places (c) 5 places (d) 1 place 11. The perimeter of two similar triangles ABC and LMN are 60 cm and 48 cm respectively . If LM = 8cm,then lenght of AB is : (a) 10 cm (b) 8 cm (c) 5 cm (d) 6 cm 12. Ratio in which the line segment joining (1,−7) and (6,4) are divided by x-axis is given as: (a) 4 :7 (b) 2 : 5 (c) 7 : 4 (d) 5 : 2 13. 119^2 − 111^2 is : (a) Prime number (b) Composite number ( c) An odd composite number (d)An odd prime number 14. Side of square , whose diagonal is 16 cm is given by: (a) 6(√(2 )) cm (b) 4(√2) cm (c) 7(√(2 ))cm (d) 8(√(2 ))cm

$$\mathrm{8}.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{A}\:\mathrm{number}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{as}\:\mathrm{a}\:\mathrm{terminating}\:\mathrm{decimal},\mathrm{if}\:\mathrm{the}\:\mathrm{denominator}\:\mathrm{has}\:\mathrm{factors}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{2},\mathrm{3}\:\mathrm{or}\:\mathrm{5}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{2}\:\mathrm{or}\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{3}\:\mathrm{or}\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{2}\:\mathrm{or}\:\mathrm{5} \\ $$$$\:\mathrm{9}.\:\:\:\:\:\:\:\:\:\:\mathrm{Given}\:\mathrm{that}\::\:\mathrm{HCF}\:\mathrm{of}\:\mathrm{2520}\:\mathrm{and}\:\mathrm{6600}=\:\mathrm{120},\:\mathrm{LCM}\:\mathrm{of}\:\mathrm{2520}\:\mathrm{and}\:\mathrm{6600}=\:\mathrm{252}×{k},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{165} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{1625} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{550} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{600} \\ $$$$\:\mathrm{10}.\:\:\:\:\:\:\:\:\:\mathrm{The}\:\mathrm{decimal}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rational}\:\mathrm{number}\:\frac{\mathrm{47}}{\mathrm{2}^{\mathrm{4}} ×\mathrm{5}^{\mathrm{3}\:} }\:\mathrm{will}\:\mathrm{terminate}\:\mathrm{after}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{3}\:\mathrm{places} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{4}\:\mathrm{places} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{5}\:\mathrm{places} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{1}\:\mathrm{place} \\ $$$$\:\mathrm{11}.\:\:\:\:\:\:\:\:\:\:\:\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{two}\:\mathrm{similar}\:\mathrm{triangles}\:\mathrm{ABC}\:\mathrm{and}\:\mathrm{LMN}\:\mathrm{are}\:\mathrm{60}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{48}\:\mathrm{cm}\:\mathrm{respectively}\:.\:\mathrm{If}\:\mathrm{LM}\:=\:\mathrm{8cm},\mathrm{then}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{is}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{10}\:\mathrm{cm} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{8}\:\mathrm{cm} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{5}\:\mathrm{cm} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{6}\:\mathrm{cm} \\ $$$$\:\mathrm{12}.\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Ratio}\:\mathrm{in}\:\mathrm{which}\:\mathrm{the}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{joining}\:\left(\mathrm{1},−\mathrm{7}\right)\:\mathrm{and}\:\left(\mathrm{6},\mathrm{4}\right)\:\mathrm{are}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}-\mathrm{axis}\:\mathrm{is}\:\mathrm{given}\:\mathrm{as}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{4}\::\mathrm{7} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{2}\::\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{7}\::\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{5}\::\:\mathrm{2} \\ $$$$\:\mathrm{13}.\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{119}^{\mathrm{2}} −\:\mathrm{111}^{\mathrm{2}} \:\mathrm{is}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{Prime}\:\mathrm{number} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{Composite}\:\mathrm{number} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{c}\right)\:\mathrm{An}\:\mathrm{odd}\:\mathrm{composite}\:\mathrm{number} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\mathrm{An}\:\mathrm{odd}\:\mathrm{prime}\:\mathrm{number} \\ $$$$\:\mathrm{14}.\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Side}\:\mathrm{of}\:\mathrm{square}\:,\:\mathrm{whose}\:\mathrm{diagonal}\:\mathrm{is}\:\mathrm{16}\:\mathrm{cm}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{6}\sqrt{\mathrm{2}\:}\:\mathrm{cm} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{4}\sqrt{\mathrm{2}}\:\mathrm{cm} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{7}\sqrt{\mathrm{2}\:}\mathrm{cm} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{8}\sqrt{\mathrm{2}\:\:}\mathrm{cm} \\ $$$$\: \\ $$

Question Number 156710 Answers: 1 Comments: 4

Question Number 156671 Answers: 2 Comments: 0

Question Number 156509 Answers: 1 Comments: 5

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Question Number 156335 Answers: 1 Comments: 1

Question Number 156316 Answers: 3 Comments: 1

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Question Number 156184 Answers: 2 Comments: 1

Question Number 155692 Answers: 1 Comments: 5

Question Number 155625 Answers: 2 Comments: 0

lim_(x→0) (((tanx)/x))^(1/x^2 ) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{{tanx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} =\:? \\ $$

Question Number 155574 Answers: 1 Comments: 0

The mean and standard deviation of 20 observation are found to be 10 and 2 respectively .On rechecking it was found that an observation 8 was incorrect.Calculate the incorrect mean and standard deviation (a)If the wrong iterm was ommited (b) If it is replaced by 12

$$\mathrm{The}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\:\mathrm{deviation} \\ $$$$\mathrm{of}\:\mathrm{20}\:\mathrm{observation}\:\:\mathrm{are}\:\mathrm{found}\:\mathrm{to}\:\mathrm{be}\: \\ $$$$\mathrm{10}\:\mathrm{and}\:\mathrm{2}\:\mathrm{respectively}\:.\mathrm{On}\:\mathrm{rechecking} \\ $$$$\mathrm{it}\:\mathrm{was}\:\mathrm{found}\:\mathrm{that}\:\:\mathrm{an}\:\mathrm{observation} \\ $$$$\mathrm{8}\:\mathrm{was}\:\mathrm{incorrect}.\mathrm{Calculate}\:\mathrm{the}\:\mathrm{incorrect} \\ $$$$\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\:\mathrm{deviation} \\ $$$$\left(\boldsymbol{\mathrm{a}}\right)\boldsymbol{\mathrm{I}}\mathrm{f}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{wrong}}\:\boldsymbol{\mathrm{iterm}}\:\boldsymbol{\mathrm{was}}\:\:\boldsymbol{\mathrm{ommited}} \\ $$$$\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{replaced}}\:\boldsymbol{\mathrm{by}}\:\mathrm{12} \\ $$

Question Number 154353 Answers: 1 Comments: 4

Question Number 154330 Answers: 1 Comments: 0

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Question Number 154172 Answers: 0 Comments: 1

Question Number 153580 Answers: 1 Comments: 0

Question Number 153108 Answers: 1 Comments: 0

∫(dθ/(sin^2 θ(3−sin θ)))

$$\int\frac{\mathrm{d}\theta}{\mathrm{sin}\:^{\mathrm{2}} \theta\left(\mathrm{3}−\mathrm{sin}\:\theta\right)} \\ $$

Question Number 152985 Answers: 0 Comments: 2

Question Number 152829 Answers: 2 Comments: 0

Question Number 151934 Answers: 1 Comments: 0

Question Number 151893 Answers: 1 Comments: 0

∫x(x^3 +a^3 )dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\int\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{a}^{\mathrm{3}} \right)\mathrm{dx} \\ $$

Question Number 151561 Answers: 1 Comments: 0

Given that x+iy=(a/(b+sin θ+icos θ)) show that (b^2 −1)(x^2 +y^2 )+a^2 =2abx

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{x}+\mathrm{iy}=\frac{\mathrm{a}}{\mathrm{b}+\mathrm{sin}\:\theta+\mathrm{icos}\:\theta} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{b}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)+\mathrm{a}^{\mathrm{2}} =\mathrm{2abx} \\ $$

Question Number 151496 Answers: 1 Comments: 0

∀x,y∈R_+ ^∗ , show that (x/(x^4 +y^2 ))+(y/(y^4 +x^2 ))≤(1/(xy))

$$\forall{x},{y}\in\mathbb{R}_{+} ^{\ast} ,\:{show}\:{that}\:\frac{{x}}{{x}^{\mathrm{4}} +{y}^{\mathrm{2}} }+\frac{{y}}{{y}^{\mathrm{4}} +{x}^{\mathrm{2}} }\leqslant\frac{\mathrm{1}}{{xy}} \\ $$

Question Number 151444 Answers: 2 Comments: 0

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