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Question Number 157725    Answers: 1   Comments: 0

form f(x,y,z) =((xy)′c)′((x′+c)(y′+z′))′ in standard SOP form and canonical SOP form

$$\mathrm{form}\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\left(\left(\mathrm{xy}\right)'\mathrm{c}\right)'\left(\left(\mathrm{x}'+\mathrm{c}\right)\left(\mathrm{y}'+\mathrm{z}'\right)\right)'\: \\ $$$$\mathrm{in}\:\mathrm{standard}\:\mathrm{SOP}\:\mathrm{form}\:\mathrm{and}\:\mathrm{canonical}\:\mathrm{SOP}\:\mathrm{form} \\ $$

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 157749    Answers: 0   Comments: 10

a^2 + b^2 + c^2 + d^2 = 4 a,b,c,d ∈ R max{a^3 + b^3 + c^3 + d^3 } = ?

$${a}^{\mathrm{2}} +\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:+\:{d}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$$${a},{b},{c},{d}\:\in\:\mathbb{R} \\ $$$${max}\left\{{a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:+\:{d}^{\mathrm{3}} \right\}\:\:=\:\:? \\ $$

Question Number 157750    Answers: 1   Comments: 0

∫_0 ^∞ ((1−cos 4x)/(xe^x )) dx=?

$$\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−\mathrm{cos}\:\mathrm{4}{x}}{{xe}^{{x}} }\:{dx}=? \\ $$

Question Number 157793    Answers: 0   Comments: 0

Question Number 157712    Answers: 2   Comments: 2

Question Number 157706    Answers: 1   Comments: 0

Question Number 157701    Answers: 2   Comments: 0

a;b;c∈N (1/(a + (1/(b + (1/c))))) = ((16)/(37)) ⇒ a+b+c=?

$$\mathrm{a};\mathrm{b};\mathrm{c}\in\mathbb{N} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}\:+\:\frac{\mathrm{1}}{\mathrm{b}\:+\:\frac{\mathrm{1}}{\mathrm{c}}}}\:=\:\frac{\mathrm{16}}{\mathrm{37}}\:\:\:\Rightarrow\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=? \\ $$

Question Number 157695    Answers: 4   Comments: 0

Question Number 157694    Answers: 1   Comments: 0

x^3 =x+c ; 0<c≤(2/(3(√3))) find x, without trigonometric cubic formula.

$$\:\:\:{x}^{\mathrm{3}} ={x}+{c}\:\:\:\:\:;\:\:\:\:\mathrm{0}<{c}\leqslant\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$${find}\:{x},\:{without}\:{trigonometric} \\ $$$${cubic}\:{formula}. \\ $$

Question Number 157688    Answers: 0   Comments: 0

lim_(x→0) ((1/(ln (x+(√(x^2 +1))))) −(1/(ln (x+1))) )=?

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

Question Number 157687    Answers: 2   Comments: 1

if A ; a ; b ∈ Z^+ and 6∙40!=A∙2^a ∙3^b find (a+b)_(max) = ?

$$\mathrm{if}\:\:\:\mathrm{A}\:;\:\mathrm{a}\:;\:\mathrm{b}\:\in\:\mathbb{Z}^{+} \:\:\mathrm{and}\:\:\mathrm{6}\centerdot\mathrm{40}!=\mathrm{A}\centerdot\mathrm{2}^{\boldsymbol{\mathrm{a}}} \centerdot\mathrm{3}^{\boldsymbol{\mathrm{b}}} \\ $$$$\mathrm{find}\:\:\:\left(\mathrm{a}+\mathrm{b}\right)_{\boldsymbol{\mathrm{max}}} \:=\:? \\ $$

Question Number 157686    Answers: 3   Comments: 0

if f(x+1)-f(x)=3 and f(25)=72 find f(2) = ?

$$\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)-\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{25}\right)=\mathrm{72} \\ $$$$\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:? \\ $$

Question Number 157665    Answers: 2   Comments: 0

Question Number 157664    Answers: 0   Comments: 3

{ ((ax+by=7)),((ax^2 +by^2 =49)),((ax^3 +by^3 =133)),((ax^4 +by^4 =406)) :} ⇒2014x+2014y−100a−100b−2014xy=?

$$\:\begin{cases}{{ax}+{by}=\mathrm{7}}\\{{ax}^{\mathrm{2}} +{by}^{\mathrm{2}} =\mathrm{49}}\\{{ax}^{\mathrm{3}} +{by}^{\mathrm{3}} =\mathrm{133}}\\{{ax}^{\mathrm{4}} +{by}^{\mathrm{4}} =\mathrm{406}}\end{cases} \\ $$$$\:\Rightarrow\mathrm{2014}{x}+\mathrm{2014}{y}−\mathrm{100}{a}−\mathrm{100}{b}−\mathrm{2014}{xy}=? \\ $$

Question Number 157663    Answers: 2   Comments: 0

Question Number 157660    Answers: 0   Comments: 0

Given x_1 = 1, x_2 , x_3 , …, is a real numbers sequence for n ≥ 1 with recurrence relation x_(n+1) − x_n = (1/(2x_n )) . [x] is expressed as the largest integer of x . [25x_(625) ] = ?

$${Given}\:\:{x}_{\mathrm{1}} \:=\:\mathrm{1},\:{x}_{\mathrm{2}} \:,\:{x}_{\mathrm{3}} \:,\:\ldots,\:{is}\:\:{a}\:\:{real}\:\:{numbers}\:\:{sequence}\:\:{for}\:\:{n}\:\geqslant\:\mathrm{1}\:\:{with}\:\: \\ $$$${recurrence}\:\:{relation}\:\:{x}_{{n}+\mathrm{1}} \:−\:{x}_{{n}} \:=\:\frac{\mathrm{1}}{\mathrm{2}{x}_{{n}} }\:\:. \\ $$$$\left[{x}\right]\:\:{is}\:\:{expressed}\:\:{as}\:\:{the}\:\:{largest}\:\:{integer}\:\:{of}\:\:{x}\:\:. \\ $$$$\left[\mathrm{25}{x}_{\mathrm{625}} \right]\:\:=\:\:? \\ $$

Question Number 157655    Answers: 1   Comments: 1

x^2 f(x^3 )+(1/((1+x)^2 )) f(((1−x)/(1+x)))=4x^3 (1+x^4 )^5 ∫_( 0) ^( 1) f(x) dx =?

$$\:\:{x}^{\mathrm{2}} \:{f}\left({x}^{\mathrm{3}} \right)+\frac{\mathrm{1}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }\:{f}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)=\mathrm{4}{x}^{\mathrm{3}} \left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\mathrm{5}} \\ $$$$\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} {f}\left({x}\right)\:{dx}\:=? \\ $$

Question Number 157647    Answers: 0   Comments: 3

bonjour ,calculer la limite suivante en utilisant les developpements limites: lim_(x→0) ((1/x^2 ) − (1/(sin^2 x))).

$${bonjour}\:,{calculer}\:{la}\:{limite}\:{suivante}\:{en}\:{utilisant}\:{les}\:{developpements}\:{limites}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}}\right). \\ $$

Question Number 157645    Answers: 1   Comments: 0

what is the latest version of this app available i m having 2.265

$${what}\:{is}\:{the}\:{latest}\:{version} \\ $$$${of}\:{this}\:{app}\:{available} \\ $$$${i}\:{m}\:{having}\:\:\:\mathrm{2}.\mathrm{265} \\ $$

Question Number 157644    Answers: 2   Comments: 0

Prove (1/2)(√(2−(√3)))=(((√6)−(√2))/4)

$$\mathrm{Prove}\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}=\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}}{\mathrm{4}} \\ $$

Question Number 157637    Answers: 2   Comments: 0

3^x =2^x y+1 {x:y} εN.

$$\:\:\:\:\:\:\mathrm{3}^{{x}} =\mathrm{2}^{{x}} {y}+\mathrm{1} \\ $$$$\:\:\:\:\:\left\{\boldsymbol{{x}}:\boldsymbol{{y}}\right\}\:\varepsilon\mathbb{N}.\: \\ $$

Question Number 157635    Answers: 0   Comments: 0

Question Number 157631    Answers: 0   Comments: 0

what is higher order derivatives? discuss its importants.

$${what}\:{is}\:{higher}\:{order}\:{derivatives}? \\ $$$${discuss}\:{its}\:{importants}. \\ $$

Question Number 157630    Answers: 1   Comments: 1

Question Number 157652    Answers: 0   Comments: 4

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