Which of the following digits have two lines of symmetry ?
`0,1,2,3,4,5,6,7,8,9`
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Which of the following functions has (have) y-symmetry or origin symmetry? (i) ` f(x) = x^(2) sin x" "(ii) f(x) = log (x+sqrt(1+x^(2)))` (iii)` f(x) =
(i) ` f(x) = (-x)^(2) sin (-x) =- x^(2) sin x =- f(x)`, hence function has origin symmetry (ii) `f(-x) = log (-x+sqrt(1+(-x)^(2)))` `= log(((-x+sqrt(1+x^(2)))(x+sqrt(1+x^(2))))/((x+sqrt(1+x^(2)))))` `= log(1/(x+sqrt(1+x^(2))))` ` = -...
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Which of the following functions has (have) y-symmetry or origin symmetry? (i) ` f(x) = x^(2) sin x" "(ii) f(x) = log ((1-x)/(1+x))` (iii)` f(x) = x/(
(i) `f(-x) = (-x)^(2) sin (-x) =- x^(2) sin x =- f(x)`, hence the function has origin symmetry (ii) `f(-x)= log((1-(-x))/(1+(-x))) = log ((1+x)/(1-x))=- f(x)`hence the function has origin symmetry...
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Consider three lines as follows. `L_1:5x-y+4=0` `L_2:3x-y+5=0` `L_3: x+y+8=0` If these lines enclose a triangle `A B C` and the sum of the squares of
Correct Answer - D Arranging the lines in desceding order of slope, we have `m_1=5,m_2=3,and m_3=-1` `therefore tan A =(m_1-m_2)/(1+m_1m_2)=(2)/(1+15)=(1)/(8)` `tan B=(m_1-m_3)/(1+m_2m_3)=(3+1)/(1-3)=-2` `tan C=(m_3-m_1)/(1+m_3m_1)=(-1-5)/(1-5)=(3)/(2)` `Sigma tan^(2)A=(1)/(64)+4+(9)/(4)=(1+256+144)/(64)=(401)/(64)` or `p+q=465`
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Find (i) the last digit, (ii) the last two digits, and (iii) the last three digits of `17^(256)dot`
We have `17^(256) = (17^(2))^(128) = (289)^(128) = (290-1)^(128)` `:. 17^(256) = .^(128)C_(0)(290)^(128)-.^(128)C_(1)(290)^(127)+.^(128)C_(2)(290)^(126)-"....."` `- .^(128)C_(125)(290)^(3)+.^(128)C_(126)(290)^(2)-.^(128)C_(127)(290)+1` `=[.^(128)C_(0)(290)^(128) - .^(128)C_(1)(290)^(127)+.^(128)C_(2)(290)^(126)-"....."` `-.^(128)C_(125)(290)^(3)]+.^(128)C_(126)(290)^(2) -.^(128)C_(127)(290)+1` `=1000m+((128)(127))/(2)(290)^(2)-128xx290+1` `= 1000 m + (128)(127)(290)(145)-128xx290-1` `= 1000m+(128)(290)(127xx145-1)+1` `=1000m+(128)(290)(18414)+1` `=1000m+683527680+1`...
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A binary number is made up to 8 digits. Suppose that the probability if an incorrect digit appearing is `p` and that the errors in different digits ar
Correct Answer - `1-(1-p)^(8)` Probability for an incorrec digit is p. hence, probability for 8 correct digit is `1-p)^(8).` Hence, required probability is `1-(1-p)^(8).`
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The number of arrangments of all digits of `12345` such that at least `3` digits will not come in its position is
Correct Answer - B `(b)` Total number of ways such that at least `3` digits will not occur in its position. `=^(5)C_(3){3!-^(3)C_(1)2!+^(3)C_(2)1!-^(3)C_(2)0!}+^(5)C_(4)[4!-^(4)C_(1)(3!)+^(4)C_(2)(2!)-^(4)C_(3)(1!)+^(4)C_(4)(0!)}+^(5)C_(5){5!-^(5)C_(1)4!+^(5)C_(2)3!-^(5)C_(3)2!+^(5)C_(4)1!-^(5)C_(5)(0!)}` `=10(2)+5(9)+(44)` `=20+45+44=109`
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Fill in the blanks with lines of your own along with the lines from the poem. 1. They have the means
1. They have the means. They can easily showcase prosperity. 2. So history is new again Charmed by glamour, nobody missed the past.
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Which of the following animals are TRUE coelomates with bilateral symmetry?
(a) Annelids are TRUE coelomates with bilateral symmetry .
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Round off each of the following to the number of significant digits indicated : i. 1.223 to two digits ii. 12.56 to three digits
i. 1.223 to two digits = 1.2 This is because the third digit is less than 5, so we drop it and all the other digits to its right. ii. 12.56 to...
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Read the following lines and add two poetic lines to rhyme with line.
weep, cardio..
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