Find the two natural numbers so that their sum cannot exceed 6 and the difference between first and second number is positive and does not exceed 2 and also the resultant sum is maximum
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A number is selected at random from the first 25 natural numbers. If it is a composite number, then it is divided by 6. But if it is not a composite n
Correct Answer - `0.2` Lec C be the event of the selected number being composite and E be the event of there being no remainder. `P(C)=(n(C))/(n(S))=15/25=3/5,P(barC)=2/5` `P(E//C)=4/15, P(E//barC)=1/10` `P(E)=P(C)P(E//C)+P(barC)P(E//barC).` `=3/5xx4/15+2/5xx1/10=4/25+1/25=1/5=0.2`
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Does not exceed ?10 lakhs, Does not exceed Rs 25 lakhs, Does not exceed Rs 2 crores.
Does not exceed Rs 25 lakhs
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The sum of two natural numbers is 28 and their product is 192.find the numbers
let two no. be x1, x2 . x1+ x2= 28..(1) x1.x2= 192 ...(2) by 1 and 2 put x1= 192/ x2 in eqn 1 and solve quadratic .x2^ 2 - 28x2+ 192 =...
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If `|z_1|=|z_2|=|z_3|=1` then value of `|z_1-z_3|^2+|z_3-z_1|^2+|z_1-z_2|^2` cannot exceed
Correct Answer - B `(b)` Let `y=|z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2)` `=(z_(1)-z_(2))(barz_(1)-barz_(2))+(z_(2)-z_(3))(barz_(2)-barz_(3))+(z_(3)-z_(1))(barz_(3)-barz_(1))` `=6-(z_(1)barz_(2)+z_(2)barz_(1)+z_(2)barz_(3)+barz_(2)z_(3)+z_(3)barz_(1)+z_(1)barz_(3))`...........`(i)` Now we know `|z_(1)+z_(2)+z_(3)|^(2) ge 0` `implies 3+(z_(1)barz_(2)+z_(2)barz_(1)+z_(1)barz_(3)+z_(3)barz_(1)+z_(2)barz_(3)+barz_(2)z_(3)) ge 0`.........`(ii)` From `(i)` and `(ii)`, `y le 9`
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A number is selected at random from the first twenty-five natural numbers. If it is a composite number, then it is divided by `5`. But if it is not a
Correct Answer - C `(c )` Let `C=` the event of the selected number being composite, `E=` the event of there being no remainder. `P(C )=(n(C ))/(n(S))=(15)/(25)=(3)/(5)`, `P(barC)=(2)/(5)` `P(E//C)=(4)/(15)`, `P(E//barC)=(1)/(10)` `P(E)=P(C...
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3. Suppose set \( A \) consists of first 250 natural numbers that are multiples of 3 and set \( B \) consists of first 200 even natural numbers. How many elements does \( A \cup B \) have? (a) 324 (b) 364 (c) 384 (d) 400
Given: n(A)=250 n(B)=200 A={3,6,9,12,.......750} B=2,4,6,8,10.......400} Therefore,A⋂B={6,12,18....396) =>n(A⋂B)=396/6=66 n(A∪B)=n(A)+n(B)-n(A⋂B) =250+200-66 ...
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Which of the following collections is not a set ? `(i)` The collection of natural numbers between `2` and `20` `(ii)` The collection of numbers which
Correct Answer - `(iv)`
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Suggest a universal set for the set given below. A = {Even numbers less than 100} B={Odd natural numbers less than 100 in natural numbers }
Correct Answer - `mu = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12---------, 99}`
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The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Correct Answer - `12, 6, 3 or 3, 6, 12`
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Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number? (a) 0.8 (b) 5.1 (c) 2
Correct Answer - (a) 0 और 1;1 `" "` (b) 5 और 6;5 (c ) 2 और 3;3 `" "` (d) 6 और 7;6 (e) 9.0 स्वयं 9 पूर्ण संख्या...
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