Biology
General
Easy

Question

Match the names of cells given under Column I with the names of organs/parts in which they occur, given under Column II) Choose the answer which gives correct combination of alphabets of two columns

  1. A = r; B = t, C = s; D = p    
  2. A = q, B = p, C = s, D = t    
  3. A = s, B = t; C = p, D = q    
  4. A = r, B = p, C = s, D = q    

The correct answer is: A = q, B = p, C = s, D = t

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Match Column - I with Column - II and select the correct option from the codes given below.

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If blank to the power of n P subscript r equals 720 comma to the power of n C subscript r equals 120  then (n,r) is

Given, blank to the power of n P subscript r equals 720 comma to the power of n C subscript r equals 120
blank to the power of n P subscript r equals 720
rightwards double arrow fraction numerator n factorial over denominator open parentheses n minus r close parentheses factorial end fraction equals 720
rightwards double arrow n factorial equals 720 left parenthesis n minus r right parenthesis factorial... space e q u space 1
blank to the power of n C subscript r equals 120
rightwards double arrow fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction equals 120
rightwards double arrow n factorial equals 120 space r factorial space left parenthesis n minus r right parenthesis factorial.... space e q u space 2
from equ 1 and 2
720(n-r)! =120 r! (n-r)!
rightwards double arrow6=r!
rightwards double arrowr=3
putting r=3 in equ 1
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rightwards double arrow fraction numerator n left parenthesis n minus 1 right parenthesis left parenthesis n minus 2 right parenthesis left parenthesis n minus 3 right parenthesis factorial over denominator left parenthesis n minus 3 right parenthesis factorial end fraction equals 720
rightwards double arrow n left parenthesis n minus 1 right parenthesis left parenthesis n minus 2 right parenthesis equals 10 cross times 9 cross times 8
rightwards double arrow n equals 10

If blank to the power of n P subscript r equals 720 comma to the power of n C subscript r equals 120  then (n,r) is

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Given, blank to the power of n P subscript r equals 720 comma to the power of n C subscript r equals 120
blank to the power of n P subscript r equals 720
rightwards double arrow fraction numerator n factorial over denominator open parentheses n minus r close parentheses factorial end fraction equals 720
rightwards double arrow n factorial equals 720 left parenthesis n minus r right parenthesis factorial... space e q u space 1
blank to the power of n C subscript r equals 120
rightwards double arrow fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction equals 120
rightwards double arrow n factorial equals 120 space r factorial space left parenthesis n minus r right parenthesis factorial.... space e q u space 2
from equ 1 and 2
720(n-r)! =120 r! (n-r)!
rightwards double arrow6=r!
rightwards double arrowr=3
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fraction numerator n factorial over denominator open parentheses n minus 3 close parentheses factorial end fraction equals 720
rightwards double arrow fraction numerator n left parenthesis n minus 1 right parenthesis left parenthesis n minus 2 right parenthesis left parenthesis n minus 3 right parenthesis factorial over denominator left parenthesis n minus 3 right parenthesis factorial end fraction equals 720
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No. of permutations that can be made using all the letters of the word FLOWER is :

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As we have to fill 8 places from 12 balls numbered 1 to 12.
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rightwards double arrow fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator left parenthesis n minus 4 right parenthesis factorial end fraction cross times fraction numerator left parenthesis n minus 5 right parenthesis factorial over denominator n factorial end fraction equals 3 over 2
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rightwards double arrow fraction numerator n plus 1 over denominator n minus 4 end fraction equals 3 over 2
rightwards double arrow 2 left parenthesis n plus 1 right parenthesis equals 3 left parenthesis n minus 4 right parenthesis
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If  left parenthesis n plus 1 right parenthesis P subscript 5 colon to the power of n P subscript 5 equals 3 colon 2then n is:

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rightwards double arrow fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator left parenthesis n minus 4 right parenthesis factorial end fraction cross times fraction numerator left parenthesis n minus 5 right parenthesis factorial over denominator n factorial end fraction equals 3 over 2
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rightwards double arrow fraction numerator n plus 1 over denominator n minus 4 end fraction equals 3 over 2
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If blank to the power of n P subscript 5 equals to the power of n P subscript 6  then n is :

Given, blank to the power of n P subscript 5 equals to the power of n P subscript 6
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rightwards double arrow open parentheses n minus 6 close parentheses factorial equals open parentheses n minus 5 close parentheses factorial
rightwards double arrow open parentheses n minus 6 close parentheses factorial equals open parentheses n minus 5 close parentheses open parentheses n minus 6 close parentheses factorial
rightwards double arrow n minus 5 equals 1
rightwards double arrow n equals 1 plus 5
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If blank to the power of n P subscript 5 equals to the power of n P subscript 6  then n is :

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Given, blank to the power of n P subscript 5 equals to the power of n P subscript 6
rightwards double arrow fraction numerator n factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction equals fraction numerator n factorial over denominator open parentheses n minus 6 close parentheses factorial end fraction
rightwards double arrow open parentheses n minus 6 close parentheses factorial equals open parentheses n minus 5 close parentheses factorial
rightwards double arrow open parentheses n minus 6 close parentheses factorial equals open parentheses n minus 5 close parentheses open parentheses n minus 6 close parentheses factorial
rightwards double arrow n minus 5 equals 1
rightwards double arrow n equals 1 plus 5
rightwards double arrow n equals 6
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If blank to the power of 10 P subscript r equals 5040 then r is :

Given, blank to the power of 10 P subscript r equals 5040
rightwards double arrow fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 10 cross times 9 cross times 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator open parentheses 10 minus r close parentheses factorial end fraction equals 1
rightwards double arrow 6 factorial equals open parentheses 10 minus r close parentheses factorial
rightwards double arrow open parentheses 10 minus 4 close parentheses factorial equals open parentheses 10 minus r close parentheses factorial
rightwards double arrow r equals 4

If blank to the power of 10 P subscript r equals 5040 then r is :

Maths-General
Given, blank to the power of 10 P subscript r equals 5040
rightwards double arrow fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 10 cross times 9 cross times 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator open parentheses 10 minus r close parentheses factorial end fraction equals 1
rightwards double arrow 6 factorial equals open parentheses 10 minus r close parentheses factorial
rightwards double arrow open parentheses 10 minus 4 close parentheses factorial equals open parentheses 10 minus r close parentheses factorial
rightwards double arrow r equals 4
parallel

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