Maths-
General
Easy

Question

If first, fifth and last terms of an A.P. is l, m, p respectively and sum of the A.P. is fraction numerator open parentheses l plus p close parentheses open parentheses 4 p plus m minus s l close parentheses over denominator K open parentheses m minus l close parentheses end fraction comma text then end text K text is end text

  1. 2    
  2. 3    
  3. 4    
  4. 5.    

The correct answer is: 2


    Let common difference = d and number of terms = n
    therefore T subscript 5 end subscript equals m rightwards double arrow l plus open parentheses 5 minus 1 close parentheses d equals m rightwards double arrow l plus 4 r equals m rightwards double arrow d equals fraction numerator m minus l over denominator 4 end fraction T subscript n end subscript equals p rightwards double arrow l plus open parentheses n minus 1 close parentheses d equals p rightwards double arrow l plus open parentheses n minus 1 close parentheses open parentheses fraction numerator m minus l over denominator 4 end fraction close parentheses equals p rightwards double arrow open parentheses n minus 1 close parentheses fraction numerator m minus l over denominator 4 end fraction equals p minus l rightwards double arrow n minus 1 equals fraction numerator 4 open parentheses p minus l close parentheses over denominator m minus l end fraction rightwards double arrow n equals 1 plus fraction numerator 4 open parentheses p minus l close parentheses over denominator m minus l end fraction equals fraction numerator m minus l plus 4 p plus 4 l over denominator m minus l end fraction equals fraction numerator 4 p plus m minus 5 l over denominator m minus l end fraction
    text Now end text S subscript n end subscript equals fraction numerator n over denominator 2 end fraction open square brackets text Firstterm end text plus text lastterm end text close square brackets equals fraction numerator 4 p plus m minus 5 l over denominator 2 open parentheses m minus l close parentheses end fraction open parentheses l plus p close parentheses
    Compare this with the given summation, we get K = 2.

    Related Questions to study

    General
    Maths-

    The sum of n terms of the series fraction numerator 1 to the power of 2 end exponent over denominator 1 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent over denominator 1 plus 2 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent over denominator 1 plus 2 plus 3 end fraction+….. is

    The sum of n terms of the series fraction numerator 1 to the power of 2 end exponent over denominator 1 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent over denominator 1 plus 2 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent over denominator 1 plus 2 plus 3 end fraction+….. is

    Maths-General
    General
    Maths-

    If every pair from among the equations x2 + px + qr = 0, x2 + qx + rp = 0 and x2 + rx + pq = 0 have a common root, then open parentheses fraction numerator s u m blank o f blank r o o t s over denominator p r o d u c t blank o f blank r o o t s end fraction close parentheses is

    If every pair from among the equations x2 + px + qr = 0, x2 + qx + rp = 0 and x2 + rx + pq = 0 have a common root, then open parentheses fraction numerator s u m blank o f blank r o o t s over denominator p r o d u c t blank o f blank r o o t s end fraction close parentheses is

    Maths-General
    General
    Chemistry-

    Which is U.P. spirit (containing ethyl alcohol by volume)?

    Which is U.P. spirit (containing ethyl alcohol by volume)?

    Chemistry-General
    parallel
    General
    Chemistry-

    When vapours of an alcohol are passed over hot reduced copper, alcohol is converted into alkene, the alcohol is:

    When vapours of an alcohol are passed over hot reduced copper, alcohol is converted into alkene, the alcohol is:

    Chemistry-General
    General
    Chemistry-

    Primary amine on treatment with N a N O subscript 2 end subscript and HCI yields:

    Primary amine on treatment with N a N O subscript 2 end subscript and HCI yields:

    Chemistry-General
    General
    Chemistry-

    Alcoholic fermentation is brought by:

    Alcoholic fermentation is brought by:

    Chemistry-General
    parallel
    General
    Chemistry-

    HBr reacts fastest with:

    HBr reacts fastest with:

    Chemistry-General
    General
    Chemistry-

    Which one of the following alcohols reacts most readily with Lucas reagent?

    Which one of the following alcohols reacts most readily with Lucas reagent?

    Chemistry-General
    General
    Chemistry-

    In this reaction,

    the molecule (A) and the reagent (B) are :

    In this reaction,

    the molecule (A) and the reagent (B) are :

    Chemistry-General
    parallel
    General
    Chemistry-

    Propene on reaction with carbon monoxide and hydrogen at high temperature under pressure in presence of cobalt carbonyl catalyst gives:

    Propene on reaction with carbon monoxide and hydrogen at high temperature under pressure in presence of cobalt carbonyl catalyst gives:

    Chemistry-General
    General
    Chemistry-

    What is the product (A) in the following reaction?

    What is the product (A) in the following reaction?

    Chemistry-General
    General
    Chemistry-

    A compound soluble in conc. H subscript 2 end subscript S O subscript 4 end subscript ' It does not decolourise bromine in C C l subscript 4 end subscript but oxidised by chromic anhydride in aqueous H subscript 2 end subscript S O subscript 4 end subscript within two seconds, turning orange solution to blue, green, and then opaque. The original compound is:

    A compound soluble in conc. H subscript 2 end subscript S O subscript 4 end subscript ' It does not decolourise bromine in C C l subscript 4 end subscript but oxidised by chromic anhydride in aqueous H subscript 2 end subscript S O subscript 4 end subscript within two seconds, turning orange solution to blue, green, and then opaque. The original compound is:

    Chemistry-General
    parallel
    General
    Chemistry-

    Free radical halogenation takes place in the presence of light or at high temperature (above 773K). Formation of halogen free radical intermediate takes place in first step called chain initiation step.
    C l subscript 2 end subscript stack ⟶ with h v on top 2 C l to the power of ring operator end exponent
    This reaction is mainly given by those compounds which have atleast one hydrogen atom present at s p to the power of 3 end exponent -hybrid carbon. Reactivity of s p to the power of 3 end exponent -hybrid carbon depends on the reactivity of reaction intermediate. The relative rate of formation of alkyl radicals by a chlorine radical is :
    text Tertiary  end text stack greater than with left parenthesis 5 right parenthesis below stack text  Secondary  end text with left parenthesis 3.8 right parenthesis below greater than stack text  Primary  end text with left parenthesis 1 right parenthesis below
    Percentage yield of the product =fraction numerator R e l a t i v e blank a m o u n t blank cross times 100 over denominator S u m blank o f blank r e l a t i v e blank a m o u n t s end fraction
    Relative amount = Number of hydrogen atoms on the respective carbon x relative reactivity.
    NBS (N-bromo succinimide) is used for bromination at allylic and benzylic carbon, whereas Br2/hv gives bromination at . benzylic, allylic and alkyl carbon.
    Arrange decreasing order of reactivity of given compounds with NBS: (N-bromo succinimide)
    I) C subscript 6 end subscript H subscript 5 end subscript minus C H subscript 3 end subscript
    II) C subscript 6 end subscript H subscript 5 end subscript minus C H subscript 2 end subscript minus C H subscript 2 end subscript minus C H subscript 3 end subscript
    III) C subscript 6 end subscript H subscript 5 end subscript minus C H subscript 2 end subscript minus C H equals C H subscript 2 end subscript
    IV) 
    Select the correct answer from the codes given below:

    Free radical halogenation takes place in the presence of light or at high temperature (above 773K). Formation of halogen free radical intermediate takes place in first step called chain initiation step.
    C l subscript 2 end subscript stack ⟶ with h v on top 2 C l to the power of ring operator end exponent
    This reaction is mainly given by those compounds which have atleast one hydrogen atom present at s p to the power of 3 end exponent -hybrid carbon. Reactivity of s p to the power of 3 end exponent -hybrid carbon depends on the reactivity of reaction intermediate. The relative rate of formation of alkyl radicals by a chlorine radical is :
    text Tertiary  end text stack greater than with left parenthesis 5 right parenthesis below stack text  Secondary  end text with left parenthesis 3.8 right parenthesis below greater than stack text  Primary  end text with left parenthesis 1 right parenthesis below
    Percentage yield of the product =fraction numerator R e l a t i v e blank a m o u n t blank cross times 100 over denominator S u m blank o f blank r e l a t i v e blank a m o u n t s end fraction
    Relative amount = Number of hydrogen atoms on the respective carbon x relative reactivity.
    NBS (N-bromo succinimide) is used for bromination at allylic and benzylic carbon, whereas Br2/hv gives bromination at . benzylic, allylic and alkyl carbon.
    Arrange decreasing order of reactivity of given compounds with NBS: (N-bromo succinimide)
    I) C subscript 6 end subscript H subscript 5 end subscript minus C H subscript 3 end subscript
    II) C subscript 6 end subscript H subscript 5 end subscript minus C H subscript 2 end subscript minus C H subscript 2 end subscript minus C H subscript 3 end subscript
    III) C subscript 6 end subscript H subscript 5 end subscript minus C H subscript 2 end subscript minus C H equals C H subscript 2 end subscript
    IV) 
    Select the correct answer from the codes given below:

    Chemistry-General
    General
    Chemistry-

    Free radical halogenation takes place in the presence of light or at high temperature (above 773K). Formation of halogen free radical intermediate takes place in first step called chain initiation step.
    C l subscript 2 end subscript stack ⟶ with h v on top 2 C l to the power of ring operator end exponent
    This reaction is mainly given by those compounds which have atleast one hydrogen atom present at s p to the power of 3 end exponent -hybrid carbon. Reactivity of s p to the power of 3 end exponent -hybrid carbon depends on the reactivity of reaction intermediate. The relative rate of formation of alkyl radicals by a chlorine radical is :
    text Tertiary  end text stack greater than with left parenthesis 5 right parenthesis below stack text  Secondary  end text with left parenthesis 3.8 right parenthesis below greater than stack text  Primary  end text with left parenthesis 1 right parenthesis below
    Percentage yield of the product =fraction numerator R e l a t i v e blank a m o u n t blank cross times 100 over denominator S u m blank o f blank r e l a t i v e blank a m o u n t s end fraction
    Relative amount = Number of hydrogen atoms on the respective carbon x relative reactivity.
    NBS (N-bromo succinimide) is used for bromination at allylic and benzylic carbon, whereas Br2/hv gives bromination at . benzylic, allylic and alkyl carbon.
    Chlorination of butane takes place as:

    Percentage yield of 2-chlorobutane will be:

    Free radical halogenation takes place in the presence of light or at high temperature (above 773K). Formation of halogen free radical intermediate takes place in first step called chain initiation step.
    C l subscript 2 end subscript stack ⟶ with h v on top 2 C l to the power of ring operator end exponent
    This reaction is mainly given by those compounds which have atleast one hydrogen atom present at s p to the power of 3 end exponent -hybrid carbon. Reactivity of s p to the power of 3 end exponent -hybrid carbon depends on the reactivity of reaction intermediate. The relative rate of formation of alkyl radicals by a chlorine radical is :
    text Tertiary  end text stack greater than with left parenthesis 5 right parenthesis below stack text  Secondary  end text with left parenthesis 3.8 right parenthesis below greater than stack text  Primary  end text with left parenthesis 1 right parenthesis below
    Percentage yield of the product =fraction numerator R e l a t i v e blank a m o u n t blank cross times 100 over denominator S u m blank o f blank r e l a t i v e blank a m o u n t s end fraction
    Relative amount = Number of hydrogen atoms on the respective carbon x relative reactivity.
    NBS (N-bromo succinimide) is used for bromination at allylic and benzylic carbon, whereas Br2/hv gives bromination at . benzylic, allylic and alkyl carbon.
    Chlorination of butane takes place as:

    Percentage yield of 2-chlorobutane will be:

    Chemistry-General
    General
    Chemistry-

    SN1 reaction is a first order nucleophilic substitution, e.g.,

    The concentration of nucleophile does not appear in the rate law expression:
    Reaction rate = k[ RX]
    In a multistep organic reaction, the rate-limiting step is the slowest step. Rate determining step is represented by the following energy level diagram:


    A reaction energy level diagram for an S subscript N to the power of 1 end exponent end subscript reaction. The rate limiting step is spontaneous dissociation of an alkyl halide to give a carbocation intermediate

    S subscript N to the power of 1 end exponent end subscript reaction is:

    SN1 reaction is a first order nucleophilic substitution, e.g.,

    The concentration of nucleophile does not appear in the rate law expression:
    Reaction rate = k[ RX]
    In a multistep organic reaction, the rate-limiting step is the slowest step. Rate determining step is represented by the following energy level diagram:


    A reaction energy level diagram for an S subscript N to the power of 1 end exponent end subscript reaction. The rate limiting step is spontaneous dissociation of an alkyl halide to give a carbocation intermediate

    S subscript N to the power of 1 end exponent end subscript reaction is:

    Chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.