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101.	The simple interest for a period of N years at R% per annum on a sum of Rs P is denoted by S. It equals the product of `(1)/(100)`,P,N and R. Express P in terms of S,N and R.
Answer» Given, `S=(PNR)/(100)` `impliesP=(100S)/(NR)`

102.	The sum of `a^(2) and cb^(3)` equals the sum of twice to d and thrice to c. express b in terms of a,c and d.A. `b=root(3)((1)/(c)(2d+3c-a^(2)))`B. `b=(1)/(c)root(3)(2d+3c-a^(2))`C. `b=(root(3)(a^(2))-2d-3c)/(c)`D. none of these
Answer» Correct Answer - A Given, `a^(2)+b^(3)c=2d+3c` `impliesb^(3)c=2d+3c-a^(2)` `impliesa=root(3)((1)/(c)(2d+3c-a^(2)))`

103.	If `(1)/(a)+(1)/(b)=(1)/(c)+(1)/(d)`, express a in terms of b,c and d.A. `a=(bcd)/(bc+cd-bd)`B. `a=(bcd)/(cd+bd-bc)`C. `a=(bcd)/(bd+bc+cd)`D. `a=(bcd)/(bd+bc-cd)`
Answer» Correct Answer - D `(1)/(a)+(1)/(b)=(1)/(c)+(1)/(d)` `implies(1)/(a)+(1)/(c)+(1)/(d)-(1)/(b)` `implies(1)/(a)=(bd+bc-cd)/(bcd)` `thereforea=(bcd)/(bd+bc-cd)`

104.	If `C=(5)/(9)(F-32)`, then express F in terms of C.A. `F=(9)/(5)C-32`B. `F=32-(9)/(5)C`C. `F=(9)/(5)(C+32)`D. `F=(9)/(5)C+32`
Answer» Correct Answer - D `C=(5)/(9)(F-32)` `implies9C=5F-160` `implies9C+160=5E` `F=(9C)/(5)+32`

105.	Find the missing numbers in the following table. (i) Changing kilometers into miles. `{:("Numbers of kilometers",5,10,15,20,25,30),("Number of miles",8,16,24,-,-,-):}` (ii) Change centrigrade `(.^(@)C)` into Fehrenheit `(.^(@)F)` where centigrade scale is divided in 100 equal parts and Fahrenheit scale is divided into 180 equal parts. `{:("Temperature in ".^(@)C,-5,0,5,10,15,20),("Temperature in ".^(@)F,23,32,41,-,-,-):}`
Answer» Correct Answer - (i) 32 km, 40 km and 48 km (ii) `50^(@),59^(@) and 68^(@)`

106.	If `M_(1)` men can complete a wrk in `D_(1)` days and `M_(2)` men can complete the same work in `D_(2)` days, write the formula relating them. Given that the number of men at work is inversely proportional to the number of days.
Answer» Given, `M_(1)=D and M_(2)=D_(2)` Also, `Mprop(1)/(D)` `impliesMD=`constant. `therefore(M_(1))/(M_(2))=(D_(2))/(D_(1))` `impliesM_(1)D_(1)=M_(2)D_(2)`

107.	A steamer can cover k kilometers by consuming l litres of diesel. Write the formula for the distance d, in km covered by the steamer which uses m litres of diesel.
Answer» Distance covered =k km diesel consumed=l 1 We know that the distance covered is directly proportional to the amount of diesel consumed. `therefore(d)/(k)=(m)/(l)` `impliesd=(km)/(l)` kilometers `therefore` Distance covered, `d=(km)/(l)` kilometers.

108.	If the sum of y and ten tims x is equal to the product of x and y, then give the formula with y as the subject.A. `y=(10x)/(x-1)`B. `y=(10x)/(1-x)`C. `y=(10x)/(x+1)`D. none of these
Answer» Correct Answer - A (i) `y+10x=xy` Apply transposition to make y as the subject (ii) Given `y+10x=xy`, make y as the subject (iii) Collect the terms involving y and write on LHS and write the remaining terms on RHS.

109.	The variable, which is expressed in terms of other variables, is called_____of a formula.
Answer» Correct Answer - Subject

110.	If `S=(a)/(1-r^(3))`, then expres r in terms of S and a.A. `r=root(3)(1+(a)/(S))`B. `r=root(3)(1+(S)/(a))`C. `r=root(3)(1-(S)/(a))`D. `r=root(3)(1-(a)/(S))`
Answer» Correct Answer - D `S=(a)/(1-r^(3))Rs` `implies1-r^(3)=(a)/(S)impliesr^(3)=1-(a)/(S)` `thereforer=root(3)(1-(a)/(S))`

111.	In the formula `p=(3x-2y)/.(2x-3y)`, make x as the subject of the formula.A. `x=(y(3p-2))/(2p-3)`B. `x=(y(3p-2))/(2p+3)`C. `x=(y(3p+2))/(2p-3)`D. `x=(y(3p+2))/(2p+3)`
Answer» Correct Answer - A (i) Apply transposition. (ii) Cross multiply the terms and bring the terms involving x to LHS.

112.	Write all the possible related auxiliary formulae from A=`pi(R^(2)-r^(2))`.
Answer» Correct Answer - `R=sqrt((A)/(pi)+r^(2)):r=sqrt(R^(2)-(A)/(pi))`

113.	What are the auxiliary formulae of the statement "sum of the angles of a quadrilateral ABCD is `360^(@)`," (The four angles of the quadrilateral are A,B,C and D)?A. `A=360^(@)-(B+C+D)` `B=360^(@)-(A+C+D)` `C=360^(@)-(A+B+D)` `D=360^(@)-(A+B+C)`B. `A=360^(@)-(B+C+D)` `B=360^(@)-(A+C+D)` `C=360^(@)-(A+B+D)` `D=360^(@)-(A-B+C)`C. `A=360^(@)-(B+C+D)` `B=360^(@)-(A-C+D)` `C=360^(@)-(A+B+D)` `D=360^(@)-(A+B+C)`D. `A=360^(@)-(B+C+D)` `B=360^(@)-(A+C+D)` `C=360^(@)-(A-B+D)` `D=360^(@)-(A-B+C)`
Answer» Correct Answer - A `angleA+angleB+angleC=360^(@)`. Make of the angles as the subject. (ii) Given, `A+B+C+D=360^(@)`, make A,B,C and D as subjects.

114.	If `s=2(lb+hb+hl)`, write all the auxiliary formulae of S.A. `l=(s-2bh)/(2(b+h)),b=(s-2hl)/(2(h+l)) and h=(s-2lh)/(2(l+h))`B. `l=(s-2bh)/(2(b+h)) and h=(s-2lb)/(2(l+b))`C. `l=(s-2bh)/(2(b+h)),b=(s-2hl)/(2(h+l)) and h=(s-2lh)/(2(l+h))`D. None of these
Answer» Correct Answer - A (i) Product of extremes=Products of means. (ii) Make, l,b and h as te subjects.

115.	Write the auxiliary formulae related to `x^(2)-y^(2)=z^(2)`.A. `x=sqrt(y^(2)+z^(2)),y=sqrt(x^(2)-z^(2)) and z=sqrt(x^(2)-y^(2))`B. `x=sqrt(z^(2)+y^(2)),y=sqrt(z^(2)+x^(2)) and z^(2)=sqrt(x^(2)-y^(2))`C. `x=sqrt(y^(2)+z^(2)),y=sqrt(x^(2)-z^(2)) and z=sqrt(y^(2)-x^(2))`D. `z=sqrt(x^(2)-y^(2)),y=sqrt(z^(2)+x^(2)) and x=sqrt(x^(2)+y^(2))`
Answer» Correct Answer - A Make u, y and z as the subjects.

116.	In the formula `l^(2)=r^(2)+h^(2)`, if r=5 and l=13, then find the value of h.A. 12B. 144C. 18D. 184
Answer» Correct Answer - A Make h the subject of the formula and evaluate it.

117.	In the formula obtained in the problem 12, make the subject as p.A. `(q^(3)-3rs)^((1)/(3))`B. `(3rs-q^(3))^((1)/(3))`C. `(q^(3)-3rs)^((1)/(3))`D. `(3rs-q^(3))^((1)/(2))`
Answer» Correct Answer - B Apply transposition.

118.	In the formula `H=(2ab)/(a+b)`, if a=5 and H=8, then find the value of b.A. `20`B. `(18)/(13)`C. `(1)/(20)`D. `(13)/(18)`
Answer» Correct Answer - A make h as the subject of the formula and evaluate it.

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