Questions asked by P dilip_k

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• What is the difference between oxidation number and oxidation state?
  
• What is the value of #cos^-1(cos12^o)-sin^-1(sin12^o)# ?
  
• ABC is an acute angled triangle. The bisector of #/_# BAC intersects BC at D. BE is a perpendicular drawn on AC from B. Points E and D are joined. Show that #/_CED>45^o# How to show?
  
• Does entropy increase or decrease during transformation of egg into chicken?
  
• Mg produces hydrogen with dilute #HNO_3# but Zn does not do so. What is the explanation of this phenomenon?
  
• How will you prove the trigonometric formula #cos(A+B)=cosAcosB-sinAsinB# by using formula of cross product of two vectors ?
  
• If #x+1/x=-1# then What is the value of #x^247+1/x^187=#?
  
• Given #secalpha=secbetasecgamma+tanbetatangamma# How will you show? #secbeta =secgammasecalpha+-tangammatanalpha#
  
• How will you prove the formula #sin(A+B)=sinAcosB+cosAsinB# using formula of scalar product of two vectors?
  
• How will you prove the formula #sin(A+B)=sinAcosB+cosAsinB# using formula of scalar product of two vectors?
  
• How will you prove the formula #sin(A-B)=sinAcosB-cosAsinB# using formula of scalar product of two vectors?
  
• How will you prove the formula #cos(A-B)=cosAcosB+sinAsinB# using formula of vector product of two vectors?
  
• Given #a^2+b^2+c^2=25 ;x^2+y^2+z^2=36 and ax+by+cz=30# for a,b,c being real. How will you prove #a/x=b/y=c/z=5/6# ?
  
• How will you show ? #5^n+1# is always divisible by 7 when n is a positive odd integer divisible by 3.
  
• Given #a^2+b^2+c^2=16;x^2+y^2+z^2=25 and ax+by+cz=20# for a,b,c being real. How will you prove #a/x=b/y=c/z# ? Find also the value of each ratio.
  
• If#""f^2(x)+g^2(x)+h^2(x)<=9# and #u_x=3f(x)+4g(x)+10h(x)#, again #(u_x)_"max"=sqrtn,"where"" "ninN# then what is the value of n?
  
• How will you show that the velocity of matter wave is always greater than that of light?
  
• Two non collinear position vectors #veca & vecb# are inclined at an angle #(2pi)/3#,where #|veca|=3 & |vecb|=4 #. A point P moves so that #vec(OP)=(e^t+e^-t)veca +(e^t-e^-t)vecb#. The least distance of P from origin O is #sqrt2sqrt(sqrtp-q)# then p+q =?
  
• If#" "veca=3hati+4hatj+5hatk and vec b= 2hati+hatj-4hatk# ;How will you find out the component of #" "veca " ""perpendicular to" " " vecb#?
  
• If#" "veca=3hati+4hatj+5hatk and vec b= 2hati+hatj-4hatk# ;How will you find out the component of #" "veca " ""perpendicular to" " " vecb#?
  
• Two non collinear position vectors #veca & vecb# are inclined at an angle #(2pi)/3#,where #|veca|=3 & |vecb|=4 #. A point P moves so that #vec(OP)=(e^t+e^-t)veca +(e^t-e^-t)vecb#. The least distance of P from origin O is #sqrt2sqrt(sqrtp-q)# then p+q =?
  
• In #DeltaABC,/_BAC=30^@;/_ACB=60^@ and BC = 6 cm#. How will you find out the area of the triangle without using trigonometry?
  
• The lengths of two parallel sides of a trapezium are 10 cm and 15 cm. The lengths of other two sides are 4 cm and 6 cm. How will you find out the area and magnitudes of 4 angles of the trapezium?
  
• 10 circular pieces of paper each of radius 1 cm have been cut out from a piece of paper having a shape of an equilateral triangle. What should be the minimum area of the equilateral triangle?
  
• Two forces #vecF_1=hati+5hatj and vecF_2=3hati-2hatj# act at points with two position vectors respectively # hati and -3hati +14hatj# How will you find out the position vector of the point at which the forces meet?
  
• Two non collinear position vectors #veca & vecb# are inclined at an angle #(2pi)/3#,where #|veca|=3 & |vecb|=4 #. A point P moves so that #vec(OP)=(e^t+e^-t)veca +(e^t-e^-t)vecb#. The least distance of P from origin O is #sqrt2sqrt(sqrtp-q)# then p+q =?
  
• How do you solve for x ? #(x-2)(x-3)=34/33^2#
  
• Let #D= a^2+b^2+c^2# where a and b are successive positive integers and #c=ab#. How will you show that #sqrtD# is an odd positive integer?
  
• Let #D= a^2+b^2+c^2# where a and b are successive positive integers and #c=ab#.How will you show that #sqrtD# is an odd positive integer?
  
• If in a triangle ABC, #sinAsinB+cosAcosBsinC=1# then how will you prove that the triangle is right angled and isosceles?
  
• If in a triangle ABC #cosAcosB+sinAsinBsinC=1# then how will you prove that the triangle is right angled and isosceles?
  
• How will you prove the formula #sin3A=3sinA-4sin^3A# using only the identity #sin(A+B)=sinAcosB+cosAsinB#?
  
• If #tan(a+b)=1 and tan(a-b)=1/7# then how will you find out the values of #tana and tanb#?
  
• Given #secalpha=secbetasecgamma+tanbetatangamma# How will you show? #secbeta =secgammasecalpha+-tangammatanalpha#
  
• #int_(1/a)^a(tan^-1x)/xdx=?#
  
• #int_(1/a)^a(tan^-1x)/xdx=?#
  
• What is the minimum value of #9sec^2x+16cos^2x#?
  
• What is the minimum value of #16sec^2x+9cos^2x#?
  
• How will you integrate ? #int(dx)/(1+x^4)^2#
  
• How will you integrate ? #int(dx)/(1+x^4)^(1/4)#
  
• How will you integrate ? #int(dx)/(1+x^4)^2#
  
• How will you find the inductance of a choke coil needed to run an arc lamp with an AC source of 410V supply at 50Hz? The arc runs at 10 A current and has an effective resistance 40 ohm. [Ans:29mH]
  
• 2 moles PCl5 are heated in a 2L flask.At equilibrium 40% PCl5 dissociates . what is the equilibrium constant for this reaction?
  
• In an isosceles trapezium diagonal is inclined at angle #45^@#with the parallel sides. The height of trapezium is 12cm. How will you find out the area of the trapezium without using trigonometry?
  
• What is the IUPAC name of the compound ?
  
• Given #x=bz+cy;" " y=az+cx and z=ay+bx# how will you prove #x^2/(1-a^2)=y^2/(1-b^2)=z^2/(1-c^2)#?
  
• If #y'(x)+y(x)g'(x)=g(x)g'(x)" ; y(0)=0 ; g(0)=g(2)=0 " where " x in RR# then #y(2)=?#
  
• How do you solve for x? #(x-5)(x-6)=25/24^2#
  
• How will you solve:#(dy)/(dx)=e^(x-y)[e^x-e^y]#?
  
• How will you arrange the followings in ascending order of acid strength and oxidising capacity? #HClO_4,HClO_3,HClO_2,HClO#
  
• What is stereo structural IUPAC name of the following compound?
  
• What is the probability of sitting 5 girls and 5 boys alternatively in a row ?
  
• A two-digit number is such that the sum of the digits is 10. When 18 is subtracted from the number, the digits of new number formed become same. What is the number?
  
• If #f(f(x))=x and f(0) =1# then #int_0^1(x-f(x))^2018dx=?#
  
• What is the answer ?
  
• Find the greatest value of #abc# for positive values of #a,b,c# subject to #ab +bc+ca=12# ?
  
• If #a+b+c+d+e+f=12 # then the greatest value of #ab+bc+cd+de+ef+fa# will be :- (A) 24,(B)36,(C) 30,(D) none of these,provided #a,b,c,d,e and f# are non negative real number.?
  
• How do you solve?
  
• In #DeltaABC, /_BAC=30^@, AB=AC and BC=10cm#. How will you find the area of #DeltaABC# without using trigonometry?
  
• In #DeltaABC, /_BAC=30^@, AB=AC=10cm#. How will you find the area of #DeltaABC# without using trigonometry?
  
• In #DeltaABC, /_BAC=45^@, AB=AC=10cm#. How will you find the area of #DeltaABC# without using trigonometry?
  
• In #DeltaABC, /_BAC=45^@, AB=AC and BC =10cm#. How will you find the area of #DeltaABC# without using trigonometry?
  
• If #abc=27846,a/6=b+4=c-4# then #a+b+c=#?
  
• There are 5 cards. 5 positive integers (May be different or equal) are written on these cards, one on each card. The sum of the numbers on every pair of cards. are only three different totals 57, 70, 83. Largest integer written on the card?
  
• How will you draw a square equal in area to a given triangle?
  
• What will be position of the final image?
  
• What will be the answer?
  
• What will be the answer?
  
• What is the option?
  
• What will be the anser?