Questions asked by Abhishek K.

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• If #(ay-bx)/c=(cx-az)/b=(bz-cy)/a#, then how to prove that #x/a=y/b=z/c#?
  
• If a+b=8 then what is the equation of the locus of a moving point which is always mid-point of (a,0) and (0,b) ?
  
• A dishonest shopkeeper has two false balances. One balance wieghs 10% more while buying the goods and other weighs 10% less while selling the goods then what is his gain percent just by weighing?
  
• The price of a commodity has increased by #15%# so that one can buy #3# more commodities for Rs 1700. What was the original price of the commodity?
  
• How to factorise #2a^6-19a^3+24#?
  
• Solve #tan2A=cot(A-18)# #0<theta<90# ?
  
• If #x=3^(1/3)+3^(-1/3)# then what is the value of #3x^3-9x=10#?
  
• How to factorise #(x+5)(x+9)(x+3)(x+7)-33#?
  
• Find #A+B# when #tanA+tanB=1# and #cosA*cosB=(3^(1/2))/2#.?
  
• How to solve cosA+cos2A+cos3A=0 ?
  
• Solve #(sqrt(3)/cos(2A))-(1/sin(2A))=4# ?
  
• Solve #cos2A=sqrt(2)(cosA-sinA)#?
  
• Prove that #(cos(33^@)-cos(57^@))/(sin(10.5^@)-sin(34.5^@))=-sqrt(2)# ?
  
• Prove that #((cos(33^@))^2-(cos(57^@))^2)/((sin(10.5^@))^2-(sin(34.5^@))^2)= -sqrt2# ?
  
• If #sin18@=(sqrt(5)-1)/4# and #cos36@=(sqrt(5)+1)/4# then prove that #(1+cos(pi/10))(1+cos((3pi)/10))(1+cos((7pi)/10))(1+cos((9pi)/10))=(1/16)#?
  
• Find the equation of circle which touches both the negative axes and has its center on the line #x-2y=3#.?
  
• Prove that #cos^3Acos(3A)+sin^3A(sin3A)=cos^3 2A# ?
  
• Prove that #csc4A+csc8A=cot2A-cot8A#?
  
• If #A+B+C=pi# then prove that #sinA+sinB+sinC=4cos(A/2)*cos(B/2)*cos(C/2)#?
  
• If #cosA+cosB+cosC=0# then prove that #cos3A+cos3B+cos3C=12cosAcosBcosC#?
  
• If #A+B+C=pi# then prove that #sin(B+2C)+sin(C+2A)+sin(A+2B)=4sin((B-C)/2)*sin((C-A)/2)*sin((A-B)/2)#?
  
• If #A+B+C+D=2pi# then prove that #cos^2(A/2)+cos^2(B/2)+cos^2(C/2)+cos^2(D/2)=2-2cos((A+B)/2)*cos((A+C)/2)*cos((A+D)/2)#?
  
• If #x-y=2# is the equation of a chord of the circle #x^2+y^2+2y=0#.Find the equation of the circle of which this chord is a diameter.?
  
• Solve #1/(tan2x-tanx)-1/(cot2x-cotx)=1#?
  
• What is the sum of integers from 1 to 100 divisible by 2 or 5?
  
• What is the sum of the series #S=1^2-2^2+3^2-4^2+...-2002^2+2003^2#?
  
• If zeroes of the polynomials #f(x)=x^3-3px^2+qx-r# are in AP then what is the relation between p, q and r?
  
• If one of the root of the equation #x^2+px+q=0# is the square of another then what is the relation between p and q?
  
• An object having 10kg mass weighs #9.81kg# on a spring balance. What is the value of #g# at that place?
  
• In a sequence the sum of the nth terms is #3n^2+5n#.If its mth term is 164, then what is the value of m?
  
• How do you prove that arithmetic mean is greater than equal to geometric mean?
  
• If the polynomial#x^4-6x^3+16x^2-25x+10# is divided by #x^2-2x+k# the remainder is #x+a# find #k# and #a#.?
  
• Find the equation of circle with radius 4 units and whose centre lies on the line #13x+4y=32# and which touches the line #3x+4y+28=0#.?
  
• If the circles #x^2+y^2+2ax+c^2=0# and #x^2+y^2+2by+c^2=0# touch externally prove that #1/(a^2)+1/(b^2)=1/(c^2)#?
  
• Ram gets an employment of #$200# in month with an annual increment of #$50#.What does he earn in 10 years? Find his salary at the 11th year.?
  
• A man repays a loan of Rs. 3250 by paying Rs. 20 in the first month and then increases the payment by Rs 15 every month.How long will it take him to clear the loan?
  
• If the second, fourth and ninth term of an arithmetic progression are in geometric progression, then what is the common ratio of the GP?
  
• In an Arithmetic sequence, #p^(th)# term is #q# and #q^(th)# term is #p#.Show that the #n^(th)# term is #p+q-n#.?
  
• How do you evaluate?
  
• If the lines represented by the equation #x^2+y^2=c^2((bx+ay)/(ab))^2# form a right angle then prove that:#1/a^2+1/b^2+1/c^2=3/c^2#?
  
• If the lines represented by the equation #x^2+y^2=c^2((bx+ay)/(ab))^2# form a right angle then prove that:#1/a^2+1/b^2+1/c^2=3/c^2#?
  
• Find the equation of the pair of lines passing through the point #(2,3)# and perpendicular to the line pair #2x^2-xy-6y^2+4x+6y=0#?
  
• Show that #16x^2+24xy+py^2+24x+18y-5=0# represents a pair of parallel straight lines and find the distance between them.?
  
• A Geometric Series has 8 terms whose sum of the first 3 terms is #13/9# and the sum of last 3 terms is #351#. Find the first term and the common ratio of the series.?
  
• The sum of first four terms of a GP is #30# and that of last four terms is #960#. If the first and the last term of the GP is 2 and 512 respectively, find the common ratio.?
  
• How do you prove?
  
• The hypotenuse of an isosceles right angled triangle has its ends at the points (1,3) and (-4,1). Which is the easiest method to find out the coordinates the third side?
  
• How do you solve this?
  
• How to prove that an exterior angle of a cyclic quadrilateral is equal to its opposite interior angle?
  
• Please solve this?
  
• Show that #(b^2-c^2)*cotA+(c^2-a^2)*cotB+(a^2-b^2)*cotC=0#?
  
• If #1/(a+c)+1/(b+c)=3/(a+b+c)# then find angle C.?
  
• Show that #(a^2sin(B-C))/(sinB+sinC)+(b^2sin(C-A))/(sinC+sinA)+(c^2sin(A-B))/(sinA+sinB)=0#?
  
• If #r_1=r_2+r_3+r# prove that the triangle is right angled.?
  
• If the cosines of the two of the angles of a triangle are proportional to the oppsite sides show that the trangle is right angled.?
  
• If #(cosA+2cosC)/(cosA+2cosB)=(sinB)/sinC# then show that the triangle is either isosceles or right angled triangle. I got #cosA+cosB+cosC=1# what to do after this?
  
• If #sinA*sin(B-c)=sinC*sin(A-B)# then show that # a^2,b^2,c^2# are in AP.?
  
• An easy method?
  
• Solve this?
  
• How to solve?
  
• How to solve?
  
• If #sinA+sinB=x# and #cosA+cosB=y# then show that #tan((A-B)/2)=+-sqrt((4-x^2-y^2)/(x^2+y^2))#?
  
• If #tan(A/2)=sqrt((1-x)/(1+x))*tan((theta)/2)# then show that #costheta=(cosA-x)/(1-x*cosA)#?
  
• If #f(x)=3x+4# and #g(x)=2(x+1)# then prove that #(fog)(x)=(gof)(x)#.?
  
• If #f(x)=1/x, xcancel(=)0# then prove that #fof^(-1)= f^(-1)of#?
  
• If #f(x)=2x-7# and #fog(x)=4x+3# find #(gof)^(-1)(x)#?
  
• What are the possible solutions of #ax^4+bx^3+cx^2+dx+e=0# where #a!=0#, #a+c+e=0# and #b+d=0#?
  
• Solve #ax^4+bx^3+cx^2+dx+e=0#?
  
• ABCD is a quadrilateral. Show that #vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(PQ)# where P and Q are the mid points of AC and BD respectively?
  
• How do you prove that #cot^2(pi/7)+cot^2((2pi)/7)+cot^2((3pi)/7)=5#?
  
• How do we Find the maximum and minimum vlaues of #1/(3sinx-4cosx+7)#?
  
• Solve this?
  
• How will you solve this?
  
• How do you prove that a triangle is equilateral iff #sinA+sinB+sinC=(3sqrt3)/2#?
  
• Please prove?
  
• Please prove?
  
• How do we prove the projection law using vectors?
  
• How do we construct a triangle equal in area to a given triangle or quadrilateral?
  
• How do we find the equation of tangents drawn from #(a,b)# to #x^2+y^2=r^2#?
  
• How do we prove that #(x+a)# is a factor of #x^n+a^n# for all odd positive integer n?
  
• If the bisector of angle W and angle Y of a cyclic quadrilateral WXYZ meet at A and B respectively then prove that AB is the diameter of the circle. ?
  
• ABC is a triangle with D and E as the mid points of the sides AC and AB respectively. G and F are points on side BC such that DG is parallel to EF. Prove that the area of triangle ABC=#2xx# area of quadrilateral DEFG.?
  
• Show by using matrix method that a reflection about the line #y=x# followed by rotation about origin through 90° +ve is equivalent to reflection about y-axis.?
  
• Show by using matrix method that a reflection about the line #y=x# followed by rotation about origin through 90° +ve is equivalent to reflection about y-axis.?
  
• Please prove?
  
• How do we find the term #n^(th)# and sum to #n^(th)# of the following series?
  
• If #f={(-3,4),(-1,5),(-2,6),(2,4),(0,3)} and g={(4,3),(5,7),(3,0),(6,0)}# then find set of ordered pair of gof and fog and represent in arrow diagram.?
  
• Please solve this?
  
• If #a,b and c# are the #p^(th)#, #q^(th)# and #r^(th)# term of an AP then show that #p(b-c)+q(c-a)+q(a-b)=0#?
  
• ABC is an isoscles triangle in which AB=AC. A circle passing through B and C intersects the sides AB and AC at D and E respectively then show that DE is parallel to BC?
  
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