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Find two positive numbers whose difference is 12 and whose A.M. exceeds the G.M. by 2

Find two positive numbers whose difference is 12 and whose A.M. exceeds the G.M. by 2
If a,b,c are in GP, then the equations ax2+2bx+c=0 and dx2+2ex+f=0 have a common root if....

If a,b,c are in GP, then the equations ax2+2bx+c=0 and dx2+2ex+f=0 have a common root if....
If one geometric mean G and two arithmetic means A1 and A2 be inserted between two given...

If one geometric mean G and two arithmetic means A1 and A2 be inserted between two given...
If x,y,z are distinct positive numbers, then prove that (x+y)(y+z)(z+x) is greater than 8xyz.

If x,y,z are distinct positive numbers, then prove that (x+y)(y+z)(z+x) is greater than 8xyz.
If x∈R, find the minimum value of the expression 3x+31−x.

If x∈R, find the minimum value of the expression 3x+31−x.
Let x be the arithmetic mean and y,z be the two geometric means between any two positive numbers...

Let x be the arithmetic mean and y,z be the two geometric means between any two positive numbers...
If a be the A.M of two numbers b and c and G1,G2 are the two G.Ms between them then prove that...

If a be the A.M of two numbers b and c and G1,G2 are the two G.Ms between them then prove that...
If tan (A + B) = √3 and tan (A – B) = 1/√3, 0° A + B ≤ 90°; A B, then find A and B

If tan (A + B) = √3 and tan (A – B) = 1/√3, 0° A + B ≤ 90°; A B, then find A and B
Two tangent TP and TQ are drawn to a circle with centre O from an external point T.Prove that ∠PTQ..

Two tangent TP and TQ are drawn to a circle with centre O from an external point T.Prove that ∠PTQ..
limx→∞ (x+1)^10+(x+2)^10+....(x+100)^10/x^10+10^10

limx→∞ (x+1)^10+(x+2)^10+....(x+100)^10/x^10+10^10
Limx→0 cosAx−cosBx/x2

Limx→0 cosAx−cosBx/x2
Evaluate the following limits :Limx→0 sin2x+sin6x/sin5x−sin3x

Evaluate the following limits :Limx→0 sin2x+sin6x/sin5x−sin3x
The value of lim y→0 (x+y)sec(x+y)−xsecx/y

The value of lim y→0 (x+y)sec(x+y)−xsecx/y
Evaluate: limx→0 sec4x−sec2x/sec3x−secx

Evaluate: limx→0 sec4x−sec2x/sec3x−secx
limx→0 1−cot 2x - cosec 2x/x^2

limx→0 1−cot 2x - cosec 2x/x^2
limx→0 sinx−2sin3x+sin5x/x

limx→0 sinx−2sin3x+sin5x/x
Evaluate limx→0 tanx+4tan2x−3tan3x/x2 tanx

Evaluate limx→0 tanx+4tan2x−3tan3x/x2 tanx
limx→0 1−cosx√cos2x/x2

limx→0 1−cosx√cos2x/x2
Evaluate: lim (x→0) ((1 – cos x cos2x cos3x)/sin22x)

Evaluate: lim (x→0) ((1 – cos x cos2x cos3x)/sin22x)
A straight line cuts intercepts from the axis of coordinates the sum of the reciprocals of which....

A straight line cuts intercepts from the axis of coordinates the sum of the reciprocals of which....
A line passes through the point (3,-2). Find the locus of the middle point of the portion the line..

A line passes through the point (3,-2). Find the locus of the middle point of the portion the line..
Find the equation of the line which passes through the point (3,4) and the sum of its intercepts....

Find the equation of the line which passes through the point (3,4) and the sum of its intercepts....
Find the equation of the line which cuts off an intercept 4 on the positive direction of x-axis.....

Find the equation of the line which cuts off an intercept 4 on the positive direction of x-axis.....
Find the equation of the line which makes equal intercepts on the axes and passes through the.......

Find the equation of the line which makes equal intercepts on the axes and passes through the.......
Find the equation of the line which cuts off equal and positive intercepts from the axes and...

Find the equation of the line which cuts off equal and positive intercepts from the axes and...
Find the equation of a straight line which passes through the point (4,-2) and whose intercept on...

Find the equation of a straight line which passes through the point (4,-2) and whose intercept on...
Find the equation of the straight line whose intercepts on X-axis and Y-axis are respectively...

Find the equation of the straight line whose intercepts on X-axis and Y-axis are respectively...
Find the equation of the line through (2,3) so that the segment of the line intercepted between...

Find the equation of the line through (2,3) so that the segment of the line intercepted between...
If the intercept of line between coordinate axes is divided by the point (−5,4) in the ratio 1:2...

If the intercept of line between coordinate axes is divided by the point (−5,4) in the ratio 1:2...
Find the equation of the line, Which passes through point P(1,−7) and meets the axes at A and B...

Find the equation of the line, Which passes through point P(1,−7) and meets the axes at A and B...