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Question : Find real and imaginary parts of (x+iy)/(x-iy) Solution : We know that Real and imaginary parts of complex Number z = a+ib are a and b respectively.So we…

Question: What is the value of Sin(15)? Solution : We shall write \[15^0=45^0-30^0 \] And apply Sin(A-B) formula \[Sin(A-B) =Sin(A)Cos(B)-Cos(A)Sin(A)\] Therefore \[Sin(15^0) = Sin(45^0-30^0) =Sin(45^0)Cos(30^0)-Cos(45^0)Sin(30^0) \] Now we shall substitute…

Question : Solve the following difference equation p(n)=-2p(n-1)+8p(n-1) , p0=1, p_1 =1 Solution : Given homogeneous linear difference equation \[ p_0=1,\ p_1=1,\] \[ p_n=-2p_{n-1}+8p_{n-2},\ \ n\geq2 \] \[p_n+2p_{n-1}-8p_{n-2}=0 \] (1)…

Question : Let (Z,o) where aob =a+b+1 for a, b in Z, is a commutative group. Let a’ be inverse of a then a’ equals to Solution : Let e…

Question : The equation of a right circular cone with vertex at the origin the axis y-axis and semi-vertical angle pi/4 is Solution : Let P(x, y, z) be any…

Question : : If the horizontal range of the projectile is equal to it’s gained maximum height then find it’s angle of projection Solution : We know horizontal range of…

Question :: The function g(x)=f(x)/x where x not equal to 0 has an extreme value, when \[f^\prime\left(x\right)=f\left(x\right)\] 2. \[g^\prime\left(x\right)=f\left(x\right)\] 3.\[f\left(x\right)=0\] 4. \[g\left(x\right)=f^\prime\left(x\right)\] Solution : Given Function \[g\left(x\right)=\frac{f\left(x\right)}{x},\ x\neq0\] has an…

Question : The length of the normal to the curve \[x=a\left(\theta+\sin{\left(\theta\right)}\right)\ ,\ y=a\ \left(1-\cos{\left(\theta\right)}\right)\] at \[ \theta=\frac{\pi}{2}\] is \[2a\] \[\frac{a}{2}\] \[a\sqrt2\] \[\frac{a}{\sqrt{2\ }}\] Solution : First we shall find derivatives…

Find The product of slopes of conjugate diameters of ellipse in the following question Solution : Two Lines \[y=m_1 x,y=m_2 x\] will be conjugate diameters of the ellipse \[x^2/a^2 +y^2/b^2…

Find PGT Mathematics Solution of the problem Solution : Focus of the parabola \[y^2\ \ =4ax\] is S(a, 0). Let P(a, 2a) and Q(a, -2a)\[SP\ =\sqrt{\left(a-a\right)^2+\left(2a-0\right)^2},\ SQ=\sqrt{\left(a-a\right)^2+\left(0+2a\right)^2}\]SP=2a,SQ=2a\[\frac{2SP\ast S Q}{SP+SQ}=\frac{2\ast2a\ast2a}{2a+2a}=2a\]Correct option…