CBSE
CBSE Study Material
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Prove that:
Answer:
Prove that:
Answer:
Prove that:
Answer:
Prove that:
Answer:
If 
, where 
, find the values of (iii) tan (x + y)
Answer: (iii)Here first we will calculate value of tanx and tany,
If , where , find the values of (i) sin (x + y) (ii) cos (x – y)
Answer: Given: $\cos x=\frac{3}{5}\,and\,\cos y=-\frac{24}{25}$ We will first find out value of sinx and siny, (i)sin(x + y) = sinx.cosy + cosx.siny (ii)cos(x - y) = cosx.cosy +...
If 
, where 
, find the values of (iii) tan (x – y)
Answer: Given: $\sin x=\frac{12}{13}\,and\,\sin y=\frac{4}{5}$ (iii)Here first we will calculate value of tanx and tany
If , where , find the values of (i) sin (x + y) (ii) cos (x + y)
Answer: Given: $\sin x=\frac{12}{13}\,and\,\sin y=\frac{4}{5}$ Here we will find values of cosx and cosy (i) sin(x + y) = sinx.cosy + cosx.siny (ii)cos(x + y) = cosx.cosy +...
If x and y are acute angles such that 
, prove that 
Answer: Given: $\cos x=\frac{13}{14}\,and\,\cos y=\frac{1}{7}$ Now we will calculate value of sinx and siny Hence, Cos(x - y) = cosx.cosy + sinx.siny
Evaluate: 
As per the given question,
Evaluate: 
As per the given question,
Evaluate: 
As per the given question,
Find the modulus of each of the following complex numbers and hence express each of them in polar form: 2 – 2i
Evaluate: 
As per the given question,
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Evaluate: 
As per the given question,
Find the modulus of each of the following complex numbers and hence express each of them in polar form:
Evaluate: 
As per the given question,
Find the modulus of each of the following complex numbers and hence express each of them in polar form: –1 + i
Find the modulus of each of the following complex numbers and hence express each of them in polar form: 1 – i
Find the modulus of each of the following complex numbers and hence express each of them in polar form: 2i
Find the modulus of each of the following complex numbers and hence express each of them in polar form: –i
Find the modulus of each of the following complex numbers and hence express each of them in polar form: –2
Evaluate: 
As per the given question,
Find the modulus of each of the following complex numbers and hence express each of them in polar form: 4
If a and b are real numbers such that a2 + b2 = 1 then show that a real value of x satisfies the equation,
Evaluate: 
As per the given question,
If z1 = (1 + i) and z2 = (–2 + 4i), prove that
Evaluate: 
As per the given question,
For all z C, prove that
Evaluate: 
As per the given question,
If z1 is a complex number other than –1 such that |z1| = 1 and z2 = then show that z2 is purely imaginary.
is purely imaginary and z = –1, show that |z| = 1.
If z2 + |z|2 = 0, show that z is purely imaginary.
Find real values of x and y for which (x4 + 2xi) – (3×2 + iy) = (3 – 5i) + (1 + 2iy).
Evaluate: 
As per the given question,
Evaluate: 
As per the given question,
Express (1 – 2i)–3 in the form (a + ib).
If (x + iy)1/3 = (a + ib) then prove that 4 (a2 – b2).
Evaluate: 
As per the given question,
If (x + iy)3 = (u + iv) then prove that 4 (x2 – y2).
Evaluate: 
As per the given question,
Evaluate: 
As per the given question,
Express each of the following in the form (a + ib) and find its multiplicative inverse:
Evaluate: 
As per the given question,
Evaluate: 
As per the given question,
Express each of the following in the form (a + ib) and find its conjugate.
Evaluate: 
As per the given question,
Evaluate: 
As per the given question,
Evaluate: 
As per the given question,
Find the complex number z for which |z| = z + 1 + 2i.
Solve the system of equations, Re(z2) = 0, |z| = 2.
purely an imaginary number and z ≠ -1 then find the value of |z|.
If (1 + i)z = (1 – i) then prove that
If z = (2 – 3i), prove that z2 – 4z + 13 = 0 and hence deduce that 4z3 – 3z2 + 169 = 0.
Find the real values of x and y for which the complex number (-3 + iyx2) and (x2 + y + 4i) are conjugates of each other.
Find the real values of x and y for which (x – iy) (3 + 5i) is the conjugate of (-6 – 24i).
Find the real values of x and y for which:
Find the real values of x and y for which:
Answer : Given: ⇒ x + 3i = (1 – i)(2 + iy) ⇒ x + 3i = 1(2 + iy) – i(2 + iy) ⇒ x + 3i = 2 + iy – 2i – i2y ⇒ x + 3i = 2 + i(y – 2) – (-1)y [i2 = -1] ⇒ x + 3i = 2 + i(y – 2) + y ⇒ x + 3i = (2 + y) +...
Find the real values of x and y for which: (1 + i) y2 + (6 + i) = (2 + i)x
Find the real values of x and y for which: x + 4yi = ix + y + 3
Find the real values of x and y for which: (x + iy) (3 – 2i) = (12 + 5i)
Find the real values of x and y for which: (1 – i) x + (1 + i) y = 1 – 3i
If z1 = (2 – i) and z2 = (1 + i), find
If a = (cosθ + i sinθ), prove that
Prove that (x + 1 + i) (x + 1 – i) (x – 1 – i) (x – 1 – i) = (x4 + 4).
Find the smallest positive integer n for which (1 + i)2n = (1 – i)2n.
Evaluate: 
Given: $=\int (cos x \;+\; sin x) dx$ $=\;sin x\;-\;cos x\;+\;c$
prove that a2 + b2 = 1
Evaluate: i.
ii. 
i. Given: ii. Given:
Evaluate: i. 
ii. 
i. Given: ii. Given: $= -\sqrt{2}\;cosx \;+\; c$
prove that x2 + y2 = 1.
find x and y.
find the values of a and b.
Evaluate: i. 
ii.
As per the given question,
Find the multiplicative inverse of each of the following:
Evaluate: i.
ii.
i. Given: Multiply and divide by $=\;sec x\;-\;tan x \;+ \;x \;+\; c$
Find the multiplicative inverse of each of the following:
Find the multiplicative inverse of each of the following:
Evaluate: i.
ii.
As per the given question,
Find the modulus of each of the following: 5
Evaluate: 
It can be written as $= \int (3\;cot x \;cosec x\; +\; 4 \;cosec^{2}x)\; dx$ By integrating w.r.t $x$ $= \;- 3 \;cosec \;x\; –\; 4 \;cot \;x\; + \;c$
Find the modulus of each of the following:
Evaluate: i. 
ii. 
i. Given: $=tan x\;-\;cot x\;+\;c$ ii. Given: $=tan x\;+\;2 \;sec x \;+ \;c$
Find the modulus of each of the following:
Find the modulus of each of the following: 3i
Find the modulus of each of the following: (7 + 24i)
Let $I=\int{_{\frac{1}{e}}^{e}\frac{1}{x\left( {{\log }_{e}}x \right)\frac{1}{3}}dx}$ $$let ${{\log }_{e}}x=t$ $\Rightarrow .$ $\Rightarrow \frac{1}{x}dx=dt$ When $t=-1$ $x=\frac{1}{e}$ And When,...
Find the modulus of each of the following: (–3 – 4i)
Evaluate: (i)
(ii)
(i) $\int sec x (sec x + tan x) dx$ It can be written as $= \int sec^{2} x \;+\; sec x\; tan x\; dx$ By integrating w.r.t x $= tan x \;+\; sec x\; +\; c$ (ii) $\int cosec x\; (cosec x\; – \;cot x)...
Find the modulus of each of the following:
Let $I=\int \frac{1}{{{e}^{x}}+{{e}^{-x}}}dx=\int (\frac{{{e}^{x}}}{1+{{e}^{2x}}}dx\text{ )}$ Let ${{e}^{x}}=t$ $\Rightarrow {{e}^{x}}dx=dt.$ When $x=0,t=1$ And When $x=1,t=e.$ Hence,...
Evaluate: 
As per the given question, By integrating w.r.t $x$ $= - cosec x – tan x + x – sec x + 2 tan x + c$ On further calculation $= - cosec x + tan x + x – sec x + c$
Find the conjugate of each of the following: (2 – 5i)2
Evaluate: 
As per the given question, Integration with respect to x, we get $=-9 cos x-7 sin x-6 tan x-3 cot x – x + c$
Find the conjugate of each of the following:
Let $\cos x=t$ $I=\int{_{0}^{\frac{\pi }{2}}}\frac{\sin x}{1+{{\cos }^{2x}}}dx$ Let $\cos x=t$ $\Rightarrow -\sin xdx=dt.$ When $x=0,t=1$ And When, $t=0.$ $x=\frac{\pi }{2}$ Hence,...
Let $I=\int{_{0}^{\frac{\pi }{6}}\frac{\cos x}{3+4\sin x}dx}$ Let $3+4\sin x=t$ $\Rightarrow 4\cos xdx=dt.$ When $x=0,t=3$ And When, $t=5.$ $x=\frac{\pi }{6}$ Hence,...
Evaluate: i. 
ii. 
(i) Given: (ii) Given: $=x - tan^{-1} x + c$
Find the conjugate of each of the following:
Find the conjugate of each of the following:
Evaluate: i. 
ii. 
i. Given: $=x-2\;tan^{-1}x + c$ ii. Given: ...
Find the conjugate of each of the following:
Find the conjugate of each of the following:
Evaluate: ![\int\left[1+\frac{1}{\left(1+x^{2}\right)}-\frac{2}{\sqrt{1-x^{2}}}+\frac{5}{x \sqrt{x^{2}-1}}+a^{x}\right] d x](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2eb90aa34883fa3ad28909898def126d_l3.png "Rendered by QuickLaTeX.com")
Given: Because, ; Then, ; And, So,
Find the conjugate of each of the following: (–5 – 2i)
Evaluate: i. 
ii. 
(i) Given: (ii) Given: $=x^{2}- 4x+8x+8\ln \left | x-2 \right |+x + c$ $= x^{2} + 5x + 8 \ln \left | x-2 \right | +...
Give an example of two complex numbers z1 and z2 such that z1≠ z2 and |z1| = |z2|.
If |z + i| = |z – i|, prove that z is real.
Find the real values of θ for which is purely real.
Evaluate: i. 
ii. 
(i) Given: (ii) Given:
Evaluate: i. 
ii. 
(i) Given: $= \int x^{6} + x^{-6} - 3x^{2} - 3x - 2 dx$ (ii) Given:
Show that
Simplify each of the following and express it in the form (a + ib):
If 
and 
are independent events such that 
and 
, find
(i) 
(ii) 
i) $\mathrm{P}\left(\overline{E_{1}} \cap \overline{E_{2}}\right)=\mathrm{P}\left(\overline{E_{1}}\right) \times \mathrm{P}\left(\overline{E_{2}}\right)$ since, $P\left(E_{1}\right)=0.3$ and...
Evaluate: ![\int\left(\sqrt{x}-\sqrt[3]{x^{4}}+\frac{7}{\sqrt[3]{x^{2}}}-6 e^{x}+1\right) d x](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f7ee2f65d6ff05fcd65d41b53249a418_l3.png "Rendered by QuickLaTeX.com")
As per the given question,
Express each of the following in the form (a + ib):
If and are independent events such that and , find
(i) 
(ii)
i) $P\left(E_{1} \cap E_{2}\right)$ We know that, when $E_{1}$ and $E_{2}$ are independent, $\begin{array}{l} P\left(E_{1} \cap E_{2}\right)=P\left(E_{1}\right) \times P\left(E_{2}\right) \\ =0.3...
Express each of the following in the form (a + ib):
Evaluate: i. 
ii. 
(i) Given: $\int(2-5x)(3+2x)(1-x)dx$ $=\int(6-11x-10x^2 )(1-x) dx$ $=\int(10 x^3+x^2-17x+6)dx$ (ii) Given: ...
If and are the two events such that 
and 
, show that and are independent events.
We know that, Hence, $P\left(E_{1} \cap E_{2}\right)=P\left(E_{1}\right)+P\left(E_{2}\right)-P\left(E_{1} \cup E_{2}\right)$ $=\frac{1}{4}+\frac{1}{3}-\frac{1}{2}$ $=\frac{1}{12}$ Equation 1 Since...
Express each of the following in the form (a + ib):
Express each of the following in the form (a + ib):
Let and be the events such that 
and 
. Find:
(i) 
, when and are mutually exclusive.
(ii) , when 
and 
are independent
(i) We know that, When two events are mutually exclusive $P\left(E_{1} \cap E_{2}\right)=0$ Hence, $P\left(E_{1} \cup E_{2}\right)=P\left(E_{1}\right)+P\left(E_{2}\right)$ $\begin{array}{l}...
Express each of the following in the form (a + ib):
An urn contains 5 white and 8 black balls. Two successive drawings of 3 balls at a time are made such that the balls drawn in the first draw are not replaced before the second draw. Find the probability that the first draw gives 3 white balls and the second draw gives 3 black balls.
Let, success in the first draw be getting 3 white balls. Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{5_{c_{3}}}{13_{c_{3}}}=\frac{10}{286}=\frac{5}{143}$...
Evaluate: 
As per the given question, By integration we get,
A bag contains 
white and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that the first ball is white and the second is black?
Let, success in the first draw be getting a white ball. Now, the Probability of success in the first trial is $\mathrm{P}_{1}(\text { success })=\frac{10}{25}$ Let success in the second draw be...
There is a box containing 30 bulbs, of which 5 are defective. If two bulbs are chosen at random from the box in succession without replacing the first, what is the probability that both the bulbs are chosen are defective?
Let, success :bulb chosen is defective .i.e $\frac{5}{30}$ Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{5}{30}$ Probability of success in the second trial...
Express each of the following in the form (a + ib):
Evaluate: i. 
ii. 
As per the given question, (i) (ii)
A card is drawn from a well-shuffled deck of 52 cards and without replacing this card, a second card is drawn. Find the probability that the first card is a club and the second card is a spade.
Let, success for the first trail be getting a club. Now, the Probability of success in the first trial is $\mathrm{P}_{1} \text { (success) }=\frac{13}{52}$ let, success for the second trail be...
Express each of the following in the form (a + ib):
Express each of the following in the form (a + ib):
Evaluate: 
As per the given question,
Evaluate: i. ![\int \sqrt[3]{\mathrm{x}^{2}} \mathrm{dx}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-929bcb5dacefb6432b825fdc4deda95f_l3.png "Rendered by QuickLaTeX.com")
ii. ![\int \frac{1}{\sqrt[4]{x^{3}}} \mathrm{dx}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-975fd5853b6a4be4d00c95fca86741e7_l3.png "Rendered by QuickLaTeX.com")
As per the given question (i) (ii)
Express each of the following in the form (a + ib):
Evaluate: i. 
ii. 
As per the given question (i) (ii)
Evaluate: i. 
ii. 
As per the given question, (i) (ii)
Simplify each of the following and express it in the form (a + ib) : (1 + i)3 – (1 – i)3
Simplify each of the following and express it in the form (a + ib) : (1 + 2i)–3
Evaluate: i. 
ii. 
As per the given question,
Simplify each of the following and express it in the form (a + ib) : (2 + i)–2
Two marbles are drawn successively from a box containing 3 black and 4 white marbles. Find the probability that both the marbles are black if the first marble is not replaced before the second draw.
Let, success : marble drawn is black.i.e Number of black marbles/Total number of marbles $=\frac{3}{7}$ Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{3}{7}$...
A bag contains 17 tickets, numbered from 1 to 17 . A ticket is drawn, and then another ticket is drawn without replacing the first one. Find the probability that both the tickets may show even numbers.
Let, success : ticket drawn is even.i.e $\frac{8}{17}$ Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{8}{17}$ Probability of success in the second trial...
Simplify each of the following and express it in the form (a + ib) :
Two integers are selected at random from integers 1 through 11 . If the sum is even, find the probability that both the numbers selected are odd.
Two integers are selected at random. The first choice has 11 options from the 11 integers, and the second choice has 10 options from the remaining 10 integers. Let $\mathrm{P}(\mathrm{A})$ be the...
In a hostel, 
of the students read Hindi newspaper, 
read English newspaper and 
read both Hindi and English newspapers. A student is selected at random. If he reads English newspaper, what is the probability that he reads Hindi newspaper?
Let $\mathrm{P}(\mathrm{A})$ be the probability of students reading Hindi newspaper. $\therefore P(A)=0.60$ Let $\mathrm{P}(\mathrm{B})$ be the probability of them reading English newspaper....
Simplify each of the following and express it in the form (a + ib) : (4 – 3i)–1
In a hostel, of the students read Hindi newspaper, read English newspaper and read both Hindi and English newspapers. A student is selected at random.
(i) Find the probability that he reads neither Hindi nor English news paper.
(ii) If he reads Hindi newspaper, what is the probability that he reads English newspaper?
Let $\mathrm{P}(\mathrm{A})$ be the probability of students reading Hindi newspaper. $\therefore P(A)=0.60$ Let $\mathrm{P}(\mathrm{B})$ be the probability of them reading English newspaper....
The probability that a certain person will buy a shirt is 
, the probability that he will buy a coat is 
and the probability that he will buy a shirt given that he buys a coat is 
Find the probability that he will buy both a shirt and a coat.
Let $\mathrm{P}(\mathrm{A})$ be the probability of a certain person buying a shirt. $\therefore \mathrm{P}(\mathrm{A})=0.2$ Let $P(B)$ be the probability of him buying a coat. $\therefore P(B)=0.3$...
The probability that a student selected at random from a class will pass in Hindi is 
and the probability that he passes in Hindi and English is 
. What is the probability that he will pass in English if it is known that he has passed in Hindi?
One student is selected at random. Let $\mathrm{P}(\mathrm{A})$ be the probability of students passing in English. Let $\mathrm{P}(\mathrm{B})$ be the probability of students passing in Hindi....
In a class, students study mathematics; 
study biology and 
study both mathematics and biology. One student is selected at random. Find the probability that
(i) he studies mathematics if it is known that he studies biology
(ii) he studies biology if it is known that he studies mathematics.
Let $\mathrm{P}(\mathrm{A})$ be the probability of students studying mathematics. $\therefore P(A)=0.40$ Let $\mathrm{P}(\mathrm{B})$ be the probability of students studying biology. $\therefore...
A couple has 2 children. Find the probability that both are boys if it is known that (i) one of the children is a boy, and (ii) the elder child is a boy.
A couple has two children. The sample space $S=\{(B, B),(B, G),(G, B),(G, G)\}$ Let $P(A)$ be the probability of both being boys. (i) Let $P(B)$ be the probability of one of them being a boy. The...
A coin is tossed and then a die is thrown. Find the probability of obtaining a 6, given that a head came up.
A coin is tossed and a die thrown. A coin having two sides have a total outcome of 2 viz. $\{\mathrm{H}, \mathrm{T}\}$ A die has 6 faces and will have a total outcome of 6 i.e. $\{1,2,3,4,5,6\}$ Let...
Two dice were thrown and it is known that the numbers which come up were different. Find the probability that the sum of the two numbers was 
Two die having 6 faces each when tossed simultaneously will have a total outcome of $6^{2}=36$ Let $P(A)$ be the probability of getting a sum equal to 5 . Let $P(B)$ be the probability of getting 2...
A die is thrown twice and the sum of the numbers appearing is observed to be 
What is the conditional probability that the number 5 has appeared at least once?
A die thrown twice will have a total outcome of $6^{2}=36$ Let $P(A)$ be the probability of getting the number 5 at least once. Let $P(B)$ be the probability of getting sum $=8$ The sample space of...
Two unbiased dice are thrown. Find the probability that the sum of the numbers appearing is 8 or greater, if 4 appears on the first die.
Two die having 6 faces each when tossed simultaneously will have a total outcome of $6^{2}=36$ Let $\mathrm{P}(\mathrm{A})$ be the probability of getting a sum greater than $8 .$ Let $P(B)$ be the...
Simplify each of the following and express it in the form (a + ib) :
Three coins are tossed simultaneously. Find the probability that all coins show heads if at least one of the coins shows a head.
When three coins are tossed simultaneously, the total number of outcomes $=2^{3}=8$, and the sample space is given by $\mathrm{S}=\{(\mathrm{H}, \mathrm{H}, \mathrm{H}),(\mathrm{H}, \mathrm{H},...
Simplify each of the following and express it in the form (a + ib) : (–3 + 5i)3
A coin is tossed twice. If the outcome is at most one tail, what is the probability that both head and tail have appeared?
A coin has 2 sides and its sample space $\mathrm{S}=\{\mathrm{H}, \mathrm{T}\}$ The total number of outcomes $=2$ A coin is tossed twice. Let $\mathrm{P}(\mathrm{A})$ be the probability of getting...
A die is rolled. If the outcome is an even number, what is the probability that it is a number greater than 
A die has 6 faces and its sample space $S=\{1,2,3,4,5,6\}$ The total number of outcomes $=6$ Let $P(A)$ be the probability of getting an even number. The sample space of $A=\{2,4,6\}$ $\therefore...
Let 
and 
be the events such that 
and 
Find
(i) 
(ii) 
.
Given - $A$ and $B$ be the events such that $2 P(A)=P(B)=\frac{5}{13}$ and $\mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{2}{5}$ Formula to be used - By conditional probability, $\mathrm{P}(\mathrm{A} /...
Simplify each of the following and express it in the form (a + ib) : (5 – 2i)2
Simplify each of the following and express it in the form (a + ib) :
Simplify each of the following and express it in the form a + ib :
Simplify each of the following and express it in the form a + ib : (3 + 4i) (2 – 3i)
Simplify each of the following and express it in the form a + ib :
Simplify each of the following and express it in the form a + ib : (1 – i)2 (1 + i) – (3 – 4i)2
Simplify each of the following and express it in the form a + ib : (8 – 4i) – (- 3 + 5i)
Simplify each of the following and express it in the form a + ib : (–5 + 6i) – (–2 + i)
Simplify each of the following and express it in the form a + ib :
Simplify each of the following and express it in the form a + ib : 2(3 + 4i) + i(5 – 6i)
Prove that
Prove that i53 + i72 + i93 + i102 = 2i
Prove that (1 + i2 + i4 + i6 + i8 + …. + i20) = 1.
Prove that
Prove that (1 – i)n= 2n for all values of n N
prove that
Prove that
Prove that (1 + i10 + i20 + i30) is a real number.
Prove that
Prove that 6i50 + 5i33 – 2i15 + 6i48 = 7i.
Prove that 1 + i2 + i4 + i6 = 0
Evaluate:
Again ${{x}^{2}}=t$ $\frac{2t+1}{t(t+4)}=\frac{A}{t}+\frac{B}{(t+4)}.......(1)$ $2t+1=A(t+4)+B(t)$ Putting $t=-4$ $2(-4)+1=A(-4+4)+B(-4)$ $-8+1=0-4B$ $-7=-4B$ $B=\frac{7}{4}$ Putting $t=0$...
Put $\frac{2}{(1-x)(1+{{x}^{2}})}=\frac{A}{1-x}+\frac{Bx+C}{{{x}^{2}}+1}.....(1)$ $A\left( 1+{{x}^{2}} \right)+Bx(1-x)+C(1-x)=2$ Put $x=1$ $2=2A+0+0$ $A=1$ Put $x=0$ $2=A+C$ $C=2-A$ $C=2-1=1$...
Put $t=cos2x$ $dt=-2sin2xdx$ $I=\int \frac{-dt/2}{\left( \left( 1-t \right)\left( 2-t \right) \right)}=\frac{1}{2}\int \frac{dt}{(t-2)(1-t)}$ Putting...
Putting $\frac{{{\left( {{x}^{2}} \right)}^{2}}}{\left( {{x}^{2}}+1 \right)\left( {{x}^{2}}+9 \right)\left( {{x}^{2}}+16 \right)}=\frac{{{t}^{2}}}{(t+1)(t+9)(t+16)}$...