Solve your IGNOU Doubts

Question:

Obtain the resolvent cubics, by Descartes’ method and by Ferrari’s method, of the equation $x^{3}+4x^{3}+8=0.$ . Are the cubics the same? Further, use either method to obtain the roots of this equation.

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Question:

Find the cubic equation whose roots are the cubes of the roots of $x^{1}+ax^{2}+bx+c=0,a,b,c \in \mathbb{R}.$

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Question:

(b) Prove that the conic passing through the points of intersection of two rectangular hyperbolas is also a rectangular hyperbola.

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Question:

(a) Trace the conic $x^2-2xy+y^2-3x+2y+3=0.$

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Question:

Check whether the following statements are true or false. Justify your answer with a short explanation or a counter example

(i) The numbers $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\frac{3}{2}$ are the direction cosines of a line.

(ii) The points $(1,2),(7,6)$ and $(4,4)$ are collinear.

(iii) The conic $12x^2+12xy+3y^2+2xy=0$ is degenerate

(iv) Intersection of the ellipsoid $\frac{x^2}{4}+\frac{y^2}{25}+\frac{z^2}{4}=1$ and the plan $y=5$ is a circle. The conicoid $3x^2+y^2+2xy+x-y-z+1=0$ is non-central.

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Question:

Using the discriminant, give the nature of the roots of $7x^{3}+x^{2}-35x=5.$ . Also solve the equation.

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Question:

Let 1 ,a b > a,0 + b = ,1 n > . Show that $\left ( a+\frac{1}{a} \right )^{n}+\left ( b+\frac{1}{b} \right )^{n}\geq \frac{5^{n}}{2^{n-1}}.$ .

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Question:

c) Find the angle between the planes $6x-4y+2z=1$ and $3x+12y-9z=2.$ Alsospecify the type of the angle obtained.

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Question:

b) Find two positive numbers x and y such tha $x+y=$ 60and $xy^3$ is maximum.

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Question:

Show that $1+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{n}}>2\sqrt{n+1}-2\,\forall n\in \mathbb{N}.$

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Question:

a) Calculate: (i) Quartile deviation and (ii) Mean Deviation from mean for the following data:

Marks	No. of Students
15-25	4
25-35	11
35-45	14
45-55	18
55-65	8
65-75	5

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Question:

The converse of the statement, ‘Every student of MTE-04 has completed FST-01’, is ‘Every student of FST-01 has completed MTE-04’.

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Question:

Every biquadratic equation has at least one real root

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Question:

Any finite set is a subset of $\mathbb{Z}.$

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Question:

c) Fit a straight line for regression of Y on X from the following table.

x	0	1	2	3	4	5	6
y	2	1	3	2	4	3	5

Find the value of y when $x=10.$

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Question:

The geometrical representation of the set $\left \{ ix\mid x\mid \in \mathbb{R} \right \}$ is a point.

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Question:

b) If $y=e^x+e^{-x},$ prove tha $\sqrt{y^{2}-4.}$

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Question:

a) A and B are two events which are independent. The probability that both A and B occur is $\frac{1}{2}$ and the probability that neither of them occurs is $\frac{1}{3}.$ Find the probability of the occurrences of A and B.