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Question 4
Classify the following numbers as rational or irrational with justification.
$\left(i\right)\sqrt{196}$
(ii)$3\sqrt{18}$
(iii)$\sqrt{\frac{9}{27}}$
(iv)$\frac{\sqrt{28}}{343}$
(v)$-\sqrt{0.4}$
(vi)$\frac{\sqrt{12}}{\sqrt{75}}$
(vii) 0.5918
(viii) $(1+\sqrt{5})-(4+\sqrt{5})$
(ix) 10.124124 ....
(x) 1.010010001....
To classify, use the definition a rational number is in the form of $\frac{p}{q}$, where p and q are integers and $q\ne 0$ and otherwise it is an irrational number.

The probability of picking the letter K from the word TREKKING is $\frac{x}{4}$. Then the value of x is ___.

By using the method of completing the square, show that the equation $2x^2+x+4=0$ has no real roots.

The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by $\frac{l^2-a^2}{k-(l+a)}$, then k =

A. S

B 2S

C 3S

D None of these

Probability to have a holiday on 15${}^{th}$ August in India is ___.

In Fig. AB = 36 cm and M is mid-point of AB. Semi-circles are drawn on AB, AM and MB as diameters. A circle with centre C touches all the three circles. Find the area of the shaded region.

A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? $(Use\pi =\frac{22}{7})$

A ladder 5 m. long rests against a wall at a height of 4.8 m form the ground. Calculate the distance of the foot of the ladder from the wall.

Consider the following steps. Which would be the correct order to solve the above-mentioned question?

1. Find the area of each unshaded region.

2. Identify the unshaded regions.

3. Subtract the sum total of areas of unshaded regions from the area of the square.

What is the simplified form of the given expression?

$x^{3}y+4x^2{y}^2+3x{y}^3+7x^2{y}^2+3x^3+4y^2+6xy+7x^{3}y+8y^2$

Rationalize the denominator

$\frac{1}{(\sqrt{7}-\sqrt{6})}$

Consider the following AP sequence: 134, 104, 74,… The $6^{th}$term is

Which of the following polynomials are binomials?

(1) p(x) = x + 1

(2) q(x) = $x^3+x$

(3)r(x) = $\sqrt{2}+x+x^2$

(4)r(u) = $u+u^2-2$

P(n): n²+n+1 is prime for n=1,2.......40. The least number for which the result does not hold is

In what ratio is the line joining the points:

(2, -3) & (5, 6) divided by the – axis.

(3, 4) & (-2, 1) divided by the y – axis.

Question 1 (i)

Find the volume of the right circular cone with:

(i) radius 6 cm, height 7 cm.

$[Assume\pi =\frac{22}{7}]$

In ___ theorem, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The mid point P of the line segment joining the points A (-10, 4) and B(-2, 0) lies on the line segment joining the points C (-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the values of y.

If the points A(4, 3) and B(x, 5) lie on a circle with the centre O (2, 3), find the value of x.

If $(tan\theta +sin\theta )=m$ and $(tan\theta -sin\theta )=n$, prove that

$(m^2-n^2{)}^2=16mn.$

In the given figure, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.

The equation of the circle having $(3,3)$ and origin as the endpoints of its diameter is

Solve the following inequation:
$\frac{x+14}{2}\ge 2x+28$

The HCF of two numbers is 145 and their LCM is 2175 if one number is 725 find the other

A contractor plans to install two slides for the children to play in a park. She prefers to have a slide whose top is at a height of √3m and is inclined at an angle of ${60}^{\circ }$ to the ground. What should be the length of the slide?

If q is the mean proportional between p and r prove that :

$\frac{p^3+q^3+r^3}{p^2{q}^2{r}^2}=\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3}$

Match the zeroes of the respective polynomials.