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If √[18-6√5] =√a-√b, then prove a + b= 18

This is a silly question but due to tension I am not able to figure this out.

(-1-2)^2 according to the formula should be =

1 + 4 - 4 = 1

But the answer is 9.

Where am I wrong?

What are the possible location(s) of circumcentre in a triangle?

The area of a circular pizza is 616 cm². Its diameter is

Determine the volume of a conical vessel having radius of the base is 5 cm and its slant height as 13 cm.

The sum of cubes of primes between $1$ and $6$ is equal to $40x$. Find the value of $x$.

Which of the following does not have volume?

In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Which of the following statements is true?

A glass is in the shape of a cylinder of radius 7 cm and height 10 cm. Find the volume of juice in litres required to fill 4 such glasses.

The time taken to travel 30 km upstream and 44 km downstream is 14 hrs. If the distance covered upstream is doubled and the distance covered downstream is increased by 11 km, then the total time taken is 11 hrs more than earlier. Find the speed of the stream and the speed of the boat.

State the quotient law of exponents.

When 0^o < θ < 90^o and 3tan²θ - 1 = 0. Then θ is equal to

A man bought a land for ₹180000 and a car for ₹320000 at the same time. The blue of the pot of land grows uniformly at the rate of 30% per annum while the value of the car depriciates by 20% in the first year and by 15% thereafter. If he sells the land as well as the car after 3 years what will be his profit or loss

Question 1
Show that in a right angled triangle, the hypotenuse is the longest side.

The maximum frequency 10 is for the observation 4. Hence the mode of the data is

Evaluate $lo{g}_{16}^{32}$ - $lo{g}_{25}^{125}$ + $lo{g}_9^{27}$

If one interior angle of an octagon is ${142}^{\circ }$ and each of the other angles are $x^{\circ }$, then x = ___

The value of |-71| - |-23 + 57| - 22 is

A field is in the shape of a trapezium whose parallel sides are 25m and 10m.The non-parallel sides are14 m and 13 m. Find the area of the field.

Define the following terms :

(i) Line segment (ii) Collinear points (iii) Parallel lines

(iv) Intersecting lines (v) Concurrent lines (vi) Ray

(vii) Half -line

A die thrown 300 times and the outcomes are noted as given below:

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 60& 72& 54& 42& 39& 33\end{array}$

When a die is thrown at random, what is the probability of getting a

(i) 3?

(ii) 6?

(iii) 5?

(iv) 1?

The product of two irrational numbers is

(a) always irrational

(b) always rational

(c) always an integer

(d) sometimes rational and sometimes irrational

Each side of an equilateral triangle is $8cm$. Its area is

(a) $24c{m}^2$

(b) $24\sqrt{3}c{m}^2$

(c) $16\sqrt{3}c{m}^2$

(d) $8\sqrt{3}c{m}^2$

Expand $(x+2y+3z{)}^2$ using algebraic identity.

Find the weight of a solid cylinder of radius 10.5 cm and height 60 cm if the material of the cylinder weight 5 g per $c{m}^3$

Express $0.8+0.\overline{7}+0.4\overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q\ne 0$.

We have a map with a scale of 1:50000000. How much would 1cm measure in actual distance?

The mean of the following distribution is 50.
$\begin{array}{cccccc}\text{x}& 10& 30& 50& 70& 90\\ \text{f}& 17& 5a+3& 32& 7a-11& 19\end{array}$
Find the value of a and hence the frequencies of 30 and 70.

In the given figure, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ, then $\Delta$PQR is _______triangle.

Find the point on 3x - y = 7 whose abscissa is -2

The mean of 8 numbers is 35. If a number is excluded then the mean is reduced by 3. Find the excluded number.

Factorise:
$\frac{3}{2}{x}^2+16x+10$

If $(3x+\frac{1}{2})(3x-\frac{1}{2})=9x^2$ -p then the value of p is
(a) 0 (b) $-\frac{1}{4}$ (c) $\frac{1}{4}$ (d) $\frac{1}{2}$

Question 90 (a)

Given that, $\frac{p}{q}$ and $\frac{r}{s}$ are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers, we say that
$\frac{☐}{☐}<\frac{☐}{☐}$, if $p\times s<r\times q$

Using a protractor, draw an angle of measure ${72}^{\circ }$. With this angle as given, draw angles of measure ${36}^{\circ }and{54}^{\circ }$.

In the adjoining figure, ABCD is a parallelogram in which $\angle A={72}^{\circ }$. Calculate $\angle B,\angle Cand\angle D$.

1. 2250

The given figure shown a circle with centre O. Also, PQ = QR = RS and $\angle$ PTS = ${75}^o$. Calculate :

(i) $\angle$ POS,

(ii) $\angle$ QOR,

(iii) $\angle$ PQR.

What is the polar of the point (2, 3) with respect to the circle $x^2+y^2-2x-4y-4=0$

Question 3
The scores (out of 100) obtained by 33 students in a mathematics test are as follows.
69, 48, 84, 58, 48, 73, 83, 48, 66, 58, 84, 66, 64, 71, 64, 66, 69, 66, 83, 66, 69, 71, 81, 71, 73, 69, 66, 66, 64, 58, 64, 69, 69.
Represent this data in the form of a frequency distribution.

$\text{If}a=\frac{2-\sqrt{5}}{2+\sqrt{5}}$ and $b=\frac{2+\sqrt{5}}{2-\sqrt{5}}$, then $(a+b{)}^2=$_______.