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(√(√5+2)+√(√5-2)/√(√5+1))-√(√3-2√2)=?

What isthe number of terms that you get on simplifying (3x+5)(x-4)?

The area of the curved surface of a cone is 60 $\pi c{m}^2$.If the slant height of the cone be 8 cm,find the radius of the base.

The median of the data arranged in ascending order 8, 9, 12, 18,
(x+2), (x+4), 30, 31, 34, 39 is 24. The value of x is
(a) 22
(b) 21
(c) 20
(d) 24

Let $\Delta$ be the area of a triangle. Find the area of a triangle whose each side is twice the side of the given triangle.

Two circular cylinders of equal volume have their heights in the ration 1:2. Ration of their radii is

(a) 1 : $\sqrt{2}$ (b) $\sqrt{2}$ : 1

(c) 1 : 2 (d) 1 : 4

The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D, as shown in the figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.

Write the value of $\sqrt[3]{37}\times \sqrt[3]{349}$

$(a-b{)}^3+(b-c{)}^3+(c-a{)}^3=$

Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

A solid sphere of radius 3 cm is melted and then cast into smaller spherical balls, each of diameter 0.6 cm. Find the number of small balls that obtained.

If two sides of a cyclic-quadrilateral are parallel; prove that :

(i) its other two sides are equal.

(ii) its diagonals are equal.

Sid is sitting at a bus stop, noting down the time interval of the buses arriving at the stop. His readings are as follows:

$\begin{array}{cccccccccccccccc}\text{Bus}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12& 13& 14& 15\\ \text{Time(hr:min)}& 8:15& 8:18& 8:23& 8:29& 8:32& 8:40& 8:45& 8:52& 8:54& 9:00& 9:07& 9:13& 9:20& 9:25& 9:32\end{array}$

What is the probability that the next bus will come within 5 minutes?(in decimals)___

For the class 90-99, 90 is called the

Three cubes of side a are joined end to end .What is the surface area of the new solid thus formed?

In the figure given below, the radius of the circle is 42 cm. The angle in the sector is ${60}^{\circ }$​. What is the area of the major segment?

Which of the following should be the SECOND sentence after rearrangement?

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.

A quadrilateral formed by joining the midpoints of sides of a quadrilateral can be -

Using Remainder Theorem, obtain the remainder when:
t (x) = 2x³ + 7x ² – 7x - 28 is divided by (x-1)

The total surface area in $m^2$ of a cuboid with dimensions of 26m, 14m and 6.5m respectively is

m${}^2$.

ABCD is a square on the cartesian plane with A, B and C having coordinates (2,2), (3,2) and (3,1) respectively. Find the coordinates of D.

1. 7.5

Anuj and Rajesh each lent the same sum of money for 2 years at 8% simple interest and compound interest respectively. Rajesh received Rs. 64 more than Anuj. Find the money lent by each and interest received.

If $f\left(x_1\right)-f\left(x_2\right)=f\left(\frac{x_1-x_2}{1-x_1{x}_2}\right)$ for $x_1,x_2ϵ$ (-1, 1), then f(x) is

A triangle cannot have more than______right angle(s).

If a=2,b=3 then find the value of (a^{​​​​​b}+b^{​​​​​​a})^-1

A rectangle with one side 4 cm is inscribed in a circle of radius 2.5cm . Find the area of the rectangle

If a and b are rational numbers and $\frac{2+\sqrt{3}}{2-\sqrt{3}}=a+b\sqrt{3}$ find the values of a and b.

If $x^a=y,y^b=z,z^c=x$ then, $abc=$___.

In the figure, ABCD is a rectangle with sides AB = 10 cm and AD = 5 cm. Find the area of $△EFG.$

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

$$\begin{array}{ccccccc}Outcome& 1& 2& 3& 4& 5& 6\\ Frequency& 165& 175& 180& 150& 145& 185\end{array}$$

(i) What is the probability of getting a multiple of 2
(ii) What is the probability of getting a multiple of 3
(iii) are (i) and (ii) mutually exclusive?

If one of the two factors of an expression which is the difference of two cubes is ($x^4$ + $x^2$y + $y^2$), then the other factor would be -

If the points P , Q, R and S are collinear points and PQ=RS then prove that PR=QS using Euclid’s postulate.

The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height, is

A point whose abscissa is -3 and ordinate 2 lies in

The value of $y$ in the following pair of equations is ___

$x+y=7$

$5x+12y=7$

Question 39
Find the value of:
(i) $x^3+y^3-12xy+64$, when x + y = - 4

(ii) $x^3-8y^3-36xy-216$, when x = 2y + 6

$In\Delta ABCand\Delta PQR,\text{it is given that AB = AC,}\angle C=\angle Pand\angle B=\angle Q.\text{Then, the two triangles are}\text{(a) isosceles but not congruent}\text{(b) isosceles and congruent}\text{(c) congruent but not isosceles}\text{(d) neither congruent nor isosceles}$

Two circular cylinders of equal volumes have their heights in the ratio 1:2 Find the ratio of their radii.

AB and CD are two parallel chords of a circle of length 24 cm and 10 cm respectively and lie on the same side of its centre O. If the distance between the chords is 7 cm, find the radius of the circle (in cm).

__

The vector area of the triangle with vertices $\hat{i}+\hat{j}+\hat{k},\hat{i}+\hat{j}+2\hat{k},\hat{i}+2\hat{j}+\hat{k}$ is

The diagonals AC and BC of a quadrilateral ABCD intersect at O, at right angles. Prove that AB²+CD²=AD²+BC².

In our daily life, there are lots of practical examples of triangles. Ram found that roof top of one building was in the shape of the triangle but he was little unsure whether it's right triangle or not. $\angle BAC=\angle BCA={45}^0$. Can you clear his confusion by finding the measure of $\angle ABC$.