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Simplify $({\sqrt{256})}^{\frac{-3}{4}}$

If sec theta + tan theta = 4 then prove that cos theta = 8/17

OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. if OE = 2√5 cm, the area of the rectangle is

Factorise 8x^3+27y^3+36x^2y+54xy^2

The rationalising factor for the number $3-7\sqrt{2}$ is

In the figure if $l||m$ and $\angle 1=(2x+y{)}^{\circ }$ , $\angle 4=(x+2y{)}^{\circ }$ and $\angle 6=(3y+20{)}^{\circ }$. Find $\angle 7$ and $\angle 8$.

Prove that cosA sin$({90}^{\circ }-A)$ = 1 - $si{n}^{2}A$

Figure depicts a racing track whose left and right ends are semi-circular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find the area of the track (in $m^2$).

If sinA=cosA, find the value of :

2 tan square A - 2sec square A +5

Where is the C.G. of a

i. Ring

ii. Rhombus

Find the value of k for which a straight line 2x-ky=3 passes through the intersection of 2 curves 3^x+y=81 and 81^x-y=3.

1. 54

If the sets A and B are defined as A = {(x, y) : y = $e^x$, x ∈ R};

B = {(x, y) : y = x, x ∈ R}, then

The standard form of a linear equation in two variables x and y, whose respective coefficients are 2 and -3 and has the constant as 4 is ____.

Which of the following is a constant polynomial?

A man starts from his house and goes 5km north, turns right and goes 5km. Again he goes 5km to his left, turns left and goes 15km further. Now in which direction is he from the house?

In the given figure, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. The measure of $\angle DAC$ is

The result obtained when we multiply $a^6-b^6$ with the product of $a^2+ab+b^2$ and $a-b$ is

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD cannot be

Prove that an equilateral triangle can be constructed on any given line segment

In a given figure, BE is a median of $△ABD$. If the area of parallelogram ABCD is $24c{m}^2$. Then the area of $△ABE$ is:

factorise:7√2-10x-4√2

AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED. [3 MARKS]

Find the length of AC in the given figure, if the sides are in the ratio $1:\sqrt{3}:2$

Directions:- Study the following information carefully to answer the question given below.

Eight persons — A, B, C, D, E, F, G and H are sitting around a regular octagonal table but not necessarily in the same order. Out of them, A and B are facing towards the centre of the table while the rest of them are facing outside. G sits second to the left of E. A sits second to the left of G. Only one person sits between A and H. B sits to the immediate right of A. D is not an immediate neighbour of G. B is not an immediate neighbour of G. Both the immediate neighbours of F face towards the outside.

What is the position of C with respect to E?

Using factor theorem, show that g(x) is a factor of p(x), when
$p\left(x\right)=x^4-x^2-12,g\left(x\right)=x+2$

$Constructa\Delta ABCinwhich\angle B={45}^{\circ },\angle C={60}^{\circ },\text{and the perpendicular from the vertex A to base BC is 4.5cm}$

The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius $3cm$ and height $10.5cm$. The Vidyalaya was to supply to the competitors with cardboard. If there were $35$ competitors, how much cardboard was required to be bought for the competition?

$(4x^2+4x-3)$=?

(a) $(2x-1)(2x-3)$

(b) $(2x+1)(2x-3)$

(c) $(2x+3)(2x-1)$

(d) None of these

On simplification, the expression $\frac{5^{n+2}-6\times 5^{n+1}}{13\times 5^n-2\times 5^{n+1}}$ equals

(a)$\frac{5}{3}$ (b)$-\frac{5}{3}$ (c)$\frac{3}{5}$ (d)$-\frac{3}{5}$

If $a^{\frac{1}{3}}+b^{\frac{1}{3}}+c^{\frac{1}{3}}=0,$ then $(a+b+c{)}^3$ = ?

Factorise
$x^2-x-156$

In the given figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected ray BD.

Write three rational numbers between $\sqrt{3}$ and $\sqrt{5}$.

The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are ${94}^{\circ }$ and ${126}^{\circ },$ Then , $\angle BAC=?$

Give an example of two irrational numbers whose sum as well as product is rational.

In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Which of the following is true.

Simplify $(32{)}^{\frac{1}{5}}+(-7{)}^0+(64{)}^{\frac{1}{2}}$

Paul wants to put 1200 steel ball bearings (which are spherical in shape) with a radius of 5 mm, into a cylindrical container which is 30 cm high and 18 cm in diameter. Will all the bearings fit into the container?

In the given figure, O is the centre of the circle and arc ABC subtends an angle of ${130}^{\circ }$ at the centre. If AB is extended to P, find $\angle PBC.$

The number of surfaces in a right circular cylinder is

(a) 1 (b) 2

(c) 3 (d) 4

Factorise
$a^6+b^6$