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Question 2(iv)
Simplify and express the result in power notation with positive exponent:

$(3^{-7}÷3^{-10})\times 3^{-5}$

$\text{If}x+\frac{1}{x}=2,\text{find the value of}{x}^{64}+\frac{1}{x^{64}}$

If $3tan\theta =5$, then $\frac{3sin\theta -5cos\theta }{3sin\theta +5cos\theta }$ is equal to

Numbers that can be expressed as a ratio of p and q where p and q are integers and $q\ne 0$ are called __numbers.

For what value of k, the pair of linear equations 3x + ky = 9 and 6x + 4y = 18 gives infinitely many solutions?

The value of 'a' when $a{x}^3+9x^2+4x-10$ is divided by $x+3$ leaving a remainder of 5 is ___

Identify the figure in which all the points could be collinear.

How many natural numbers are there in the list given below?

$12,34.66,0,900000$

The distance between the points (4,8) and (k,-2) is 10. Find the value of k

Simplify: (5-x) (6-5x) (2-x)

In 🔺 PQR, if angle P - angle Q = 42° and angle Q - angle R =21°.Find angle P, angle Q and angle R

Multiply $(x–8)(x+9)$

The value of $0.\overline{23}+0.\overline{22}$ is

Distance between the points $(x_1,-y_1)and(-x_2,y_2)$ =.

Write the distance of point $p(2,-1)$ from the $y$- axis.

Construct a $\angle$ABC = 30${}^{\circ }$. Mark a point D on BC such that BD = 5 cm. Find the radius of the circle to touch AB at B and also pass through D.

Prove that :

(i) the parallelogram, inscribed in a circle, is a rectangle.

(ii) the rhombus, inscribed in a circle, is a square.

What is the value of cotangent of an angle in a right angled triangle?

Given that $x^{3}y$ and $7x^{3}y$ are like terms, then the sum of these two terms is _____.

These seals show mythical belief

1. 30

If (3, 2) is a solution of the equation $4x-ky=10$, then find the value of $k$.

Let M and N be two 3 $\times$ 3 skew - symmetric matrices such that MN = NM. If $P^T$ denotes the transpose of P, then $M^2{N}^2\left(M^{T}N{)}^{-1}\right(M{N}^{-1}{)}^T$ is equal to

Draw a line segment AB and bisect it. Bisect one of the equal parts to obtain a line segment of length $\frac{1}{2}$(AB).

What are different ways to represent data graphically?

If $sin\theta =\frac{4}{5}andcos\theta =\frac{3}{5},$$findtan\theta$.

If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.

If a = $x{y}^{p-1},b=x{y}^{q-1}andc=x{y}^{r-1}$, prove that $a^{q-r}{b}^{r-p}{c}^{p-q}$ = 1,

The simplest form of 0.12$\overline{3}$ is

(a)$\frac{41}{330}$ (b)$\frac{37}{330}$ (c)$\frac{41}{333}$ (d) none of these

ABCD is a parallelogram. E and F are the mid-Points of BC and AD respectively. Show that the segments BF and DE trisect the diagonal AC. [4 MARKS]

Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

If the linear equation y = 7x - 4 is written in standard form, the standard form being ax +by +c =0, then what is the value of a, b and c?

Draw the graph of the equation $\frac{x}{3}+\frac{y}{4}=1.$ Also, find the area of the triangle formed by the line and the coordinates axes.

The product of$8x+3y$ and $3x^2$ is .

A hemispherical bowl made of brass has inner diameter of 10.5 cm. Find the cost of tin - plating it on the inside at the rate of Rs. 4 per $100c{m}^2$.

Find the mean.

$$\begin{array}{cccccc}Observation& 3& 6& 7& 9& 10\\ frequency& 8& 10& 15& 9& 8\end{array}$$

Two equal chords, $AB$ and $CD$ are at a distance of 10 cm from each other. Find the distance of chord $AB$ from the centre.

Match the two columns :
$\begin{array}{cc}\text{Column - I}& \text{Column - II}\\ \text{A) Sum of all the angles}& \text{P) Right angles}\\ \text{of a quadrilateral is}& \\ \text{B) In a}\parallel \text{gm, the angle}& \text{Q) Rectangle}\\ \text{bisectors of two adjacent}& \\ \text{angles intersect at}& \\ \text{C) Angle bisectors of}& \text{R)}{45}^{\circ }\\ \text{a}\parallel \text{gm form a}& \\ \text{D) The diagonals of a}& \text{S) 4 right angles}\\ \text{square are equal and}& \\ \text{bisect each other at}& \\ \text{an angle of}& \end{array}$

Choose the correct option:

Through $A,B$ and $C$ lines $RQ,PR$ and $QP$ have been drawn, respectively parallel to sides $BC,CA$ and $AB$ of a $\Delta ABC$ as shown in figure. Show that $BC=\frac{1}{2}QR$.

If the $5^{th}$ term of a G.P. containing positive terms is $\frac{1}{3}$ and $9^{th}$ term is $\frac{16}{243}$, then the $4^{th}$ term will be

If $x+y+z=0,$
then find the value of $x^3+y^3+z^3.$

In an event there are two possible outcomes, the probability of occurrence of one outcome is 1. The probability of occurrence of the other outcome is ____.

The value of : $\frac{tan{26}^{\circ }}{cot{64}^{\circ }}$ equals :

Represent 0.462462… in a rational form. [3 MARKS]

ABC is a triangle. Number of circles that can be drawn circumscribing this triangle is/are ?