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Question 1 (ii)
Without actually performing the long division, state whether $\frac{17}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

P lies in the exterior of 🔘 (O,5 )such that op=13. Two tangents are drawn .to the circle which touch the circle in A and N.find AB

Find the quotient when $x^3+2x^2$ - x - 2 is divided by (x + 2)

If x = 6 is a root of the quadratic equation $3x^2-mx-24=0$, then the value of m is __

Water flows at a rate of $10m/minute$ through a cylindrical pipe $5mm$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40cm$ and depth $24cm$?

1. -7

2 women and 5 men together finish an embroidery work in 4 days while 3 women and 6 men can together finish within 3days .Find the time taken by 1 women alone to finish the work and also 1 men to finish.

From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find :
(i) the surface area of remaining solid,
(ii) the volume of remaining solid,
(iii) the weight of the material drilled out if it weighs 7 gm per $c{m}^3$.

The $y$ coordinate is known as __

An aeroplane is 30 m long and its model is 15 cm long. If the total outer surface area of the model is 150 cm^2, find the cost of painting the outer surface of the aeroplane at the rate of Rs.120 per sq. m. Given that 50 sq. m of the surface of the aeroplane is left for windows.

In a factory, the cost of a machine is ₹ 6,00,000. If its value depreciates 15% the first year, 13.5 % the next year, 12% the third year, and so on. Calculate its value at the end of 10 years, applying all percentages to the original cost?

$If\sqrt{x-2}<\sqrt{2x-6},thevalueofxis$

BC is chord of a circle with centre O. A is a point on major arc BC. Find the total measure of $\angle BAC$ and $\angle OBC$.

A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. Find the volume of the tent and the area of the cloth used for making it.

Given $\text{A}=\{x:11x-5>7x+3,xϵR\}$ and $\text{B}=\{x:18x-9\ge 15+12x,xϵR\}.$
Find the range of set $A\cap B$.

Find the angle of inclination of the straight line whose slope is $1\sqrt{3}$

Prove 7/3√2 an irrational??

What is the sum of the first 30 odd numbers?

The equation of sides rectangle ABCD are given as follows:

Equation of AB: = –2, equation of BC: = 2, equation of CD: = 6, equation of AD: = –1. Find the coordinates of A, B, C, D. Hence find the equation of the diagonal AC.

A cylinder and a cone are of same base radius and of same height. The ratio of the volume of cylinder to that of the cone is:

In a class there are 4 more girls than boys . When only 8 boys were absent the number of girls were twice the number of girls.what is the total number of girls and boys in the class. Please answer it with all steps.

The radius of the circle given above is $7cm$ and the angle subtended by the arc is ${60}^{\circ }$. If the area of $△OAB$ is $21{cm}^2$, then the area of segment $APBA$ is___ .[Take the value of $\pi$ as $\frac{22}{7}$]

In a triangle ABC, BC ||DE If AD=1.5, DB=4.5, AE=1.3, EC=?

Show that the lines 2x + 5y = 1, x - 3y = 6 and x + 5y + 2 = 0 are concurrent.

A cylindrical container is of depth 20 m and radius 0.7 m. Calculate the curved surface area of the cylindrical vessel.

Find the ratio in which the midpoint of A(12, 8) and B(4, 6) divides the points of trisection of the line AB.

If the cardinality of two disjoint sets A and B are 10 and 15 respectively, what is the cardinality of A $\cup$ B?

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

If 5, 15, 45, 135, 405, 1215.... are in GP, which series is also in GP?

The equation whose roots are the squares of the roots of the equation
$2x^2+3x+1=0$ is

If the roots of the equation a\({x}^{2}\) + bx + c = 0 are reciprocal to each other, then :

A card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a spade?

Solve:
$x-2y=0and3x-y=5$

Decide whether the real number with decimal expansion as $125.\overline{987654321}$ is rational or not. If rational, and of the form $\frac{p}{q}$, what can you say about the prime factors of $q$?

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of ${60}^0$. Find the value of $\angle$ AOB.

You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

In $\Delta ABC,D$ is the midpoint of BC and $AE\perp BC$. If $AC>AB$, show that $A{B}^2=A{D}^2-BC.DE+\frac{1}{4}B{C}^2$.

For what value of ‘n’ would $4^n$ end with zero?

Which among the following is the exclamatory form of the assertive sentence?
I am very worried about the outcome of this test.

Which of the following trigonometric expressions is equal to ${\text{sec}}^6\theta$ ?

The area of the triangle formed by joining the origin to the points of intersection of the line $x\sqrt{5}+2y=3\sqrt{5}$ and

circle $x^2+y^2=10$ is

D and E are respectively the points on the sides AB and AC of a $\Delta ABC$ such that AB = 5.6 cm. AD = 1.4 cm. AC = 7.2 cm and AE = 1.8 cm. Show that $DE\parallel BC$. [1 MARK]

If $20–5x<5(x+8)$ ,then the highest integral value of x is,

If A and B are two matrices, match the following to their equivalent expressions.

The given data shows the population of different cities. What is the median of this data ?