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A : What is the name of the line which meets the circle at only one point?

B : Collection of all points equidistant from a fixed point is ______.

1: Chord

2: Tangent

3: Circle

4: Curve

5: Secant

Which is of the following is the correct matching?

Solve the following systems of equations:

$\frac{6}{x+y}=\frac{7}{x-y}+3$

$\frac{1}{2(x+y)}=\frac{1}{3(x-y)}$

1. 0.4

Write the next term of the $AP:\sqrt{2},\sqrt{8},\sqrt{18},...$

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), then which of the following is correct

There are 2 identical cubes each having a total surface area equal to ‘A’. Let ‘S’ be the surface area of the solid obtained by joining these 2 cubes end to end. Which of the following statements is true?

A chord of a circle which is twice as long as radius is called

The equation of a line which passes through (1,0) and has a slope of 2 is

A circle is inscribed inside a square of area 100 ${cm}^2$. Radius of the circle is ___ $cm.$

If N is the sum of first 13986 prime numbers, then N is always divisible by:

There is a conical tent whose slant height is 14 $m$. If the curved surface area of cone is 308 $m^2$, then find its base area.

In the given figure if 'O' is the centre of the circle then $\angle AOB$ =___

$△$ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm.$△$ DEF is similar to $△$ABC. If EF = 4 cm, then the perimeter of $△$DEF is -

Question 127

Below u, v, w and x represent different integers, where u = (-4) and x $\ne$ 1. By using following equations, find each of the values $u\times v=u,x\times w=wandu+x=w$
(a) v
(b) w
(c) x
Expain your reason, using the properties of integers.

If $tan\theta =\frac{a}{b}$, find the value of $\frac{cos\theta +sin\theta }{cos\theta -sin\theta }$

Determine the AP whose third term is 16 and the $7^{th}$ term exceeds the $5^{th}$ term by 12.

The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km then total time taken increases by 11 hours. Find the speed of the stream and speed of the boat.

Question 79

In a throw of a die, the probability of getting an even number is the same as that of getting an odd number ?

Question 1 (i)

Find the roots of the quadratic equations by using the quadratic formula in the following question$2x^2-3x-5=0$.

If sin(A - B) = sinA cos B - cosA sinB and cos(A - B)= cos A cos B + sin Asin B then find
sin15 and cos 15 .

How many three-digit numbers are divisible by 7?

Solve the following systems of equations:

$\frac{3}{x+y}+\frac{2}{x-y}=2$

$\frac{9}{x+y}-\frac{4}{x-y}=1$

Question 127(ii)

An insect is on the 0 point of a number line, hopping towards 1. It covers half the distance from its current location to 1 with each hop.
So, it will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.



Where will the insect be after n hops?

The times (in seconds) taken by 150

athlete to run a 110 m hurdle race are tabulated below

$\begin{array}{ccccccc}\text{Class}& 13.8-14& 14-14.2& 14.2-14.4& 14.4-14.6& 14.6-14.8& 14.8-15\\ \text{Frequency}& 2& 4& 5& 71& 48& 20\end{array}$

The number of athletes who completed the race in less than 14.6 seconds is _______.

1. 82

Find the quadratic polynomial, the sum of whose zeros is 0 and their product is -1. Hence, find the zeros of the polynomial.

The figure shows the cross section of an ice cream cone consisting of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 10.5 cm. The outer shell ABCDEF is not filled with ice cream. AE = DC = 0.5 cm, AB || EF and BC ||FD.

Calculate