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1. 10

In the figure below, O is the centre of the circle.

What is the diameter of the circle?

If the coordinates of a triangle are A(2,1), B(6,1), C(6,5) then find the length of BC.

Question 152

What will the following machine do to a 2 cm long piece of chalk ?

If $sin\theta +si{n}^2\theta =1$, then $co{s}^4\theta +co{s}^2\theta -1=$

Question 10

To draw a histogram to represent the frequency distribution.

$\begin{array}{cccccc}\text{Class interval}& 5-10& 10-15& 15-25& 25-45& 45-75\\ \text{Frequency}& 6& 12& 10& 8& 15\end{array}$

The adjusted frequency for the class 25 - 45 is:



A) 6

B) 5

C) 3

D) 2

If the polynomials $a{x}^3+4x^2+3x-4and{x}^3-4x+a$ leave the same remainder when divided by (x - 3), find the value of a.

Question 1 (i)

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p\left(x\right)=x^3-3x^2+5x-3,g\left(x\right)=x^2-2$

Which of the following parameters given in the figure are enough to construct the figure (choose the minimum number of parameters possible):

Distance AO = d

Radius of the bigger circle (with center A) = R

Radius of the smaller circle (with center B) = r

$\angle$POA = $\theta$

Note that other than the parameters given in an option, nothing else is given and you have to come up with the figure as given above.

Find out the missing number in the series given below :

$3,12,27,48,75,?$

In the given figure, PA and PB are the tangent segments to a circle with centre O. Show that the points A,O, B and P are concyclic.

Four equal circles, each of radius 5 cm, touch each other as shown in Fig. Find the area included between them (Take $\pi =3.14$)

The sum up to n terms of an AP in which the first term is a, last term is l, and the common difference is d, is

The sum of interior angles of an equilateral triangle, a regular quadrilateral, a regular pentagon.....etc written as a sequence is

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

I fold a rectangular piece of plane paper into a circular fold. The radius of the circle along which fold is done is 2K cm. The length of unfolded dimension is M cm. I get a solid figure. What is the figure and what is its surface area (in $c{m}^2$)?

In how many ways can 7 different books be arranged in a shelf? In how many ways can we arrange three particulars books so that they are always together?

If volume of a cube is 1512 cu ft, the side of the cube will be ______ ft.

The value of $k$ if (2, 3) lies on $2x=3y-k$.

LCM of $(2^3\times 3\times 5)and(2^4\times 5\times 7)is$

Five cards−−the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

What is the value of $sin\theta \times cosec\theta \times cot\theta$ ?

Prove that $\sqrt{5}+\sqrt{3}$ is irrational.

What is the range of 6, 3, 9, 12, 0, 1?

Solve the following system of equations: 8v - 3u = 5uv. 6v - 5u = -2uv.

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then,

In a right angle triangle $\Delta ABC$, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $\Delta ABD$ and $\Delta BCD$?