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The vector component of $\overrightarrow{a}=2\hat{i}+3\hat{j}+2\hat{k}$ perpendicular to the direction of $\overrightarrow{b}=\hat{i}+2\hat{j}+\hat{k}$ is

On a graph paper, draw the lines x=3 and y=-5.

Now,on the same graph paper,draw the locus of the point which is equidistant from the given lines.

$\text{In the figure given below,}\text{O is the center of the circle, CA is}\text{tangent at A and CB is tangent at B}\text{drawn to the circle.}$

$\text{If}\angle ACB={75}^{\circ },\text{then}\angle AOB=$ ______.

Question 48

Which pair of ratios are equal? and why?

(i) $\frac{2}{3},\frac{4}{6}$
(ii) $\frac{8}{4},\frac{2}{1}$
(iii) $\frac{4}{5},\frac{12}{20}$

The volume of two hemispheres are in the ratio of 8:27. Find the ratio of their radii.

Find the area of copper sheet required to make a bucket of height 8 cm and radii 9 cm and 3 cm.

Find all pairs of consecutive even positive integers,both of which are larger than 5,such that their sum is less than 23.

Question 2 (i)

Find the surface area of a sphere of diameter:

(i) 14cm $[Assume\pi =\frac{22}{7}]$

The median class for the given data is

$$\begin{array}{ccccccc}\text{Height (in cm)}& \text{Less than 140}& \text{Less than 145}& \text{Less than 150}& \text{Less than 155}& \text{Less than 160}& \text{Less than 165}\\ \text{No. of girls}& 4& 11& 29& 40& 46& 51\end{array}$$

Find the sum of first $n$ natural numbers.

Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.

If the distance between the top of two trees of height 20 m and 28 m is 17 m, then the horizontal distance between the trees is:

Divide 32 into four parts which are the four terms of an AP such that the product of the first and the fourth terms is to the product of the second and the third terms as 7:15 .

ABC is the right angled triangle with $\angle ABC={90}^{\circ }$. The centre of the circle passing through ABC lies on _______.

1. 210

The least number which leaves a remainder of 3 when divided by 2, 5, 7, 10 and 15 is

___ multiples of 4 lie between 10 and 250.

A cylindrical vessel is filled with water up to some height. If a sphere of diameter 8 cm is dropped into the cylinder the water level rises by half of the initial level. Instead, if a second sphere of diameter 16 cm is dropped the water level rises to a height $h_2$. What percentage of this new height $h_2$ to the initial level of water?

1. 0

Show that the points A(-3, 2), B(-5, -5), C(-1, 4) and D(-2, -1) are the vertices of a rhombus. Find hte are of this rhombus.

In the figure, given below, O is the centre of the circumcircle of triangle XYZ. Tangents at X and Y intersect at point T. Given $\angle XTY={80}^{\circ }$ and $\angle XOZ={140}^{\circ }$, calculate the value of $\angle ZXY$.

PQR is an acute angle triangle and $PS\perp QR$, where S is on QR. Which of the following is always true?

Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line segment Y = -1 is

Sachin wants to make a pet house for his dog with length, breadth, and height of 3 m, 2 m, and 1 m respectively. What is the area of walls inside the pet house that has to be painted?

Two A.P's have the same common difference.If the difference between their 20^th terms is 30, find the difference between their 30^th terms