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In the given figure, $AB$ and $CD$ are straight lines through the centre $O$ of a circle. If $\angle AOC={80}^{\circ }and\angle CDE={40}^{\circ }$ , find (i) $\angle DCE,\left(ii\right)\angle ABC.$

If P and R are the centres of their respective circles, then what will be the measure of $\angle SPQ$?

Twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. Thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. Find the smallest even number.

Which of the following has a terminating decimal ?

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

State the condition for the congruency of two figures.

Given below is age group of different children and Cumulative Frequency
Below 4 0
Below 7 85
Below 10 140
Below 13 243
Below 16 300

Find the number of children in the age of 10 -13
Which of the age group had least number of Children

AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d, find BP

Find the area of the triangle with sides, 56 cm, 52 cm, 60 cm.

On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under:

$\begin{array}{cccc}\text{Type of vehicle}& \text{Two-wheelers}& \text{Three-wheelers}& \text{Four-wheelers}\\ \text{Frequency}& 84& 68& 88\end{array}$

Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?

Cartesian plane consists of two fixed perpendicularly intersecting lines to represent the position of a point on a plane. What are the horizontal and vertical lines, respectively known as?

XYZ is an equilateral triangle and PQRS is a square. The figure has been cut and rearranged in the form of a trapezium.

What is the area of the triangle BCE in the given trapezium ABEF?

Find the X and Y intercepts of 3x + 5y = 15

Solve $1010\times 990$ using standard identity.

Question 9

A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Without finding cubes find the value(1\4)³ +(1\3) ³-(7\12)³

Question 3 (i)

Express $0.\overline{6}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

The outer surface of a sphere of radius R is painted with minimum amount of blue paint. How many circles of radius R can be painted with same amount of blue paint?

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that

(i) D is the mid-point of AC

(ii) $MD\perp AC$

(iii) $CM=AM=\frac{1}{2}AB$

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. The correct mean is
(a) 38.6
(b) 39.4
(c) 39.8
(d) 39.2

In the given figure PQ is the diameter of a circle with centre O, and is perpendicular to the chord AB. If AB = 8cm and QM = 2cm, find the radius of the circle.

$\text{Find the value of x if x if}|x+2|$= 3

The median class for the given data is

$$\begin{array}{ccccccc}Height\left(incm\right)& Lessthan140& Lessthan145& Lessthan150& Lessthan155& Lessthan160& Lessthan165\\ CumulativeFequency& 4& 11& 29& 40& 46& 51\end{array}$$

Standard deviation about mean $\left(\overline{x}\right)$ for a given discrete frequency distribution $x_1,x_2,x_3,.....x_n$ with frequencies $f_1,f_2,f_3,...f_n$ is :

If the radius of a sphere is tripled, the ratio of the surface area of original sphere to that of the second is

Six persons are sitting in a circle. $A$ is facing $B,$ $B$ is to the right of $E$ and left of $C.$ $C$ is to the left of $D.$ $F$ is to the right of $A.$ Now $D$ exchanges his seat with $F$ and $E$ with $B.$ Who will be sitting to the left of $D$?

The inner diameter of a circular well is 3.5 m . It is 10 m Deep find it's curved surface area. The cost of plastering this curved surface at the rate of Rs.40. per m square.

The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are: