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In given figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, $\angle$B = ${90}^{\circ }$ and DS = 5 cm, then the radius of the circle (in cm.) is :

Prove that if a diagonal of a quadrilateral bisect each other, it is a parallelogram.

If n! =840*4320,then find the value of n.

Assertion: $ABCD$ and $PQRC$ are rectangles and $Q$ is the mid - point of $AC.$ Then $DP=PC.$

Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it.

If n ∈ N, then $x^{2n-1}+y^{2n-1}$ is divisible by

If $x=0.\overline{18}$, which of the following statements are true?

(i) $100x=18.\overline{18}$

(ii) $100x-x=17.\overline{18}$

(iii) $99x=18$

If R is the set of real numbers and Q is the set of rational numbers, then what is R - Q?

Question 11

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

In the given figure, BOC is a diameter of a circle with centre O. If $\angle BCA={30}^{\circ }\text{then}\angle CDA=?$

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${50}^{\circ }$

In a deck of 52 cards, there are 4 kings, 4 queens, and 4 jacks, known as the face cards. If a card is drawn from the deck, what is the probability that it is a face card?

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that:

ar $\left(△APB\right)\times ar\left(△CPD\right)=ar\left(△APD\right)\times ar\left(△BPC\right)$

Find three different irrational numbers between the rational numbers and.

Write 1296 in the expanded form. [1 MARK]

Find the Measure of an angle which is supplement of itself is :

The area of a circular field is 88704 sq. m. How long will it take to go round 10 times at the speed of 4.5 km per hour?

Find the length of the side of a cube whose total surface area is $1536c{m}^2$.

The altitude of a right-angled triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the measure of other two sides (in cm).

A circle is cut into 16 equal sectors and the sectors are arranged as shown below.


The given figure can be visualised as

√5+√20+√45

Pair of straight lines perpendicular to each other represented by [Roorkee 1990]

The reason for the equations $x+2y=5$ and $4x+8y=20$ to have infinite solutions is :

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three vectors such that $|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=4$ and angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\pi /3,$ angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\pi /3$ and angle between $\overrightarrow{c}$ and $\overrightarrow{a}$ is $\pi /3.$

The volume (in cubic units) of the parallelopiped whose adjacent edges are represented by the vectors $\overrightarrow{a},\overrightarrow{b}$and$\overrightarrow{c}$ is

Question 35

The compound interest on Rs 8000 for one year at 16% per annum compounded half-yearly is___ , given that $(1.08{)}^2$ = 1.1664.

Find the measure of $\angle$2, $\angle$3 and $\angle$4 from the given figure.

The weights of newborn babies (in kg) in a hospital on a particular day are as follows:
$2.3,2.2,2.1,2.7,2.6,3.0,2.5,2.9,2.8,3.1,2.5,2.8,2.7,2.9,2.4$
(i) Rearrange the weights in descending order.
(ii) Determine the highest weight.
(iii) Determine the lowest weight.
(iv) Determine the range.
(v) How many babies weigh below 2.5 kg?