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Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle (in cm) which touches the smaller circle.

Find the probability of getting at least 1 Head, if 3 coins are tossed.

If $\alpha$, $\beta$ are the roots of the equation $x^2-5x+6=0$, then the value of ${\alpha }^2-{\beta }^2$ is:

BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are respectively the midpoints of AH, AB and BC. ∠PQR =

i) Percentage of people in the height range of 149.5 -159.5 cm is equal to ______

ii) Percentage difference between height group 159.5 - 169.5 cm and 169.5 - 179.5 cm

Given that $2x=3+\sqrt{7}$

Find the value of $4x^2+\frac{1}{x^2}$

Question 71

To find the distance around a circular disc, multiply the diameter of the disc by 3.14
What is the distance around the disc, when
(a) the diameter is 18.7 cm?
(b) the radius is 6.45 cm?

What is ${\left(\frac{2}{5}\right)}^{-3}$?

The area of the quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is

$\text{If}x=9+4\sqrt{5},\text{then}\sqrt{x}-\frac{1}{x}=$ _______.

Consider the data

$\begin{array}{cccccccc}\text{Class}& 65-85& 85-105& 105-125& 125-145& 145-165& 165-185& 185-205\\ \text{Frequency}& 4& 5& 13& 20& 14& 7& 4\end{array}$

The difference of the upper limit of the median class and the lower limit of the modal calss is
(a) $0$
(b) $19$
(c) $20$
(d) $38$

Solution set of the inequality
$\frac{1}{2^x-1}>\frac{1}{1-2^{x-1}}is$

Consider the following statements about e-Biz Mission Mode Project:

Which of the above statements is/are correct?

In the given figure, two parallel lines l and m are intersected by two parallel lines p and q.

$\text{Show that}\Delta ABC\cong \Delta CDA.$

In the given figure, AB and CD are two parallel chords of a circle. If BDE and ACE are straight lines, intersecting at E, prove that $△$AEB is isosceles.

ABC is a triangle in which $\angle A={72}^{\circ }$, the internal bisectors of angles B and C meet in O. Find the magnitude of $\angle BOC$.

Factorise:
$x^2-2x+\frac{7}{16}$

The distance between two points $\frac{-1}{2}$ and $\frac{2}{3}$ on the number line is

If each observation of a data is increased by 5, then their mean

A and B solved a quadratic equation. In solving it , A made a mistake in the constant term and obtained the roots as 5, -3 while B made a mistake in the coefficient of x and obtained the roots as 1, -3. The correct roots of the equation are

$\begin{array}{cc}\text{Assertion (A)}& \text{Reason (R)}\\ \text{If three angles of a quadrilateral}& \text{The sum of all the angle of a}\\ \text{are}{130}^{\circ },{70}^{\circ }and{60}^{\circ }\text{then the}& \text{quadrilateral is}{360}^{\circ }.\\ \text{fourth angle is}{100}^{\circ }.& \end{array}$
The correct answer is: (a)/(b)/(c)/(d).

The numbers 42, 43, 44, 44, (2x+3), 45, 45, 46, 47 have been arranged in an ascending order and their median is 45. Find the value of x. Hence, find the mode of the above data.

Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

Factorise:
$1+2ab-(a^2+b^2)$

Two coins are tossed simultaneously. The probability of getting at least one head is __.

P is the vertex of cuboid and Q, R and S are three points on the adjacent edges passing through P as shown. PQ = PR = 2 cm and PS = 1 cm. Then the area of $\Delta QRS\left(inc{m}^2\right)$ is:

In a sphere, the number of faces is

An isoceles right triangle has an area of 8 cm²​​​​​​. Find the length of its hypotenuse

Construct a triangle ABC in which BC is 6 cm, $\angle B$ is ${70}^{\circ }$ and AB+AC=14cm by using method of perpendicular bisector. [4 Marks]

Which of the following is a correct statement?

Given that one of the zeroes of $a{x}^3+b{x}^2+cx+d$ is 0, whats the product of the other 2?

Which of the following is correct for some $\theta$, such that $0^{\circ }$ $\le \theta <$ ${90}^{\circ }$

Prove area of equilateral triangle formula

In fig., if m||n and ∠a : ∠b = 2 : 3, the measure of ∠h is

Two distinct points in a plane determine ...............

Find the sum of deviations of the observations given below from their mean:

3, 4, 6, 7, 8, 14