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The figure shows a circle with centre O and radius 8 cm. $\angle$ BOD =${72}^{\circ }$. The radius of the smaller circle is 4 cm. A point is selected randomly inside the larger circle, find the probability that the point lies neither inside the smaller circle nor inside the sector.

Find the value of the side AC of the $△$ABC in terms of AB, whose length is $\sqrt{3}$ units

The roots of a quadratic equation $x^2-4x-a=0$ are real. Then what is the least value of $a$ ?

In triangle $ABC$, right angled at $B$, find the expressions of $\tan A$ and $\cot C$​

What are the possibilities of outcomes when 2 coins are tossed in the air?

In $\Delta$ABC, right angled at B, if $\angle A$ is made smaller and smaller till it becomes zero, find the value of sin A and cos A.

If $\alpha \&\beta$ are the zeros of $6x^2-x-2$ , then $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=?$

The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively. If PQ = 12 cm, find AB.

In the given figure, $\frac{AB}{BC}$ = $\frac{3}{4}$.Find the value of $si{n}^{2}A$ + $co{s}^{2}A$ =

A girl of height $90cm$ is walking away from the base of a lamp-post at a speed of $1.2m/sec$. If the lamp is $3.6m$ above the ground, find the length of her shadow after $4$ seconds.

If $sin\theta =\frac{4}{5}$ , then the value of cos$\theta$

Which of the following is a solution to $3x+4y=38?$

1. 30

Find the value of the given expression.
$3(sinx-cosx{)}^4+6(sinx+cosx{)}^2+4(si{n}^{6}x+co{s}^{6}x)$

Give an example of two irrational numbers whose
a. sum is rational.
b. product is rational.
c. quotient is rational.

nP4=20(nP2) then find the value of n

Why is 1 neither prime nor composite numbers?

If a and b are two odd positive integers such that a>b, then prove that one of the two numbers a+b/2 and a-b/2 is odd and the other is even .

Mr A earns Rs 30000 in a month. He spends Rs 25000 on his needs. What is the probability of his savings?

In the given figure, $\frac{QT}{PR}=\frac{QR}{QS}$ and $\angle 1=\angle 2$.

Which of the following is true?

If altitude of the sun is 60^o, the height of a tower which casts a shadow of length 30 m is:

Question 4
The angle of elevation of the top of a tower from a point on the ground which is 30 m away from the foot of the tower is ${30}^{\circ }$. Find the height of the tower.

Check whether the following is a quadratic equation: $(x+2{)}^3=2x(x^2-1)$

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1

Prove the following trignometric identities:

$ta{n}^2\theta co{s}^2\theta =1-co{s}^2\theta$

The sides of a triangle are in the ratio $5:12:13$, and its perimeter is $150m$. Find the area of the triangle.

(i) $si{n}^2\theta +\frac{1}{(1+ta{n}^2\theta )}=1$ (ii) $\frac{1}{1+ta{n}^2\theta }+\frac{1}{1+co{t}^2\theta }=1$

$\Delta ABC$ is an equilateral triangle of side $2\sqrt{3}cm$. P is any point in the interior of $\Delta ABC$. If x, y, z are the distances of P from the sides of the triangle, then x + y + z =

In $△ABC,AB=3cm,AC=4cm$ and AD is the bisector of $\angle$A. Then, $BD:DC$ is

In fig., PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and

Area $△$POB = 150 ${cm}^2$ find the area of $△$QOA.

Find the 10th term of the G.P. :

12, 4, $1\frac{1}{3}$,............ .

Find the slope and y-intercept of the line :

(i) y = 4 (ii) ax - by = 0

(iii) 3x - 4y = 5

Find the zeroes of 25x(x+1) + 4.

In two concentric circles, prove that all chords of the outer circle which touch the inner circle are of equal length

$\begin{array}{cc}\text{Marks}& \text{Cumulative Frequency}\\ 0& 100\\ 10& 87\\ 20& 65\\ 30& 55\\ 40& 42\\ 50& 36\\ 60& 31\\ 70& 21\\ 80& 18\\ 90& 7\\ 100& 0\end{array}$

Find the frequency for the clas interval 80 - 90.

In right angled triangle ABC, $AB=20m$ and $\angle CAB={60}^{\circ }$. Find BC.

Fill in the blank with a modal auxiliary showing past probability.
We ______ have reached the venue on time if the car had not broken down.

If a, b, c belong to R and equations $a{x}^2+bx+c=0and2x^2+4x+6=0$ have a common root. Also given that a + b + c = 18. Find the value of $a^{2}bc$

Find a and b if
$a\left[\begin{array}{c}1\\ 7\end{array}\right]-\left[\begin{array}{c}3\\ b\end{array}\right]=\left[\begin{array}{c}2\\ 24\end{array}\right]$

Which of the following sets given below may represent the magnitude of 3 vectors adding up to 0?

A) 2,4,8 B)4,8,16 C)1,2,1