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In the given figure, A, B, and C are three points on a circle with centre O such that $\angle BOC={30}^{\circ }$ and $\angle AOB={60}^{\circ }$. If D is a point on the circle other than the arc ABC, find $\angle ADC$.

Solve for $\theta$ if $4co{s}^2\theta$ + 2$sin\theta$ – 4 = 0, where $0^{\circ }$ $\le$ $\theta$ $\le$${90}^{\circ }$.

Solve equation, given below, using factorisation method:

$x=\frac{3x+1}{4x}$

ABC is a right angled triangle in which $\angle A={90}^{\circ }$. Find the area of the non-shaded region if AB = 6 cm, BC=10 cm & O is the center of the incircle of ABC.

Mr. Saurabh purchased 80 shares of FV ₹60 at a premium of ₹20. If the company is paying 15% dividend, then the rate of return on investment is .

Solve the pair of linear equations by substituting method:-

√2x+√3y=0

√3x-√8y=0

A dice is thrown twice. Find the probability of getting a bigger value on the first throw.

Q... TWO DISTINCT POLYNOMIALS f(x) and g(x) are defined as follows;

f(x) = x²+ax+2 g(x) = x²+2x+a

IN THE EQUATION f(x)=0 and g(x) = 0 have a common root then sum of the roots of the equation f(x)+g(x) =0 is ?

An AP has first term 1 with a common difference also 1 and has 49 as its last term. Find its sum. 1,2,3,4 ........49

Relation between Exradius ,semiperimeter and circumradius can be given by
($r_1$ is the radius of the circle opposite the angle A)

If the diameter of semicircular protractor is 14 cm, then its perimeter is:

The outer and inner diameters of a circular ring are 34 cm and 32 cm respectively. The area of the ring is:

In $\Delta ABC,\angle A={60}^{\circ },BC=10cm.$ The circumdiameter of the triangle is $[sin{60}^{\circ }=0.87]$

Mid-point of the line segment joining the points (0,0) and (6,8) is

The algebraic form of an arithmetic sequence is 4n+2. The numbers of terms required to get the sum as 880

If D and E are points on sides AB and AC respectively of $\Delta ABC$ such that DE || BC and BD = CE. Prove that $\Delta ABC$ is isoscles.

ABCD is a trapezium in which AB || CD. The diagonals AC and BD intersect at O. Prove that :
(i) $\Delta AOB\sim \Delta COD$
(ii) If OA = 6 cm, OC = 8 cm,
Find:

(a) $\frac{Area\left(\Delta AOB\right)}{Area\left(\Delta COD\right)}$
(b) $\frac{Area\left(\Delta AOD\right)}{Area\left(\Delta COD\right)}$

A triangle PQR is drawn to circumsribe a circle of radius 8 cm such that the segements QT and TR, into which QR is divided by the point of contact T, are of lengths 14 cm and 16 cm respectively. If area of $\Delta PQR$ is $336c{m}^2$, find the sides PQ and PR.

Two taps running together can fill a tank in $3\frac{1}{13}$ hours. If one tap takes 3 hours more than the other to fill the tank then how much time will each tap take to fill the tank?

Draw a circle with center A and radius $5cm$. Draw any one of the diameters. With same center A, draw another circle with radius $3cm$. Draw any one of the diameters for this circle too. If you join the ends of both the diameters, the figure you will get is:

The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on the same axes.

$\begin{array}{ccccccccccc}\text{Height(in cm)}& 124& 128& 132& 136& 140& 144& 148& 152& 156& 160\\ & to& to& to& to& to& to& to& to& to& to\\ & 128& 132& 136& 140& 144& 148& 152& 156& 160& 164\\ \text{No. of Children}& 5& 8& 17& 24& 16& 12& 6& 4& 3& 1\end{array}$

What is cos ${45}^{\circ }$sin ${45}^{\circ }$..............

The radius and height of a right circular cone are in the ratio $1:2$. If its volume is $144{cm}^3$, find its slant height.

Three vertices of a parallelogram ABCD are A(3, -1, 2), B(1, 2, -4) and C (-1, 1, 2). Find the coordinates of the fourth vertex D.

If the lines $(p+1)x+y=3$ and $3y-(p-1)x=4$ are perpendicular to each other, find $p$.

If (√x+2)+(√x+8)=10 ,then the value of (X+191/100)=?

Without solving find the nature of the root 5x²-3x-4

The numerator of a fraction is $3$ less than its denominator. If $2$ is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is $\left(\frac{29}{20}\right)$. Find the original fraction.

Find the two consecutive positive integers, such that sum of their squares is 365.

A box has length, breadth and height of $10cm,$ $20cm$ and $5cm$ respectively. The lateral surface area of the box is equal to

A gear system has the driving wheel of radius 2 cm and driven wheel of radius 20 cm. Find the gear ratio.

If one root of the polynomial p(y)=5y² +13y + m is reciprocal, find the value of m.

In the given figure, if QS = 7 units and h₁ + h₂ = 5 units, then the area of the quadrilateral PQRS is ______ .

The graph of a quadratic polynomial is a parabola which cuts the X- axis at