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ABCD is a parellelogram, AD is produced to E so that DE = DC = AD and EC produced meets AB produced in F. Prove that BF = BC.

Find the value of k if x-3 is a factor of k²x³-kx²+3kx-k.

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that angle ABC is equal to half the difference of the angles subtended by the chords AC and DE at the center.

Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm.

Find the square of $\frac{2\sqrt{5}}{5}$

Find the equation of a line whose slope is -1 and y-intersection is 0.

x = 7, y = 3 satisfies which of the following equations?

If $l$ is the length of a diagonal of a cube of volume $V$, then

Factorize: $3a^2-1-2a$

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

Express $0.4\overline{7}$ in the form of $\frac{p}{q}$.

Solve the given expression, and choose the correct option.



$(6\frac{6}{7}-\frac{2}{7})+(4\frac{4}{7}-\frac{1}{7})$

A cube weighing 24.5 N is placed on a floor. It exerts a pressure of 2450 Nm⁻² on the floor.

What is the volume of the cube?

Find the sum of $5\frac{3}{8}$ and $3\frac{4}{6}$.

If dividend = $x^4+x^3-2x^2+x+1$ and divisor = $(x-1)$, find the quotient, $q\left(x\right)$ and remainder $r\left(x\right)$.

Two points A & B are marked on the number line as shown in the figure. A = -3 and the distance between them is 7 units. The point B is

Let E denote the event "India scores less than 300” in a cricket match between India and South Africa. How many elements are there in the sample space which will favour the event E?

In the given figure, the arms of two angles are parallel to one another. If $\angle ABC={70}^{\circ }$, then find $\angle DGC$



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If sets A and B are defined as
$A=\left\{\right(x,y)|y=\frac{1}{x},x\ne 0,xϵR\},B=\left\{\right(x,y)|y=-x,xϵR\}$, then

Pavan filled water in a cylindrical vessel of radius $6cm$ and height $11cm$. Then he gently dropped a spherical ball of radius $3cm$ inside the cylindrical vessel. What should be the maximum level of water in the cylindrical vessel before the spherical ball is dropped so that it doesn't get overflowed?

If $\Delta ABC$ is isosceles with AB = AC and C(O,r) is the incircle of the $\Delta ABC$ touching BC at L, prove that L bisects BC.

A sum compounded annually becomes $\frac{49}{16}$ times itself in 2 years. The rate of interest per annum is _____.

A solid sphere with centre 'O' of certain radius fits exactly into a right circular cone as shown in the diagram given below. If the volume of the sphere is 4186.67 ${cm}^3$, find the total surface area of the cone. (Take $\pi$ = 3.14). It is known that slant height of the cone is two times the radius of the base of the cone and the ratio of AO to DO is 2:1.

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Consider the square plot given below with the green portion as garden. Express the part of plot used as garden in decimals.

Which of the following is a false statement ?

(a) A median of a triangle divides it into two triangles of equal area.

(b) The diagonals of a ||gm divide it into four triangles of equal area.

(c) In a $△ABC$,if E is the midpoint of median AD then ar($△ABC$)=$\frac{1}{4}ar\left(△ABC\right)$.

(d) In a trap. ABCD,it is given that AB||DC and the diagonals AC and BD intersect at O.Then,ar$\left(△AOB\right)=ar\left(△COD\right)$.