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In given figure, AD = 4 cm, BD = 3 cm and BC = 12cm, then cot C =

A fraction becomes $\frac{4}{5}$, if 1 is added to both numerator and denominator. If, however, 5 is subtracted from both numerator and denominator, the fraction becomes $\frac{1}{2}$. Find the fraction

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional ?

In the given figure, OA = 3 cm, OP = 5 cm. Find PQ.

The equation of the circle having $(-2,1)$ and $(4,-1)$ as the endpoints of its diameter is

Solve : $11(x-5)+10(y-2)+54=0$

$7(2x-1)+9(3y-1)=25$

D and E are points on the sides AB and AC respectively of a $△$ABC such that DE || BC and DE divides $△$ABC into two parts, equal in area. Find $\frac{BD}{AB}$.

In what ratio is the line segment joining $(-1,3)$ and $(4,-7)$ is divided by the point $(2,-3)$?

In fig., LM $\parallel$ AB. If AL = $x$ - 3, AC = 2$x$, BM = $x$ - 2 and BC = 2$x$ + 3, Find the value of $x$.

The side of an equilateral triangle is equal to the radius of a circle whose area is 154 $c{m}^2$. The area of the triangle is

(a) 49 $c{m}^2$ (b) $\frac{49\sqrt{3}}{4}c{m}^2$ (c) $\frac{7\sqrt{3}}{4}c{m}^2$ (d) 77 $c{m}^2$

State whether the given statement is ture or false.

(i) The sum of two rationals is always rational.

(ii) The product of two rationals is always rational.

(iii) The sum of two irrationals is always an irrational.

(iv) The product of of two irrationals is always an irrational.

(v) The sum of a rational and an irrational is irrational.

(vi) The product of a rational and an irrational is irrational.

Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex.

If 2 : 9 :: x : 18, then find the value of x.

If $\alpha and\beta$ are the zeroes of the polynomial $a{x}^2+bx+c$, then find the polynomial whose zeroes are $2\alpha +3\beta ,3\alpha +2\beta$.

Prove that the tangent to a circle is perpendicular to the radius through the point of contact.

A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.

A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Then the length of M'N', if MN = 8cm is

If 2 to the power a = 3 to the power b = 6 to the power c, find the relation between a, b, c .

Can i find HCF of 1.2 and 0.2? Why?

Number of zeroes of polynomial $a{x}^2+bx+c$ if the value of a is zero,

In the given figure, PAQ is the tangent. BC is the diameter of the circle. If $\angle BAQ={60}^{\circ }$, then $\angle ABC$ = _____.

If a,a-2 and 3a are consecutive terms of an AP,

then find the value of a

The sum of the ages of two friends is 20 yeras. Four years ago the prosuct of their ages was 48. Show that thses statements can not be true.

A point C on the level ground is at some distance from a 15 m pole AB. If the angle of elevation of the top of the pole from point C is 30°, then how far is point C from the foot of the pole?

If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P. Show that : $x^2,b^2,y^2$ are in A.P.

Factorize $x^3$ + $2x^2$ – 4x + 1 using synthetic division method.

Find the mean proportional between :

(i) $6+3\sqrt{3}$ and $8-4\sqrt{3}$

(ii) a - b and $a^3-a^{2}b.$

Two dice are thrown at the same time. Find the probability of getting the same number on both dice.

For what value of ‘k" is the pair of equations x- ky + 4 = 0 and 2x - 4y - 8 = 0 inconsistent?

Two dice are thrown at a time .What is the probability that sum of the numbers appearing on them is an even number?

AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Select the statements that are true.

Determine the ratio of the largest length of rods that can be fitted in a sphere and cube, given that the sphere exactly fits inside the cube.

The value of k if (2, 3) lies on 2x=3y-k.

A is four times as efficient as B & A can complete a work in 90 days less time than B. Find in how many days B can complete the work

If A:B:C = 2:3:4, then $\frac{A}{B}:\frac{B}{C}:\frac{C}{A}$ is equal to _________________

A two digit number is 3 more than 4 times the sum of its digits if 18 is added to the number its digits are reversed find the number

ABCDEF is a jogging track, in which area of the semi-circle BCD is $\frac{5000}{\pi }{m}^2$. If OO' is $\frac{100}{\pi }m,$ Find the area of the shaded region.

Two chords AB and CD of a circle intersect at a point P outside the circle. Prove that

(1) $\Delta PAC\sim \Delta PDB$

(2) $PA.PB=PC.PD$.