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Find the value of a when the distance between the points (3,a) and (4,1) is $\sqrt{10}$.

Find the area of shaded portion in the given figure. [2 MARKS]

Factories 32760 using tree method

Solve the equations: $\frac{x}{a}$ + $\frac{y}{b}$ = 1 and the $xaxis$.

The longest chord of a circle is called a/an ___ of the circle.

The ordinate of a point lying on the line joining the points (6, 4) and (7, -5) is -23. Find the co-ordinates of that point.

To the given figure, BC is parallel to DE Area of triangle $ABC=25c{m}^2,$

Area of trapezium BCED $=24c{m}^2$ and DE =14 cm.

The length of BC = ___ cm.

What is the sum of 4 arithmetic means between 3 and 23?

Two bodies are thrown with the same initial velocity at angles $\theta$ and $({90}^{\circ }-\theta )$ respectively with the horizontal, then their maximum heights are inthe ratio:

if 3 is a solution of 3x²+(k-1)x+9=0, then k=?

'a' and 'b' are two positive integers such that the least prime factor of 'a' is 3 and the least prime factor of 'b' is 5.Then find the least prime factor of (a+b).

Swapnil invests Rs 14950 in Rs 100 shares of a company, paying $14\%$ dividend. If her annual income from shares be Rs 1610, what will be the market value of each share?

1. 36

The pair of equations y = 0 and y = -7 has :

Using the properties of proportion, solve for x: $\frac{\sqrt{a+x}+\sqrt{a-x}}{\sqrt{a+x}-\sqrt{a-x}}=b$

If H.C.F of $x^3{y}^4{z}^2$, $x^6{y}^8{z}^4$ is 'a' and H.C.F of $x^5{y}^6{z}^3$, $x^6{y}^7{z}^4$ is 'b' then $a/b=$ ___

The points B (1, 3) and D (6, 8) are two opposite vertices of a square ABCD. Find the equation of the diagonal AC.

The difference of a number and its positive squareroot is 42. Express this in quadratic equation form. [Assume positive square root of the number be $x$]

Select the meaning of the given phrases/idioms: pie in the sky

A circle is drawn with y-axis as a tangent and its centre at the point which is the reflection of (3, 4) in the line y = x. The equation of the circle is

In the figure below P,Q,R are the points where the incircle of $△ABC$ touches the sides

$\angle AQR$ and $\angle ARQ$ are ______ , ______ respectively.

The centre of circle passing through (0, 0) and (1, 0) and touching the circle $x^2+y^2=9$ is
(2002)

Lines AB and CD intersect at point O. If $\angle AOD={50}^{\circ }$, then match the following.

If A = ${60}^o$ and B = ${30}^o$, find the value of
$(sinA.cosB+cosA.sinB{)}^2$ + $(cosA.cosB-sinA.sinB{)}^2$.

Sum of the area of two squares is 500 sq m. If the difference between their perimeter is 40 m. Find the side of both the squares.

Question 2(ii)
Represent the following situations in the form of quadratic equations.
(ii) The product of two consecutive positive integers is $306$. We need to find the integers.

Evaluate $lo{g}_{10}\frac{1}{10000}$.

Let $f:[0,\infty )\to$ [0,2] be defined by $f\left(x\right)=\frac{2x}{1+x}$ , then f is

Find the coordinate of the circumcentre of the triangle whose vertices are (8,6),(8,-2) and (2,-2). Also, find its circumradius.

AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d, then BP = _____.

Write a pair of irrational numbers whose difference is rational.

If $cosec(A+B)=\frac{2}{\sqrt{3}}$, sec(A-B)=$\frac{2}{\sqrt{3}}$,
$0^{\circ }<A+B\le {90}^{\circ }$,
Find A and B.

Which among the following is a cubic polynomial?

What is the value of cos $\theta$ in the given triangle?

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8.If the first two pH reading are 7.48 and 7.85,find the range of pH value for the third reading that will result in the acidity level being normal.

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are $1\frac{1}{2}$ times the corresponding sides of the isosceles triangle.

${14}^{\frac{1}{7}}\times {14}^{\frac{1}{7}}$ can be represented as ___________.

Find points on the x-axis, each of which is at a distance of 10 units from the point A(11, -8).

Solve each of the following systems of equations by using the method of cross multiplication:

$7x-2y=3,22x-3y=16.$

The diagonal of a trapezium shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field(in m²).