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Boundaries of surfaces are

(a) lines

(b) curves

(c) polygons

(d) none of these

The mean of 15 observations is 8. If the mean of the first eight observations is 7 and that of the last eight observations is 10, then find the value of the 8^th observation.

A dance floor has to be built as a triangular glass platform with the dimensions $\text{7 m, 8 m and 9 m}$. The total surface area of the glass required to build such a platform is equal to ___$m^2$.

A chord of length 30 cm is drawn in a circle of radius 17 cm. Find its distance from the centre of the circle.

If xyz=1 , then show that (1+x+y^{​​​​​​-1})^-1 + (1+y+z^{​​​​​​-1})^-1 + (1+z+x^{​​​​​​-1})^-1 =1

How to find five rational numbers between two fractions with different denominator?

(a+b)3-a-b

If the point $P(a,5)$ lies on the line $2x-3y-5=0$, then find the value of $a$.

If $\frac{a}{b}+\frac{b}{a}=1,then{a}^3+b^3=$

If f(x) = $2x^3-13x^2$ + 17x + 12, find

(i) f(2) (ii) f(-3) (iii) f(0)

$\text{If the ratio of the volumes of two spheres is 1:8 then ratio of their surface areas is}\left(a\right)1:2\left(b\right)1:4\left(c\right)1:8\left(d\right)1:16$

The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is

Find the volume of a right circular cone with:

(i) radius 6 cm, height 7 cm

(ii) radius 3.5 cm, height 12 cm

(iii) height 21 cm and slant height 28 cm

In the figure, O is the centre of the circle. If $\angle$BAC = 52${}^{\circ }$, then $\angle$OCB in degree is equal to-

1. 75

The angles of a quadrilateral are in the ratio 1:2:5:7. The angles of the quadrilateral are:

The decimal number 0.625 when expressed as a fraction is

$4a^2-(4b^2+4bc+c^2$)

Question 1
Classify the following polynomials as polynomials in one variable, two variables etc.

(i) $x^2+x+1$

(ii) $y^3-5y$

(iii) $xy+yz+zx$

(iv) $x^2–xy+y^2+1$

In the fig. below, if AB || CD, $\angle$APQ = 50${}^{\circ }$ and $\angle$PRD = 127${}^{\circ }$, find x and y.

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In the adjoining figure, AD is a median of $\Delta ABC$ and DE || BA. Show that BE is also a median of $\Delta ABC$.

Factorise:
$6\sqrt{3}{x}^2-47x+5\sqrt{3}$

Two lines are respectively perpendicular to two parallel lines Show that they are parallel to each other.

D and E are points on sides AB and AC respectively of $△ABC$ such that $ar\left(△BCD\right)=ar\left(△BCE\right)$.Prove that DE||BC.

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.

Verify : $x^3$+ $y^3$= (x + y) ($x^2$ – xy + $y^2$)

Find the value of 1/a+1/b

Solve the inequation $\frac{2x-3}{4}+9\ge 3+\frac{4x}{3}$. Also represent the solution on number line.

Construct a $\Delta PQR$ in such a way that $\angle PQR={60}^{\circ }$, $\angle PRQ={30}^{\circ }$ and QR = 8 cm. Construct a rectangle, the area of which is equal to the area of $\Delta PQR$. What are the dimensions of the rectangle.

GST in India has replaced all ___ taxes.

If the probability of winning a game is 0.9 , then find the probability of losing the game

In the below figure, ABCDEF is a regular hexagon, and its center is point O. Find the value of x?

A square is formed by reducing the length of a rectangle by 4 cm and increasing it's width by 3 cm. Both the figures have the same area. Find the perimeter of the original rectangle.

Simplify: $\frac{cose{c}^{2}A}{1+co{t}^{2}A}$ [1 MARK]

When the fare of a certain journey by an airline was increased in the ratio 5 : 9, the cost of the ticket for the journey became Rs. 2021. Find the increase in the fare.

Question 2 (ii)
1500 families with 2 children were selected randomly, and the following data was recorded:
$\begin{array}{cccc}\text{Number of girls in a family}& 2& 1& 0\\ \text{Number of families}& 475& 814& 211\end{array}$
Compute the probability of a family, chosen at random, having 1 girl.

Choose the correct statement

In ΔABC, AB = AC and the bisector of ∠B and ∠C meet at a point O, then ΔOBC is

Use the following information to answer the next question.

What is the area of trapezium ABCD?

$IfmatrixA=[a_{ij}{]}_{3\times 3},matrixB=[b_{ij}{]}_{3\times 3}where{a}_{ij}+a_{ji}=0and{b}_{ij}-b_{ji}=0,then|A^4.B^3|is$

What is the probability of getting a sum of 7 on two rolls of a die?