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John wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 8 cm respectively. The area of the aluminium sheet required to make the cone is approximately _____.

$(Use\pi =\frac{22}{7})$

Find the equation of the straight line that has y - intercept 5 and is parallel to the straight line x - 3y = 3

Question 3(e):

Draw any circle and mark:

A segment

What is the discriminant of the equation $2x^2-5x-2=0$ ?

If $3x=cosec\theta and\frac{3}{x}=cot\theta ,\text{find the value of}3(x^2-\frac{1}{x^2}).$

The median class for the given data is

$\begin{array}{ccccccc}\text{Height (in cm)}& \text{Less than 140}& \text{Less than 145}& \text{Less than 150}& \text{Less than 155}& \text{Less than 160}& \text{Less than 165}\\ \text{No. of girls}& 4& 11& 29& 40& 46& 51\end{array}$

A solid is hemispherical at the bottom and conical above. If the curved surface area of the two parts are equal, then what is the ratio of the height and radius of the conical part?

Evaluate :
$\cos {48}^{\circ }-\sin {42}^{\circ }$___

In the quadrilateral $MARE$ inscribed in a unit circle $C,$ $AM$ is a diameter of $C,$ and $E$ lies on the angle bisector of $\angle RAM.$ Given that triangles $RAM$ and $REM$ have the same area. Then area (in sq. units) of the quadrilateral $MARE$ is equal to

If $(\frac{a}{2},3)$ is the midpoint of the line joining the points (0, 6) and (6, 0). Then the value of the term $a^3+18$ is:

In the given figure, obtain all the points equidistant from lines m and n; and 2.5 cm from O.

If $3sin\theta +4cos\theta =5$, then the value of $sin\theta$ is

Transpose of $\left[\begin{array}{ccccc}1& 2& 3& 4& 5\end{array}\right]$ is a ___matrix

The following table represents the relation between x and y. Which of the following graphs show the missing values in the table?

If the distance of a point $A(1,2)$ is 13 units from a point $B(a,14)$, then the value of $a$ is

In the figure given below, ABCD is a rectangle with AB = 24 cm & AD = 20 cm & P & Q are the mid-points of sides BC & DC respectively. Find the area of the unshaded portion.

The sum of first q terms of an A.P. is $63q-3q^2$. If its pth term is -60, find the value of p. Also, find the 11th term of this A.P.

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft. by 8 ft. What would be the size in inches of the tile required that has to be cut and how many such tiles are required?

Question 1(h):

From the figure, identify:

A segment

In parallelogram ABCD, A(2,3), B(6,5) and D(4,7). Then the coordinates of C is

A bag contains 12 balls of which '$x$' are white.
(i) If one ball is drawn at random, what is the probability that it will be a white ball?
(ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in case (i), Find $x$. [4 MARKS]

If two adjacent vertices of a parallelogram are (3, 2) and (-1, 0) and the diagonals intersect at (2, -5), then the other two vertices are

The set $A=\{x:xϵR,x^2=16and2x=6\}$ equals

Solve each of the following equation:

$(x^2+5x+4)(x^2+5x+6)=120$

Find the LCM and HCF of the following pair of integers and verify that LCM x HCF=product of the two numbers : 26 and 91 [2 MARK]

Does the line 3x - 5y = 6 bisect the join of (5, -2) and (-1, 2) ?

A 60cm tall girl spots a balloon moving with the wind in a horizontal line. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. Find the height of balloon from the ground if the wind speed is 5m/s. It travelled for 12s during the interval.

The value of $\xi$ in the mean value theorem of $f\left(b\right)-f\left(a\right)=(b-a)f^{\prime }\left(\xi \right)$ for $f\left(x\right)=A{x}^2+Bx+C$ in $(a,b)$ is

In the given figure, AC = AE.

Show that :

(i) CP = EP

(ii) BP = DP.

Solve : A/B x - B/A y = A+B and Ax - By =2AB