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The length of the minute hand of a clock is 14 cm. What is the area swept by the minute hand in 5 minutes?

Find the value of k for which each of the following systems of equations has no solution:
$kx+3y=k-3,12x+ky=k.$

A sum of 2800 is to be used to award four prizes. If each prize after the first is 200 less than the preceding prize, find the value of each of the prizes.

A piece of equipment cost a certain factory Rs.600,000. Ifit depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

The radii of two circles are 8 cm and 6 cm. Find the radius of hte circle having area equal to the sum of the areas of the two circles.

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m, the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take :$\pi$ = 22/7)

If sin 3A = cos (A - ${10}^o$) and 3A is acute then $\angle$ A = ?

(a) ${35}^o$ (b) ${25}^o$ (c) ${20}^o$ (d) ${45}^o$

If cot $\theta =2$, find the values of all T-ratios of $\theta$.

A point P is its own image under the reflection in a line l. Describe the position of the point P with respect to the line l.

A circular garden of radius 10m has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants area. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in $m^2$? It is given that cos ${53}^{\circ }$ = $\frac{3}{5}$.

A right circular cone of height 33 m is recasted into a cylinder in such a way that radius of cylinder is same as the radius of the cone. Find the height of the cylinder.

An arc AB forms $\angle AOB$ at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will __ the $\angle AOB$.

IF $A=\left[\begin{array}{cc}1& 4\\ 1& -3\end{array}\right]andB=\left[\begin{array}{cc}1& 2\\ -1& -1\end{array}\right]$ Find
$\left(i\right)(A+B{)}^2$ (ii) $A^2+B^2$
(iii) Is (A + B)^2 = A^2+ B^2?\)

If $\sec \theta =\frac{17}{8}$, verify that $\frac{3-4si{n}^2\theta }{4co{s}^2\theta -3}=\frac{(3-ta{n}^2\theta )}{(1-3ta{n}^2\theta )}$.

Two different dice are thrown together. find the probability that the numbers obtained
(i) have a sum less than 7 (ii) have a product less than 16
(iii) is a doublet of odd numbers.

Consider the following table:

$\begin{array}{cccccc}Classinterval& 10-14& 14-18& 18-22& 22-26& 26-30\\ Frequency& 5& 11& 16& 25& 19\end{array}$

The mode of the above data is

(a) 23.5 (b) 24 (c) 24.4 (d) 25

If the pair of linear equations 3x-5y=11 and (5a+b)x-(7a-b)y=4(3a-2b)+1 have infinitely many solutions then find the value of a and b

If the product of two numbers is 21 and their difference is 4, then the ratio of the sum of their cubes to the difference of their cubes is:

Look at the figure given below. Can you find the measure of $\angle y$ in the figure?

Solve the following systems of equations:

$x+\frac{y}{2}=4$

$\frac{x}{3}+2y=5$

The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :

(i) the gradient of PQ;

(ii) the equation of PQ;

(iii) the co-ordinates of the point where PQ intersects the x-axis.

Write the value of (1 + $ta{n}^2\theta$) $co{s}^2\theta$.

How to solve a quadratic equation by spreading middle term?

And I want to know that how to spread middle term and solve a equation..

8 women and 12 girls can finish a piece of work in 10 days while 6 women and 8 girls can finish it in 14 days find the time taken by 1 women alone and by that of one girl alone to finish the same work

The areas of two circles are in the ratio 4 : 9. What is the ratio between their circumferences ?

Ramesh takes 18 minutes to complete a round of a ground which Aslam takes 24 minutes to complete the same round. Suppose they start from the same point and at the same time and go in the same direction. After how many minutes will they meet again? How many times will they meet in 6 hours?

Without using trigonometric tables , prove the following:

(ii) sin11 cos79 + cos 11 sin79 = 1

To get the census of the country, the government collected data from hospitals for the number of births and deaths of people.

What does this data known as?

The sum of two numbers is 8. Determine the numbers, if their reciprocal is 8/5.

Solve the following quadratic equation by factorization.
$\frac{x+3}{x+2}=\frac{3x-7}{2x-3},x\ne -2,\frac{3}{2}$

The median of first 8 prime numbers is

(a) 7 (b) 9 (c) 11 (d) 13

The sum of n terms of two APs are in ratio 7n+1/4n+27.

Find the ratio of their 11th terms

Find the quadratic polynomial, the sum and product of whose zeros are -3 and 2,

The co-ordinates of the vertices of ΔABC are A (4, 1), B(–3, 2) and C(0, k). Given that the area of Triangle ABC is 12 ${unit}^2$. Find the value(s) of k.

Write the sum and product of the zeroes of the polynomial x^3-4x

The outer circumference of a circular race-track is 528 m. The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre. (Use $\pi =\frac{22}{7}$)

In the figure given below, all the four sides are equal. The construction of which figure is shown in the diagram?

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the ${20}^{th}$ term.

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2+x-2, find the value of 1\alpha-1\beta