One-fourth of a herd of camels was seen in a forest. Twice the square root of the herd had gone to mountains and the remaining 15camels were seen on the bank of a river. Find the total number of camels.

If sum of five numbers in A.P. is 40, then find the middle term.

PQ is tangent to circle with centre O. Find the radius of the circle, if PO = 5 cm and PQ = 4 cm.

If the probability of an event is p, then the probability of its complementary event

Draw a parallelogram LMNO with LM = 6.5 cm, MN = 4 cm and angle LMN = 45^o , divide it into two triangles triangle LMN and triangle LNO by joining its diagonal LN. Construct triangle LM'N' similar to triangle LMN with scale factor \(\frac { 2 }{ 3 } \). Draw line O'N' \(\parallel \) ON. Is LM'N'O' a parallelogram?

Construct a tangent to a circle of radius 3 cm from a point on the concentric circle of radius 5 cm and measure its length. Also, verify the measurement by actual calculation.

Find the centroid of a triangle whose vertices are (3, -7), (-8, 6) and (5, 10).

Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

A tree is broken by the wind, the top struck the ground at an angle of 60⁰ and at a distance of 20m from the root of the tree.Then find the whole height of the tree.

If x is a positive integer such that the distance between the points P(x,2) and Q(3,-6) is 10 units, then x=?

What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length 6\(\pi\) cm.

The internal and external diameters of a hollow hemispherical vessel are 24cm and 25cm respectively.The cost to paint 1cm² of the surface is Rs.0.05.Find the total cost to painting the vessel all over.

If the product of the zeroes of the polynomial (ax²-6x-6) is 4, then find the value of a.

If \(\tan { \theta } =1\) and \(\sin { \phi } =\frac { 1 }{ \sqrt { 2 } } \), find the value of \(\cos { (\theta +\phi ) } \) where \(\theta\) and \(\phi \)  are both acute angles.

If (5, 2), (-3, 4) and (x, y) are collinear, show that x + 4y - 13 = 0.

In the given figure, diameter AB is 12 cm long. AB is trisected at points P and Q. Find the area of the shaded region.

A vertical tower is  \(2\sqrt { 3 } m\) high and the length of its shadow is 2 m. Find the angle of elevation of the source of light.  

Anita, Sita, Gita and Rita are four friends. What is the probability that (in a non-leap year)
(i) all will have same birthday
(ii) their birthdays fall in the month of October.
(iii) their birthdays fall on 10th day of the months.
(iv) their birthdays fall in January or February

If an isosceles ∆ABC in which AB = AC = 6 cm is inscribed in a circle of radius 9 cm, then find the area of the triangle

Let ABC be a right angled triangle, in which AB=15 cm, BC=8 cm and \(\angle B=90°\) . BD is the perpendicular from B on AC. The circle through B, C and D is drawn. Construct the tangents from A to this circle.

The frequency distribution of agricultural holdings in a village is given below:

Find the modal agricultural holdings of the village

The sum of first q terms of an A.P. is 63q - 3q². If its pth term is -60, find the value of p. Also, find the 11th term of this A.P.

If ABC is an obtuse angled triangle, obtuse angled at B and if AD \(\bot \) CB. Prove that:
AC² = AB² + BC² + 2BC \(\times\)BD

Find the values of a and b for which x=\(\frac { 3 }{ 4 } \)and x=-2 are the roots of the equation ax²+bx-6=0

The angle of depression of two ships from the top of a lighthouse are 45⁰ are 30⁰ towards east.If the ships are 200m apart, find the height of the lighthouse.

Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively.They are thrown and the sum of the numbers on them is noted.Find the probability of getting each sum from 2 to 9 separately

A farmer has two types of fields-In the form of a triangle and a rectangle. Rani is allowed to cut grass of triangular part (shaded) and Ramu of rectangular field (shaded). Calculate the areas of the shaded portion. What value is depicted by the farmer?

If \(\sqrt { 3 } \sin { \theta } =\cos { \theta } \), find the value of \(\frac { \tan { \theta } (1+\cot { \theta } ) }{ \sin { \theta } +\cos { \theta } } .\)

Find median for the following data.

If polynomial 6x⁴+8x³+17x²+21x+7 is divided by another polynomial 3x²+4x+1, then what will be the quotient and remainder?

Solve the following pair of linear equations by cross-multiplication method.
(i) ax+by=a², bx-ay=ab
(ii) (a-b)x+(a+b)y=2a²-2b².
ax-by=a²+b²
(iii) \(\frac { x }{ a } +\frac { y }{ b } =a+b,\frac { x }{ { a }^{ 2 } } +\frac { y }{ { b }^{ 2 } } =2\)
(iv) \(ax+by=1,\quad bx+ay=\frac { 2ab }{ { a }^{ 2 }+{ b }^{ 2 } } \)

The difference between the inner and outer surfaces of a cylinder 14 cm long is 88cm² If the volume of the cylinder is 176 cm³, then find its inner and outer radii.

Is product of a rational number and an irrational number, a rational number? Is product of two irrational numbers. rational or irrational number? Justify by giving examples.