Find the value of k, for which the quadratic equation \(4x^{2}+4\sqrt{3x} \ + \ k = 0\)  has equal roots.

Find the 25th term of an A.P.  -5, \(\frac{-5}{2}\), 0,\(\frac{5}{2}\),.........

In the figure, AB, AC and AD are tangents. If AB - 5 cm, find AD.

The probability of guessing the correct answer to a certain test is p/12. If the probability of not guessing the correct answer to this question is 3/4, then find the value of p?

The coordinates of one end point of a diameter of a circle are (4,-1) and the coordinates of the centre are (1,-3).
(i) Find the coordinates of the other end of the diameter.
(ii) Find the diameter of the circle.
(iii) Calculate the area of circle,

For what value of p, are 2p - 1, 7 and 3p three consecutive terms of an A.P.?

Construct a triangle ABC in which BC = 8 cm, angle B = 45^o and angle C = 30^o. Construct another triangle similar to triangle ABC such that its sides are \(\frac { 3 }{ 4 } \) of the corresponding sides of triangle ABC.

Draw tangents to a circle of radius 6 cm from a point P at a distance of 10 cm from its centre.

From a parachute vertically above a straight road, the angles of depression of two accidental vehicles, at an instant is found to be 45⁰ and 60⁰.If the vehicles are 100m apart, find the height of the parachute.
Which precautions one should take to avoid accidents on roads?

Find the ratio in which the line segment joining (2,-3) and (5,6) is divided by x-axis.

A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm² . [take, \(\sqrt3\) = 1.732]
 

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

For a quadratic polynomial, whose one zero is 8 and the product of zeroes is -56.

If \(\sin { { \theta }_{ 1 } } +\sin { { \theta }_{ 2 } } +\sin { { \theta }_{ 3 } } =3,\)\({ 0 }^{ 0 }<{ \theta }_{ 1 },{ \theta }_{ 2 },{ \theta }_{ 3 }\le { 90 }^{ 0 },\) find the value of  \(\cos { { \theta }_{ 1 } } +\cos { { \theta }_{ 2 } } +\cos { { \theta }_{ 3 } } .\)

An aeroplane is at an altitude of 1200 m. Find that two ships are sailing towards it in the same direction. The angles of depression of the ships as observed from the aeroplane are \(60°\) and \(30°\) , respectively. Find the distance between both ships.

Three coins are tossed simultaneously.Find the probability of getting:
(a)Three heads
(b)Exactly 2 heads
(c)At least 2 heads

If R(x,y) is a point on the line segment joining the points P(a,b) and Q(b,a) then prove that x+y=a+b

In fig., OABC is a square of side 7cm,.If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region.

Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class

Form the frequency distribution table for the above data. 

The sum of the first term and the fifth term of an ascending AP is 26 and the product of the second term by the fourth term is 160. Find the sum of the first seven terms of this AP.

A village Panchayat constructed a circular tank to serve as a bird bath. A fencing was made in the shape of a quadrilateral. Sides of the quadrilateral touched the circle as shown in the figure. If AB = 5 m, CD = 6 m and BC = 7 m, then
(a) findAD.
(b) what values does village Panchayat depict through this action?

Draw a line segment PQ of length 9cm. Taking P as centre, draw a circle of radius 4.5cm and taking Q as centre, draw circle of radius 3cm.  Construct tangents to each circle from the centre of the other circle.

In the given figure, ABC is a right angled triangle, right angled at C and \(DE \bot AB\) .
(i) Prove that \(\triangle ABC\sim \triangle ADE\) 
(ii) Find the lengths of AE and DE.
(iii) Find the area of ΔABC.

The time taken by a person to cover 150km was \(2{1\over2}\)jhrs. more than the time taken in the return journey. If he returned at a speed of 10km/h more than the speed of going, what was the speed per hour in each direction?

The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are 60^o and 30^o respectively. Find the height of the tower.

The inside perimeter of a running track is 400 m as shown in the figure. The length of each of the straight portion is 90 m and the ends are semicircles. If the track is everywhere 1.4 m wide, find the area of the track. Also, find the length of the outer running track.

If cot \(\theta \) =\(\frac { 7 }{ 8 } \) , evaluate   \(\frac { (1+sin\theta )(1-sin\theta ) }{ (1+cos\theta )((1-cos\theta ) } \) 

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Find the zeroes of the following quadratic polynomials and verify the relationship betwee the zeros and its coefficients.
(i) x²-2x-8
(ii) 4s²-4s+1
(iii) 6x²-3-7x
(iv) 4u²+8u
(v) t²-15
(vi) 3x²-x-4

In a painting competition of a school a child made Indian national flag whose perimeter was 50 cm. Its area will be decreased by 6 square cm, if length is decreased by 3 cm and breadth is increased by 2 cm then find the dimension of flag.What does the Saffron colour in flag signify?

A milk tanker cylindrical in shape having diameter 2 m and length 4·2 m supplies milk to the two booths in the ratio 3 : 2. One of the milk booths has cuboidal vessel having base area 3·96 sq. m. and the other has a cylindrical vessel
having radius 1 m. Find the level of milk in each of the vessels.\(\left[ Use\quad \pi =\frac { 22 }{ 7 } \right] \)

Express number as a product of its prime factor 140