If 11th term of A.P. is 110 and 110th term is 11 and its nth term is zero, then find the value of n.

   A pole 10m high cast a shadow 10m long on the ground, then find the sun,s elevation.

If a point P is 17 cm from the centre of a circle of radius 8 cm, then find the length of the tangent drawn to the circle from point P.

The radius of a circle is 50cm.  If the radius is decreased by 50% then find the percentage decrease in its area.

Solve the following equation for x : \({1\over x+1}+{2\over x+2}={5\over x+4}, \ x\ne -1,-2,-4\)

If \(\alpha\) and \(\beta\) are the zeroes of the polynomial 2x² - 4x + 5, find the value of :
(i) \({ \alpha }^{ 2 }+{ \beta }^{ 2 }\)
(ii) \(\frac{1}{\alpha}+\frac{1}{\beta}\)
(iii) \(\left( \alpha -\beta \right) ^{ 2 }\)
(iv) \(\frac { 1 }{ { \alpha }^{ 2 } } +\frac { 1 }{ { \beta }^{ 2 } } \)
(v) \({ \alpha }^{ 3 }+{ \beta }^{ 3 }\)

In the given figure, two circles with centres A and B of radius 5 cm and 3 cm touching each other internally. If the perpendicular bisector of segment AB, meets the bigger circle at P and Q, find the length of PQ.

In the given figure, from each corner of a square ABCD, of side 4 cm, quadrant of a circle of radius 1 cm each is cut and a circle of radius 1 cm is cut from the centre. Find the area of the shaded region.

Two dice are thrown simultaneously. Find the probability that the sum of the two numbers appearing on the top is less than or equal to 10.

Solve for x, y:
(a) \(\frac { x+y-8 }{ 2 } =\frac { x+2y-14 }{ 3 } =\frac { 3x+y-12 }{ 11 } \)
(b) 7(y+3) - 2(x+2) = 14, 4(y-2) + 3(x-3) = 2

Draw a circle of radius 4 cm. Take two points A and B on one of its extended diameter each at a distance of 8 cm from its centre. Draw tangents to the circle from these points A and B.

A bucket made up of a metal sheet is in the form of a frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs. 20 per litre and the cost of the metal sheet used, if it costs Rs. 10 per 100 cm² .  \(\left[ Use\quad \pi =3.14 \right] \)

Which of the following are APs? If they form an AP, then find the common difference d and write three more terms.

\(-\frac { 1 }{ 2 } ,-\frac { 1 }{ 2 } ,-\frac { 1 }{ 2 } -\frac { 1 }{ 2 } ,...\)

If the height and length of the shadow of a man are the same, then find the angle of elevation of the sun. 

AC and BD are two perpendicular diameters of circle ABCD. Given that, the area of the shaded portion is 308 cm², calculate :
(i) the length of AC and
(ii) the circumference of the circle.

An agriculture field is the form of a rectangle of length 20 m, width 14 m. A 10 m deep well of diameter 7 m is dug in a corner of the field and the soil taken out of the well is spread evenly over the remaining part of the field. Find the rise in its level.

PQR is a right angled triangle right angled at Q.PQ=5cm, QR=12cm.A circle with centre O is inscribed in \(\Delta\)PQR, touching its ll sides.Find the radius of the circle.

Polynomial x⁴ + 7x³ + 7x² + px + q is exactly divisible by x² + 7x + 12, then find the value of p and q.