1)Find a quadratic polynomial whose one zero is 2 and product of zeroes is 12. (ans. x^2-8x+12)
2)Find a quadratic polynomial whose one zero is 6 and sum of zeroes is -11. (ans. x^2+11x-102)
3) If A,B are the zeroes of the polynomial 2x^2+5x-6.Then find the value of A+B+AB (ans. -11/2)
4)If A,B are the zeroes of the polynomial 5x^2-3x-1. Then find the value of 1/A+1/B+2 (ans. -1)
5)Find a cubic polynomial whose zeroes are 0 , 2/3 , -2/3. (ans.9x^3-4x)
6) Find a cubic polynomial whose zeroes are 2 , -3 and 5. (ans. X^3-4x^2-11x+30)
7)Divide 3x^2-x ^3-3x+5 by x-1-x^2 and verify the division algorithm.
8)Find all the zeroes of polynomials x^4+x^3-9x^2-3x+18 , if it is given that two of its zeroes are – √ 3 and √ 3. (ans. – √ 3 ,√ 3 , -3 , -2 )
9)If the zeroes of the polynomial x^3- 3x^2+ x+ 1 are a-b , a+b , find a and b. (ans a=1 , b=+- √ 2 )
10)On dividing 6x^3+8x^2-3x+8 by a polynomial g(x) the quotient and remainder were 3x+4 and 6x+20 respectively , find g(x). ( ans. 2x^2 -3x-3)

POSTED BY:
PARAS JAIN

Areas Related to Circles

1. Find the perimeter of a semicircle having a radius of 14cm.

2. Find the area of a ring shaped region enclosed between two concentric circles of radii 20 cm and 15cm.

3. If the diameter of the semi-circular protractor is 14cm. Find its perimeter.

4. Find the perimeter of a quadrant of a circle whose diameter is 7cm.

5. The circumference of a circle is 176cm. Find its diameter.

6. The length of a wire which is tied as a boundary of Semi-circular Park is 72cm. Find the radius of the semi- circular park and its area.

7. Prove that the area of a circular path of uniform width b, surrounding a circular region of radius r is πb(2r+b).

8. A wire is in the form of a circle of radius 35cm. Find the side of the square into which it can be bent.

9. A bicycle wheel makes 5000 revolutions in moving 11km. Find the diameter of the wheel.(Take π = 22/7)

10. If the area of the semi-circular region is 77cm^2, find its perimeter.

11. The short and long hand of a clock are 4cm and 6cm long respectively. Find the sum of the distances travelled by their tips in two days.

12. The perimeter of a sector of a circle of radius 5.2cm is 16.4cm. Find the area of the sector.

13. Four horses are tethered at four corners of a square field of side 50cm, so that they just can reach one another. What is the area of the field will be ungrazed.

14. Four equal circles each of radius 5cm touch each other. Find the area between them.

ASSIGNMENT –HEIGHT AND DISTANCE

1. An electric pole is ten metres high . If its shadow is 10square root3 m in length , find the elevation of the sun.[ Ans 30 degree]
2. The angle of elevation of the top of a tower , from a point on the ground and at a distance of 150m from its foot, is 30 degree . find the height of the tower correct to one decimal place .[ Ans 86.6m]
3.From a point P on the level ground, the angle of the elevation of the top of the tower is30 degree if the tower is high, how far is P from the foot of tower?[ans 173.2m]
4.A kite is flying at a height of 75 metres from the level of ground, attached to a string inclined of 60 degree to the horizontal. Find a length of the string to the nearest metre.[ans 86.6m]
5.if the length of the shadow cast by a pole be square root 3 times the length of the pole , find the angle of elevation of the sun[ans 30 degree].
6.Averticle tower is 20m high . A man at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 2/3 . How far is he standing from the foot of the tower?[ans 17.92m]
7.The angle of elevation of a jet plane from appoint A on the ground is 60 degree . After a flight of 15 seconds , the angle of elevation changes to 30 degree . If the jet plane flying at a constant height of 1500square root 3 m ,find the speed of the jet plane .
[ans720 km/hr]
8 Determine the height of a mountain if the elevation of its top at an unknown distance from the base is 45 degree and at a distance 10 km further off from the mountain, along the same line, the angle of elevation is 30 degree. [Use tan 30 degree = 0.5774]{ans 13.66km}
9. The angle of elevation of the top of a rock from the top and the foot of a 100 m high tower are 30 degree and 45 degree respectively. Find the height of the rock[ans236.6m].
10. A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45 degree and the angle depression of the base is 30 degree. Calculate the distance of a cliff from the ship and the height of the cliff.[ans 27.712m,43.712m]
11. From the top a cliff 50 m high, the angle of depression of the top and the bottom of a tower are observed to be 30 degree and 45 degree respectively. Find the height of the tower.[ans 21.13m]
12. An aeroplane,when 3000 m high, passes vertically above another aeroplane at an instant when the angle of elevation of the two aeroplanes from the same point on the ground are 60 degree and 45 degree respectively. Find the vertical distance between the
aeroplanes at the instant [ans 1268m].
13. The angle of elevation of the top of a hill at the foot of a tower is 60 degree and the angle of elevation of the top of the tower from the foot of the hill is 30 degree. If the tower is 50 m high, what is the height of the hill.[ans 150m]
14. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60 degree and the of depression of the point A from the top of the tower is 45 degree. Find the height of the tower.[ans 6.83m]
15. As observed from the top of a 150 m tall lighthouse, the angle of two ships approaching it are 30 degree and 45 degree. If one ship is directly behind the other, find the distance between the two ships.[ans 109.8m]
16. A tower is 50 m high. Its shadow is x m shorter when the sun’s attitude is 45 degree than when it is 30 degree. Find x correct to the nearest cm .[ans3660cm]
17. A 7 metres long flagstaff is fixed on the top of a tower on the horizontal plane. From a point of on the ground, the angles of elevation of the top and bottom of the flagstaff are 60 degree and 45 degree respectively. Find the height of the tower correct to the one place of decimal.[ans 9.56m]
18. From the top of a building 100m high, the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree. Find the height of the tower and its distance on the ground from the building.[ans 273.2m,100m]
19. A tree is broken by wind. The top stuck the ground at an angle of 30 degree and at a distance of 30 metres from the root. Find the whole height of the tree.[ans 51.96m]
20. The angle of elevation of a cloud from a point 60 m above the lake is 30 degree and the angle of depression of the reflection of the cloud in the lake is 60 degree. Find the height of the cloud.[ans 200m]
BY ANJALI

QUADRATIC EQUATION

1) For each of the following, determine whether the given equations have root(s). If so find the root(s)
i) √7y^2 – 6y -13√7=0
ii) (x+4) (x+5) = 3(x+1) (x+2) + 2x
iii) 1/x+1 + 2/x+2 = 4/x+4

2) In each of the following, determine value(s) for which the given equation has real roots:-
i) 5px^2 - 8x +1 =0
ii) 4x^^2 + 8x – p =0
iii) 4x2 – 3px + 9=0

3) Solve
i) abx^2 + (b^2-ac)x –bc =0
ii) x-1/x-2 + x-3/x-4 = 10/3
iii) x+1/x-1 + x-2/x+2 = 3

4) Divide 12 into 2 parts such that their product is 32.
[ans. 4 or 8]
5) Divide 12 into 2 parts such that the sum of their square is 74.
[ans. 5 or 7]
6) The sum of a no. and its reciprocal is 10/3. Find the no.
[ans. 3 or 1/3]
7) The denominator of a fraction is one more than twice the numerator. If the
sum of the fraction and its reciprocal is 58/21. Find the fraction.
[ans. 3/7]
8) The product of Ramu’s age 5 yrs ago and his age 9 yrs later is 15. Determine
Ramu’s age.
[ans. 6 yrs]
9) There are 3 consecutive +ve integers such that the sum of the square of the first
and the product of the other 3 is 154. What are the integers?
[ans. 20, 21, 22]
10) The sum of the ages of a father and hid son is 45 yrs. 5
yrs ago, the product of their ages was 124. Determine
their present ages.
[ans. 18 yrs and 27 yrs]
11) A passenger train takes 2 hrs less for a journey of 300 km, if its speed is increased
by 5 km/hr from the usual speed. Find its usual speed.
[ans. 25 km/hr]
12) Vikram wishes to fit 3 rods together in the shape of a right triangle. The
hypotenuse is to be 2 cm longer than the base and 4 cm longer than the altitude.
What should be the lengths of the rods.
[ans. 10 cm, 8 cm, 6 cm]
13) A motor boat, whose speed is 15 km/hr in still water, goes 30 km downstream and
comes back in a total time of 4 hrs 30 mins. Find the speed of the stream.
[ans. 5 km/hr]
14) A journey of 192 km from Mumbai to pune takes 2 hr less by a super fast train
than by an ordinary train. If the average speed of the slower train is 16 km/hr less
than that of the faster train. Determine their average speeds.
[ans. 32 km/hr and 48 km/hr]
15) A farmer wishes to grow a 100sq. m rectangular vegetable garden. Since he has
with him only 30 m barbed wire, he fences 3 sides of his garden letting compound
wall of his house act as a fourth side fence. Find the dimensions of his garden.
[ans. 10 x 10 or 5 x 20]
16) The sum S of n successive odd natural nos. starting from 3 is given by the
relation S=n (n+2). Determine n, if the sum is 168.
[ans. 12]
17) Some students arranged a picnic. The budget for food was Rs.240. Because 4
students of the group failed to go, the cost of food to each student got increased by
Rs.5. How many students went for the picnic?
[ans. 12]
18) If a student had walked 1km/hr faster, he would have taken 15 mins less to walk 3
km. Find the rate at which he was walking.
[ans. 3 km/hr]
19) Sum of the area of 2 squares is 468 sq.m. If the difference of their perimeter is
24m, find the sides of the 2 squares.
[ans. 18 m and 12 m]
20) A fast train takes 3 hrs less than a slow train for a journey of 600 km. If the speed
of the slow train is 10 km/hr less than that of the fast train, find the speed of the 2
train.
[ans. 40 km/hr and 50 km/hr]

Made by:
Nitika Rattan

1)2[cos^2 20+cos^2 70/sin^2 25+sin^2 65]-tan 45+[tan13 tan23 tan30 tan67 tan77]
[ans. [3+sq.rt.3] / 3
2) sinA cosA - (sinA cos{90-A}cosA/sec{90-A})–(cosA sin{90-A}sinA/cosec{90-A})
[ans.0]
3)[–tanA cot{90-A}+secA cosec{90-A}+sin235+sin255] /[tan10 tan20 tan45 tan70 tan80] {ans.0}

PROVE
4) [1+tan^2 A] sinA cosA = tanA
5) sin^2 A cot^2 A + cos^2 A tan^2 A = 1
6) Find A if 07) sec^4 A-sec^2 A = tan^2 A + tan^4 A
8) [tan A + tan B]/[cot A + cot B ] = tanA tanB
9) [cosec A - sin A] [sec A - cos A] [tan A + cot A]=1
10) {[1+sinA]^2+[1-sinA]^2} / 2cos^2 A = [1+sin^2 A] /[1-sin^2 A]
11) 1/[sec A – tan A]= sec A+ tan A
12) Find A if 0 sin A / (1-cosA) + sinA / (1+cosA) = 4
13) Prove that sinA sin(90-A) – cosA cos(90-A) = 0
14) cos A/(1-sin A) + (1-sin A)/cos A = 2sec A
15) (1+ tan^2 A) (1+ cot^2 A)=1/(sin^2 A – sin^4 A)
16) (tan A + sec A -1)/(tan A - sec A+1) = (1 + sin A )/cosA
17) (sin A-sec A)^2 + (cos A-cosec A)^2 = (1- sec A cosec A)^2
18) 1/[sec A + tan A]-1/cos A = 1/cos A-1/[sec A- tan A]
19) [cot^2 A cosec^2 B]-[cot^2 B cosec^2 A] = cot^2 A-cot^2 B
20) For A=30, show that
Cos3A=4cos3A-3cosA

POSTED BY
NISHANT

1 Comment

1)Which term of an A.P. 36 , 34, 32………… is zero. (ans. 19th)
2)Find the values of middle terms of the A.P. 2,9,16…………205 (ans. 100 & 107)
3)Which term of A.P. 21,62/3,61/3……….. is the first negative term (ans. 65th term)
4)The sum of three terms of A.P. is 21 and the product of first and third term exceeds the second term by 6. Find the numbers. (ans. 1,7,13)
5)For what value of n, the nth term of the series 2,7,12……… and 74,71,68……are equal. ( ans. 10)
6)Find the three terms in A.P. such that their sum is 6 and product is -24, find the numbers. (ans. -2,2,6 or 6,2,-2)
7)A sum of Rs. 1000 invested at 8% interest per year. If interest is calculated at the end of each year, then find interest at the end of 30 years. (ans. 2400)
8)Which term of A.P. 3,6,9…….. is 21 less than 30th. (ans.23)
9)If in an A.P. mth term is 1/n & nth term is 1/m, find (mn)th term. (ans. 1)
10)If p times the pth term is equal to q times the qth term of an A.P. Show that the (p+q)th term is zero.

Posted By:
PARAS JAIN