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Chapter No: 1

Real Numbers

5 Marks

Qno1. Show any Positive odd integer is in the form of 6q+1, 6q+3,or 6q+5 where q is some integer ?

Qno2. Given HCF (306,657)=9 find LCM (306,657).

Qno3. Prove that √2 is irrational.

Qno4.  Prove that √5 is irrational.

    Chapter No 2

Polynomials

5 Marks

1. Divide concept

2. Middle term split 

Qno1.  Obtain all other  zeroes of 3x4+ 6x³-2x²-10x-5

Qno2. P(x)=x⁴-3x²+4x+5,  g(x)=x2+1-x

Chapter No 3

Pair of linear equation in two variable

7 Marks 

Qno. Aftab tells his daughter seven years ago i was seven times as old as you were then. Also three years from now i shall be three times as old as yoy will be . Represent this situation algebraically.

Qno2. Ex 3.3 All

Qno3. Five years ago Nuri was thrice as old as sonu. Ten years later. Nuri will be twice as old as sinu. How old are Nuri and sonu.

Qno4. The sum of the digits 9f a two digit number is 9. Also nine times this number is twice the number obtained by reversing the order of the digits. Find the Number. 

Qno5. If we add 1 to the numerator and subtract 1 from the denominator va fraction reduce to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction.

Chapter No 4

Quadratic equation

10 Marks

Qno1. A train travels a distance of 480km At a unifirm speed . If the speed had been 8Km/h less.then it w8uld have taken 3 hours more to cover the same distance. We need to find the speed of train .

Qno2. Rohans mothers age is 26 years older than him . Th3 product of their ages 3 yeqrs from now will be 360. Find the present age of rohan. 

Qno3. Find two consecutive odd positive integer sum of whise square is 290.    { EXAMPLE 11}

Note: Method of Completing the square is Very Important 

Qno4. The diagonals of a rectangular Field is 60 metres  More than the shorter side . if the longer side is 30 metres more than the shorter side find the sides if the field.

Qno5. The difference of squares of a two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Qno6. A train travels 360 Km at a uniform speed. If the speed had been 5 Km/h more,it would have taken 1 hour less for the same journey. Find the speed of the train.

Qno7. Sum of the areas of two squares is 468m. If the difference of their perimeter is 24m find the sides of the two  squares.

Chapter no 5

A.P

7 Marks

Ex :5.2 only 

Chapter no 6

Triangles.

9 Marks

Qno1. BPT Theorem [ Theorem 6.1]

Qno2. Converse Of BPT [ Theorem 6.2]

Qno3. ABCD is a trapezium in which AB parallel to DC and its diagonals interest each other at point O . show that AO/BO=CO/DO.

Qno4. The diagonals of a quadrilateral ABCD intersect each other  at the point O such that AO/BO=CO/DO. Show that ABCD is a trapezium.

Qno5. If AD and PM are medians of a triangle ABC and PQR respectively where Triangle ABC is sililar to Triangle PQR prove that AB/PQ=AD/PM.

Qno6. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.   [ Theorem 6.6]

Qno7. Pythagoras Theorem (6.8)

Qno8. Converse Of Pythagoras Theorem(6.9)

Qno9. BL and CM are medians of Triangle ABC right angled at A. Prove that 4(BL²+ CM²)= 5BC² ( Example 13)

Qno10. ABC is an isosceles Triangle with AC =BC. If AB²= 2AC² Prove that ABC is an right Triangle.

Qno11. D and E are points on side CA and CB respectively of a triangle ABC right angled at C . Prove that AE²+ BD²= AB²+ DE².

 

Qno12. If the Ares of two similar triangles are equal prove that they are congruent.

Qno13. Ex 6.3 Qno 7

Chapter No 7

Coordinate Geometry

8 Marks

Qno1. Qno 1   EX 7.1 ( 2 Marks)

Qno2. Find the relation between x and y such that the point (x,y)is equidistant from the point (3,6) and(-3,4).

Qno3. Find the coordinates Of the point of trisection of the line segment joining (4,-1) and (-2,-3)

Qno4. Find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided by the x-axis. Also find the coordinates of the point of division.

Qno5. If  (1,2) , (4,y) ,(x,6), and (3,5) are the vertices of a parallelogram taken in order find x and y.

Qno6. Find the area  of rhombus if its vertices are (3,0),(4,5),(-1,4)and (-2,-1) Taken in order.

Qno7. Qno 1. Ex 7.3

Qno8. Find the area of quadrilateral whose vertices taken in order are (-4,-2),(-3,-5),(3,-2) and (2,3).

Chapter No 8

Introduction to Trigonometry

7 Marks

Qno1. Ex 8.1.     Qno 7, 8,5

Qno2. If sin 3A= cos(A-26°)where 3A is an acuta angle find the value of A [Example 10 ]

Qno3. Ex 8.4.  Qno 5.  All parts are very Important.....

Chapter No 9

Some Applications Of Trigonometry

7 Marks

Qno1. Example 6   (V.V Important)

Qno2. Example 7

Qno3. A tree breaks due to a strome and the broken parts fall so that the top touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

Qno4. A kite is flying at a height of 60m above the ground. The string attached to the kite is temporary tied to a point on the ground. The inclination of the string with the ground is 60°. Find the height of the string, assuming there is no slack in the string.

Qno5. From a point on a ground the angle of elevation of the bottom and a top of a transmission tower fixed at a top of a 20m Hugh building are 45° and 60° respectively. Find the height of the tower.

Qno6. A statue 1.6m tall stand on the top of a pedestal From the point on the ground the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45° Find the height of the pedestal.

Qno7. The angle of elevation of the top of the building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60° . if the tower is 50m high find the height of the building.

Qno8. From the top of a 7m high building the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45° . determine the height of tower.

Chapter No 10

Circles

6 Marks

Qno1. Theorem 10.1

Qno2. Theorem 10.2. (V.V important)

Qno3. Prove that parallelogram circumscribing a circle is a rhombus

Qno4. Prove that tangents drawn at the ends if diameter of a circle are parallel.

Qno5. Two concentric circles are of radii 5cm and 3cm. Find the length of the chord of the larger circle which touchés the smaller circle.

Qno6. If TP and TQ are two tangents to a circle with centre O so that angle POQ=110° then angle PTQ is equal to 

Chapter No 11

Construction

7 Marks

Qno1. Ex 11.1.  Qno 2,3,4,6 are important

Qno2. Ex 11.2. Qno 1,2,4 are Important

Chapter No 12

Area related to circles

4 Marks

Qno1. Ex 12.2 Qno 1,2,3,4 are important

Chapter No 13

Surface area and volume

7 Marks

Qno1. Ex 13.1 Qno 2,3,4 are important

Qno2. Ex 13.3 Qno 3,4,6 are important

Qno3. Ex 13.4 Qno 2,3 are important

Chapter No 14 

Statistics

7 Marks

Qno1. Ex 14.1 only

Chapter No 15 

Probability

4 Marks

Qno1. Example 4 is important

Qno2. Ex 15.1 Qno 8,9,13,14,15,18 are important

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