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CBSE Academic releases study material for open text based assessment (OTBA)

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CBSE has released the material for its mandatory Open text exam which is part of the Summative Assessment II of Std IX, and annual examination of Std XI . The open text based assessment (OTBA) is part of the overall assessment for which the material is provided directly by the board, a couple of months after the session starts. Students are required to study the material in detail and later answer questions which are based on 'higher order thinking skills (HOTS)'. 

NCERT Mathematics Question Paper (Class - 9)

 

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(Mathematics) Chapter 3 Coordinate Geometry

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EXERCISE 3.1 

Question 1. How will you describe the position of a table lamp on your study table to another person?

Question 2. (Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

(i) The perpendicular distance of the point P from the y - axis measured along the positive direction of the x - axis is PN = OM = 4 units.
(ii) The perpendicular distance of the point P from the x - axis measured along the positive direction of the y - axis is PM = ON = 3 units.
(iii) The perpendicular distance of the point Q from the y - axis measured along the negative direction of the x - axis is OR = SQ = 6 units.
(iv) The perpendicular distance of the point Q from the x - axis measured along the negative direction of the y - axis is OS = RQ = 2 units. Now, using these distances, how can we describe the points so that there is no confusion? We write the coordinates of a point, using the following conventions:

(i) The x - coordinate of a point is its perpendicular distance from the y - axis measured along the x -axis (positive along the positive direction of the x - axis and negative along the negative direction of the x - axis). For the point P, it is + 4 and for Q, it is – 6. The x - coordinate is also called the abscissa.
(ii) The y - coordinate of a point is its perpendicular distance from the x - axis measured along the y - axis (positive along the positive direction of the y - axis and negative along the negative direction of the y - axis). For the point P, it is + 3 and for Q, it is –2. The y - coordinate is also called the ordinate.
(iii) In stating the coordinates of a point in the coordinate plane, the x - coordinate comes first, and then the y - coordinate. We place the coordinates in brackets. Hence, the coordinates of P are (4, 3) and the coordinates of Q are (– 6, – 2). Note that the coordinates describe a point in the plane uniquely. (3, 4) is not the same as (4, 3).

EXERCISE 3.2

Question 1.Write the answer of each of the following questions:

(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.

Questions 2. See Fig.3.14, and write the following:

(i) The coordinates of B.
(ii) The coordinates of C.
(iii) The point identified by the coordinates (–3, –5).
(iv) The point identified by the coordinates (2, – 4).
(v) The abscissa of the point D.
(vi) The ordinate of the point H.
(vii) The coordinates of the point L.
(viii) The coordinates of the point M.

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(Mathematics) Chapter 4 Linear Equations in Two Variables

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EXERCISE 4.1

Question 1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs x and that of a pen to be Rs y).

Question 2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

(i) 2x + 3y = 9.35
(ii) x – 5 y – 10 = 0
(iii) –2x + 3y = 6
(iv) x = 3y
(v) 2x = –5y (
vi) 3x + 2 = 0
(vii) y – 2 = 0
(viii) 5 = 2x

EXERCISE 4.2

Question 1.Which one of the following options is true, and why? y = 3x + 5 has

(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions

Question 2. Write four solutions for each of the following equations:

(i) 2x + y = 7
(ii) πx + y = 9
(iii) x = 4y

Question 3. Check which of the following are solutions of the equation x – 2y = 4 and which are not:

(i) (0, 2)
(ii) (2, 0)
(iii) (4, 0)
(iv) ( 2 , 4 2)
(v) (1, 1)

Question 4. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.

EXERCISE 4.3

Question 1. Draw the graph of eachof the following linear equations in two variables:

(i) x + y = 4
(ii) x – y = 2
(iii) y = 3x
(iv) 3 = 2x + y

Question 2. Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

Question 3. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.


Question 4. The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.

Question 5. From the choices given below, choose the equation whose graphs are given in Fig. 4.6 and Fig. 4.7. For Fig. 4. 6 For Fig. 4.7

(i) y = x
(i) y = x + 2
(ii) x + y = 0
(ii) y = x – 2
(iii) y = 2x
(iii) y = –x + 2
(iv) 2 + 3y = 7x
(iv) x + 2y = 6

Question 6. If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is (i) 2 units (ii) 0 unit

Question 7. Yamini and Fatima, two students of Class IX of a school, together contributed Rs 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs x and Rs y.) Draw the graph of the same.

Question 8. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: F = 9 C + 32 5

(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.
(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?
(iii) If the temperature is 95°F, what is the temperature in Celsius?
(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?
(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

EXERCISE 4.4

Question 1. Give the geometric representations of y = 3 as an equation

(i) in one variable
(ii) in two variables

Question 2. Give the geometric representations of 2x + 9 = 0 as an equation

(i) in one variable
(ii) in two variables

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(Mathematics) Chapter 7 Triangles

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EXERCISE 7.1

Question 1. In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see Fig. 7.16). Show that Δ ABC Δ ABD. What can you say about BC and BD?

Question 2 . ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that

(i) Δ ABD Δ BAC
(ii) BD = AC
(iii) ∠ ABD = ∠ BAC.

Question 3. AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

Question 4. l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that Δ ABC Δ CDA.

Question 5. line l is the bisector of an angle ∠ A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A (see Fig. 7.20). Show that:

(i) Δ APB Δ AQB
(ii) BP = BQ or B is equidistant from the arms of ∠ A.

Question 6. In Fig. 7.21, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Show that BC = DE.

Question 7 . AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see Fig. 7.22). Show that

(i) Δ DAP Δ EBP
(ii) AD = BE

Question 8. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see Fig. 7.23). Show that:

(i) Δ AMC Δ BMD
(ii) ∠ DBC is a right angle.
(iii) Δ DBC Δ ACB
(iv) CM = 1 2 AB

EXERCISE 7.2

Question 1. In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that :

(i) OB = OC
(ii) AO bisects ∠ A

Question 2. In Δ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that Δ ABC is an isosceles triangle in which AB = AC.

Question 3. ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.

Question 4. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that

(i) Δ ABE Δ ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.

Question 5. ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ ABD = ∠ ACD.

Question 6. ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠ BCD is a right angle. 7. ABC is a right angled triangle in which ∠ A = 90° and AB = AC. Find ∠ B and ∠ C.

Question 7. Show that the angles of an equilateral triangle are 60°each.

EXERCISE 7.3

Question 1. Δ ABC and Δ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that

(i) Δ ABD Δ ACD
(ii) Δ ABP Δ ACP
(iii) AP bisects ∠ A as well as ∠ D.
(iv) AP is the perpendicular bisector of BC.

Question 2. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that

(i) AD bisects BC
(ii) AD bisects ∠ A.

Question 3. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of Δ PQR (see Fig. 7.40). Show that:

(i) Δ ABM Δ PQN
(ii) Δ ABC Δ PQR

Question 4. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Question 5. ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠ B = ∠ C.

EXERCISE 7.4

Question 1. Show that in a right angled triangle, the hypotenuse is the longest side.

Question 2. In Fig. 7.48, sides AB and AC of Δ ABC are extended to points P and Q respectively. Also, ∠ PBC < ∠ QCB. Show that AC > AB. 3. In Fig. 7.49, ∠ B < ∠ A and ∠ C < ∠ D. Show that AD < BC.

Question 3. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Fig. 7.50). Show that ∠ A > ∠ C and ∠ B > ∠ D.

Question 4. In Fig 7.51, PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.

Question 5. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

EXERCISE 7.5

Question 1 . ABC is a triangle. Locate a point in the interior of Δ ABC which is equidistant from all the vertices of Δ ABC.

Question 2. In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Question 3. In a huge park, people are concentrated at three points (see Fig. 7.52):

A : where there are different slides and swings for children,
B : near which a man-made lake is situated,
C : which is near to a large parking and exit. Where should an icecream parlour be set up so that maximum number of persons can approach it? (Hint : The parlour should be equidistant from A, B and C)

Question 4. Complete the hexagonal and star shaped Rangolies [see Fig. 7.53(i) and (ii)] by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

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(Mathematics) Chapter 8 Quadrilaterals

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EXERCISE 8.1

Question 1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

Question 2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Question 3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Question 4. Show that the diagonals of a square are equal and bisect each other at right angles.

Question 5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Question 6. Diagonal AC of a parallelogram ABCD bisects ∠ A (see Fig. 8.19). Show that

(i) it bisects ∠ C also
(ii) ABCD is a rhombus.

Question 7. ABCD is a rhombus. Show that diagonal AC bisects ∠ A as well as ∠ C and diagonal BD bisects ∠ B as well as ∠ D.

Question 8. ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that:

(i) ABCD is a square
(ii) diagonal BD bisects ∠ B as well as ∠ D.

Question 9. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that:

(i) Δ APD Δ CQB
(ii) AP = CQ
(iii) Δ AQB Δ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram

Question 10. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that :

(i) Δ APB Δ CQD
(ii) AP = CQ

Question 11. In Δ ABC and Δ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that :

(i) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) Δ ABC Δ DEF.

Question 12. ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that:

(i) ∠ A = ∠ B
(ii) ∠ C = ∠ D
(iii) Δ ABC Δ BAD
(iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

EXERCISE 8.2

Question 1. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that :

(i) SR || AC and SR = 1 2 AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.

Question 2. ABCD is a rhombus and P, Q, R and S are ©wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Question 3. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Question 4. ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.

Question 5. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD.

Question 6. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Question 7. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that:

(i) D is the mid-point of AC
(ii) MD ⊥ AC
(iii) CM = MA = 1 2 AB

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(Mathematics) Chapter 9 Areas of Parallelograms and Triangles

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EXERCISE 9.1

Question1. Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels. 

EXERCISE 9.2

Question 1. In Fig. 9.15, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Question 2. If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) = 1 ar (ABCD) 2 .

Question 3. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).

Question 4. In Fig. 9.16, P is a point in the interior of a parallelogram ABCD. Show that:

(i) ar (APB) + ar (PCD) = 1 ar (ABCD) 2
(ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD) [Hint : Through P, draw a line parallel to AB.]

Question 5. . In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that

(i) ar (PQRS) = ar (ABRS)
(ii) ar (AX S) = 1 ar (PQRS)

Question 6. A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?

EXERCISE 9.3

Question 1. In Fig.9.23, E is any point on median AD of a Δ ABC. Show that ar (ABE) = ar (ACE).

Question 2. In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = 1 ar(ABC) 4 .

Question 2. Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Question 4. In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that ar(ABC) = ar (ABD).

Question 5. D, E and F are respectively the mid-points of the sides BC, CA and AB of a Δ ABC. Show that

(i) BDEF is a parallelogram.
(ii) ar (DEF) = 1 4 ar (ABC)
(iii) ar (BDEF) = 1 2 ar (ABC)

Question 6. In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:

(i) ar (DOC) = ar (AOB)
(ii) ar (DCB) = ar (ACB)
(iii) DA || CB or ABCD is a parallelogram. [Hint : From D and B, draw perpendiculars to AC.]

Question 7. D and E are points on sides AB and AC respectively of Δ ABC such that ar (DBC) = ar (EBC). Prove that DE || BC.

Question 8. XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively, show that ar (ABE) = ar (ACF)

Question 9. The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see Fig. 9.26). Show that ar (ABCD) = ar (PBQR). [Hint : Join AC and PQ. Now compare ar (ACQ) and ar (APQ).]

Question 10. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

Question 11. In Fig. 9.27, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that

(i) ar (ACB) = ar (ACF)
(ii) ar (AEDF) = ar (ABCDE)

Question 12. A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Question 13. ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY). [Hint : Join CX.]

Question 14. In Fig.9.28, AP || BQ || CR. Prove that ar (AQC) = ar (PBR).

Question 15. . Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

Question 16. In Fig.9.29, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

EXERCISE 9.4

Question 1. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

Question 2. In Fig. 9.30, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC). Can you now answer the question that you have left in the ‘Introduction’ of this chapter, whether the field of Budhia has been actually divided into three parts of equal area? triangles ABD, ADE and AEC of equal areas. In the same way, by dividing BC into n equal parts and joining the points of division so obtained to the opposite vertex of BC, you can divide ΔABC into n triangles of equal areas.]

Question 3. In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

Question 4. In Fig. 9.32, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, show that ar (BPC) = ar (DPQ). [Hint : Join AC.]

Question 5. In Fig.9.33, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:

(i) ar (BDE) = 1 4 ar (ABC)
(ii) ar (BDE) = 1 2 ar (BAE)
(iii) ar (ABC) = 2 ar (BEC)
(iv) ar (BFE) = ar (AFD)
(v) ar (BFE) = 2 ar (FED)
(vi) ar (FED) = 1 8 ar (AFC) [Hint : Join EC and AD. Show that BE || AC and DE || AB, etc.]

Question 6. Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar (APB) × ar (CPD) = ar (APD) × ar (BPC). [Hint : From A and C, draw perpendiculars to BD.]

Question 7. P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that :

(i) ar (PRQ) = 1 2 ar (ARC)
(ii) ar (RQC) = 3 8 ar (ABC)
(iii) ar (PBQ) = ar (ARC)

Question 8. In Fig. 9.34, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX ⊥ DE meets BC at Y. Show that:

(i) Δ MBC Δ ABD
(ii) ar (BYXD) = 2 ar (MBC)
(iii) ar (BYXD) = ar (ABMN)
(iv) Δ FCB Δ ACE
(v) ar (CYXE) = 2 ar (FCB)
(vi) ar (CYXE) = ar (ACFG)
(vii) ar (BCED) = ar (ABMN) + ar (ACFG) Note : Result
(vii) is the famous Theorem of Pythagoras. You shall learn a simpler proof of this theorem in Class X.

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(Mathematics) Chapter 10 Circles

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EXERCISE 10.1

Question 1. Fill in the blanks:

(i) The centre of a circle lies in of the circle. (exterior/ interior)
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in of the circle. (exterior/ interior)
(iii) The longest chord of a circle is a of the circle.
(iv) An arc is a when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and of the circle.
(vi) A circle divides the plane, on which it lies, in parts.

Question 2. Write True or False: Give reasons for your answers.

(i) Line segment joining the centre to any point on the circle is a radius of the circle.
(ii) A circle has only finite number of equal chords.
(iii) If a circle is divided into three equal arcs, each is a major arc.
(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.

EXERCISE 10.2

Question 1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Question 2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

EXERCISE 10.3

Question 1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Question 2. Suppose you are given a circle. Give a construction to find its centre.

Question 3. If two circles intersect at two points, prove that their centres lie on the perpendicular

EXERCISE 10.4

Question 1. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Question 2. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Question 3. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Question 4. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).

Question 5. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

Question 6. A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

EXERCISE 10.5

Question 1. In Fig. 10.36, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC

Question 2. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Question 3. In Fig. 10.37, ∠ PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠ OPR.

Question 4. In Fig. 10.38, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

Question 5. In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.

Question 6. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC is 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD.

Question 7. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Question 8. If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Question 9. Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 10.40). Prove that ∠ ACP = ∠ QCD.

Question 10. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Question 11. ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠ CAD = ∠ CBD.

Question 12. Prove that a cyclic parallelogram is a rectangle.

EXERCISE 10.6

Question 1. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Question 2. Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

Question 3. The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Question 4. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

Question 5. Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

Question 6. ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.

Question 7. AC and BD are chords of a circle which bisect each other. Prove that :

(Download) NIOS Practical Exam Papers Of Mass Communication Senior Secondary

 

(Download) NIOS Practical Papers Of Mass Communication Senior Secondary

PRACTICAL 1

Objective:

To understand the concept of a message in communication and to learn how to construct/ write a clear message.

Introduction:

You have learnt to define communication in lesson no. 1. You may recall the example of an SMS where you learnt the importance of clarity of a message so that a receiver understands what exactly the message means. In this exercise, you will send a message or an SMS from your mobile phone to your friend’s mobile phone for taking a specific action of receiving you at the railway station.

Procedure :

1. Prepare a short and concise message giving the following details :

(a) Give the train name and number, the day and time of arrival in the station where your friend should receive you.
(b) Give the name of the railway station as there can be more than one railway station in a city.

2. Send the message to your friend’s mobile number.

Conclusion:

1. On the basis of this exercise, can you now give a simple definition of communication?
2. What are the two conditions for communication to take place ?PRACTICAL 2

Objective :

To understand how non verbal communication is used in different situations using gestures and facial expressions.

Introduction :

You have learnt in lesson 1 about the importance of non verbal communication and that almost 80% of all communication is non verbal. In this exercise you will go through newspapers and magazines and identify photographs which show different non verbal communication situations without captions.

Procedure:

1. Select a few newspapers and magazines.
2. Identify 6 photographs which depict various non verbal communication situations.
3. Cut them out and paste them on plain paper
4. Mention clearly what it means clearly below each photograph.

Conclusion:

When you look at the six photographs what can you make out? You would have understood how people communicate non verbally.

1. Identify the photographs where hand movements are used.
2. Identify those where facial expressions are used.
3. Identify the photographs where gestures are used.PRACTICAL 3

Objective

(Download) NIOS Practical Papers Of Mass Communication Senior (Hindi Medium) Secondary

जनसंचार

पाठ्य सामग्री : विहंगम दृष्टि में

- 1
जनसंचार परिचय

1.  संचार-एक परिचय
2.  जनसंचार
3.  जन माध्यमों की भूमिका तथा प्रभाव
4.  विकास संचार

- 2
मुद्रित माध्यम

5 . मुद्रित माध्यम - एक परिचय
6 . समाचार7ण् समाचार संकलन तथा संपादन
8 . भारत में भाषाई प्रेस

- 3
रेडियो

9.    रेडिया की विशेषताएँ
10.  रेडियो स्टेशन
11.  रेडियो कार्यक्रमों के फाॅर्मेट
12.  रेडियो कार्यक्रम निर्माण

- 4
टेलीविजन

13.  भारत में टेलीविजन
14.  एक जन माध्यम के रूप में टेलीविजन की भूमिका
15.  टेलीविजन चैनल
16.  टेलीविजन कार्यक्रम निर्माण

- 5
विज्ञापन और जनसंपर्क

17.  विज्ञापन-एक परिचय18ण् विज्ञापन उद्योग
19 . जनसंपर्क: एक परिचय
20.  जन संपर्क - एक उपकरण

- 6
न्यू मीडिया

(Download) NIOS Practical Papers Of Painting Senior Secondary

Time: 6 hrs.

Max. Marks: 70

Three practical words:-Marks 20+20+15)

1. Object Drawing                                        20Marks
2. Painting and Composition -                       20Marks
3. Folk Art as Motif -                                   15Marks
Portfolio submission (Home Assignment)-     15Marks

Total: 70Marks

List of Practical works:-

1. Object Drawing

Marks: 20

For exam object drawing by placing the object in front of the student and to let them draw.

For example:-

(i) A pot and glass to be arrange on the table.
(ii) A book placed under the apple to be arrange on the table.
(iii) Chair table and flower vase placed on the table etc.
(Should be done with pencil or water colour)

2. Painting and composition

Marks: 20

Free hand drawing directly from life of Human Figures, Building, Interior of a Room, Bus stop, Market, place, Vehicles, etc. paint on a given topic like e.g. Festival, Fair, Railway Station, Man reading a book or newspaper, playing with your pet, Eating out, Night scene, rainy day, wedding, Gram Panchayat, pollution, Library, Mother&Child etc. using imagination and everyday sketches.

(Water colour or Acrylic colour or colour pencil would be used)

3. Folk Art as Motif

Marks: 20

Use the motif of folk art of your locality or any well known India folk art.
(Example-Madhubani, Worli, Kalamkari, Kalighat, Phar and Alpana/Rangoli etc)
To re arrange a composition in your own style.

(Any colour or black and white are allowed only for folk painting)

Port-folio submission