**KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD
**

**Malleshwaram, Bengaluru - 560003.**

**2020-21 MODEL PAPER - 2**

**Subject : MATHEMATICS**

*Time : 3 hrs. 15 minutes*

**Subject Code : 81E**

**Max. Marks : 80**

**English Medium**

**Regular Fresh**

**General Instructions to the Candidate :**

**1.** This question Paper consists of objective and subjective types of 38 questions.

**2.** This question paper has been sealed by reverse jacket. You have to cut on
the right side to open the paper at the time of commencement of the
examination. Check whether all the pages of the question paper are intact.

**3.** Follow the instructions given against both the objective and subjective types of
questions.

**4.** Figures in the right hand margin indicate maximum marks for the questions.

**5.** The maximum time to answer the paper is given at the top of the question paper. It
includes 15 minutes for reading the question paper.

**I. Four alternatives are given for each of incomplete statement / questions.
Choose the correct answer and write the complete answer along with
its letter of alphabet. 8 x 1 = 8 **

**1.** The Pair of lines a1
x+b1
y+c1
=0 and a2
x+b2
y+c2
=0 are intersecting lines then the
ratio of their coefficients is ;

**2.**2, x, 14 are in Arithmetic progression, then the value of x is :

A. 28 B. 16

C. 7 D. 8

**3.** The standard form of quadratic equation is :

A. ax2 ˗bx+c=0 B. ax2 +bx+c=0

C. ax2 ˗bx˗c=0 D. ax2 +bx˗c=0

**4.** Sin (90-θ) is equal to :

A. Cos θ. B. tan θ.

C. Sec θ. D. Cot θ.

**6.** In the given graph. The co-ordinate of point A is :

A. (-1, 0) B. (1, -1)

C. (0, 2) D. (2, 0)

**7.** The emperical relationship between the three measures of central tendency is :

A. 2 Median = Mode + 3 Mean

B. 3 Median = Mode + 2 Mean

C. Median = Mode + Mean

D. Median = Mode ˗ Mean

**8.** In the given figure ST||QR then PS**/**SQ is equal to :

**II. Answer the following questions. 8 x 1 = 8**

**9.** In equation x+y=7, if x=3, then find the value of y ?

**10.** In the given figure “P” is a midpoint of BC, write the formula to find the coordinate of P ?

**11.**Write the measure of angle formed between tangent to a circle and radius drawn from the centre of the circle to the point of contact of the tangent.

**12.** Write the formula to find the total suface area of a right cylinder ?

**13.** Write the formula to find the volume of a solid sphere ?

**14.** Write the mathematical relation between slant height (l) height (h) and radius
(r) of a cone ?

**15.** In an arithmetic progression if an
= 3n-2, then find the second term of the
progression.
16. If, 15 cot A=8, then find the value of tan A?

**III. Answer the following questions. 8 x 2 = 16**

**17.** Solve by using elimination method ?

x + y = 8

2x ˗ y = 7

**18.** Find the 10th term of arithmetic progression 2, 7, 12 .......... using the formula.

**19. **Find the sum of 2+5+8+................. to 20 terms using the formula.

**20.** Find the discriminant of the equation 3x2
−5x+2=0 and hence write the nature
of its roots.
21. Solve x2
−2x+3=0 by using the quadratic formula.

**OR **

Solve by Factorisation x2 +5x+6=0

**22.** Find the distance between the points A(3, 6) and B(5, 7) using distance formula.

**OR**

Find the co-ordinates of the point P, which divides the line joining A(0, 0) and B(5, 10) in the ratio of 2:3.

**23.** Construct a tangent to a circle of radius 4cm at any point P on its circumference.

**24.** In the given figure, find the value of sin∝ + cosθ ?

**25.**A train travels 480 km at a uniform speed. If the speed had been 10km/h more, it would have taken 4 hours less for the same journey, find the speed of the train?

**OR**

Find two consecutive odd positive integers, sum of whose squares is 290. 26. Prove that {Cosec (90-θ) - Sin (90-θ)} {(Cosecθ - Sin θ) (tanθ + cotθ)} = 1

**OR**

**27.**From the top of a building 50 (ROOT 3) M high the angle of depression of a car on the ground is observed to be 600 . Find the distance of the car from the Foot of a building.

**28.**Find the area of triangle ABC, whose co-ordinates are A(4, -6), B(3, -2) and C(5, 2) then find the length of the median AD?

**29.**Find the mean of the following data, by direct method.

**OR**

Find the mode of the following data

**30.**Prove that “length of tangents drawn from an external point to a circle are equal.

**31.** The slant height of a frustrum of a cone is 4cm and perimeters of its circular
bases are 18cm and 6cm, find the curved surface area of the frustrum of a cone.

**OR**

The circumference of the base of a cylinder is 132cm and its height is 25cm. Find the volume of the cylinder?

**32.** Draw a “less than type ogive” for the data given in the following table

**33.**Construct tangents to a circle of radius 5cm such that the angle between the tangents is 60 (Degree).

**V. Answer the following. 4 x 4 = 16**

**34.** Find the Solution to the given pair of linear equations by graphical method.

x + y = 5

2x ˗ y = 4

**35.** The third term of an arithmetic progression is 8 and its ninth term exceeds three
times the third term by 2 find the sum of the first 19 terms.

**OR**

In an arithmetic progressive the sum of the three terms is 24, and their product is 480, write three terms of the arithmetic progression?

**36.** A toy is in the form of a cone mounted on a hemisphere with the some radius
is as shown in the figure. If the diameter of the conical portion is 6cm and its
height is 4cm, then find the surface area of the toy

**37.**Construct a triangle ABC of its sides BC=4cm, AB=6cm and AC=4.5cm then construct a triangle similar to it, whose sides are 2

**/**3 of the corresponding sides of the triangle ABC.

**VI. Answer the following question. 1 x 5 = 5**

**38.** State and Prove “Basic proportionally theorem”

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