__VIKAS PRE UNIVERSITY COLLEGE, MANGALURU__

__S.S.L.C. MODEL QUESTION PAPER – II__

__MATHEMATICS__

**Time allotted: 3 Hours Max. Marks: 80**

**FOUR alternative are given for each of the following questions/ incomplete statements. Only one of them is correct or most appropriate. Choose the correct alternative and write the complete answer along with its letter in the space provided against each question. **** 8 ´ 1 = 8**

**SINGLE CORRECT ANSWER:**- The y-coordinate of any point lying on x-axis is
- a) zero b) 1
- c) -1 d) Any number other than zero
- The formula used to find the coefficient of variation.
- a) ´ 100 b) ´ 100 c) s ´ ´ 100 d)
- The n
^{th}term of 3, 7, 11, 15, …… is - a) 4n -1 b) 4n + 1 c) 4n + 3 d) 3n + 4
- In a throw of dice, what is the probability of getting number greater than 5?
- a) b) c) d)
- The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
- a) 8 b) 10 c) 12 d) 15
- cos q . cosec q =
- a) sin q b) cot q c) cos q d) sec q
- The slope of the line joining the points (3, -2) and (4, 5) is
- a) 1/7 b) 1 c) 7 d) 3/7
- The number of zeroes of the polynomial x
^{3}– x – 3 – 3x^{2}is - a) zero b) 1 c) 2 d) 3
**Answer the following: 6****´****1 = 6**- State the Pythagoras theorem.
- Find the total surface area of a hemisphere of radius r.
- Write a number which is neither prime nor composite.
- In the figure, BC is the diameter what is the measure of x?

- If A and B are non-empty sets such that A/B = A ; then find A Ç B.
- In the polynomial, g (x) = x – 2; q (x) = x
^{2}– x + 1 and r (x) = 4; find p (x)

**III. ****Answer the following (TWO marks questions) 16 ****´**** 2 = 32**

- Find the value of
- The height of a right circular cylinder is 14 cm and the radius of its base is 2 cm. Find its
- a) CSA b) TSA

**OR**

The volume of a solid hemisphere is 1152 p cm^{3}. Find its curved surface area.

- A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC
- Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.
- In a H.P. T
_{5 }= and T_{11}= ; find T_{25} - There are 15 buses running between two towns. In how many ways can a man go to one town and return by a different bus?
- Prove that is an irrational number.
- Find the product of and
- In D ABC, AD is the median and PQ || BC, prove that PE = EQ.
- Find the radius of a circle whose centre is (-5, 4) and which passes through the point

(-7, 1)

- If v
^{2}= u^{2}+ 2as; solve for ‘v’ and find the value of ‘v’ if u = 0; a = 2; s = 100 - Calculate the area of the field shown in the diagram below:

(Measurements are in metres)

- In a group of passengers, 100 know Kannada, 50 know English and 25 know both. If passengers know either Kannada or English, how many passengers are in the group? Find how many can speak only Kannada.
- Nine rotten mangoes are mixed with 30 good ones. One mango is chosen at random. What is the probability of choosing a
- a) good mango b) rotten mango
- Rationalise the denominator and simplify
- If the polynomials 2x
^{3}+ ax^{2}+ 3x – 5 and x^{3}+ x^{2}– 4x – a leave the same remainder when divided by (x – 1), find the value of a.

**OR **

If ‘m’ and ‘n’ are the roots of the quadratic equation x^{2} – 3x + 1 = 0 ; then the value of

**Answer the following (THREE marks questions) 6****´****3 = 18**- The perimeter of a right angled triangle is 30 cm and its hypotenuse is 13 cm. Find the length of the other two sides of the triangle.
- Three circles touch each other externally find the radii of the circles if the sides of the triangle formed by joining the centres are 7 cm, 8 cm and 9 cm respectively.
- There are 16 cricket players in a club, of whom 5 are batsmen, 4 are bowlers, and the rest are allrounders. In how many ways a team of 11 be selected so as to contain 3 batsmen, 2 bowlers and the remaining allrounders?
- A two digit number is such that the product of the digits is 12. When 36 is added to this number, the digits interchange their places. Determine the number.

**OR **

The ages of Kavya and Karthik are 11 years and 14 years. In how many years’ time will the product of their ages be 304?

- In a study of diabetic patients in a village, the following observations were noted:

Age in years | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

No .of patients | 2 | 5 | 12 | 19 | 9 | 4 |

Calculate the mean and standard deviation. Also interpret the results.

- Prove that
**Answer the following (FOUR marks questions) 4****´****4 = 16**- Draw a transverse common tangent to two congruent circles of radii 2.5 cm, whose centres are at 8 cm apart.
- In an A.P. whose first term is 2, the sum of the first five terms is one fourth the sum of the next five terms. Show that T
_{20}= -112. Find S_{20}.

OR

A person saved every year half as much he saved in the previous year. If he totally saved Rs. 19,375 in 5 years, how much did he save in the first year?

- Prove that “In two similar triangles, the ratio of the areas of the triangles is equal to the ratio of the squares of the corresponding sides”
- Solve y = (x + 2) (2 – x) by graphically.

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VIKAS PRE UNIVERSITY COLLEGE, MANGALURU S.S.L.C. MODEL QUESTION PAPER – II MATHEMATICS