__VIKAS PRE UNIVERSITY COLLEGE, MANGALURU__

__S.S.L.C. MODEL QUESTION PAPER – I__

__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:**- In a geometric progression if T
_{n}= 2 ´ 3^{n-1}, then T_{5}is equal to - a) 486 b) 243 c) 162 d) 81
- If 3, x, 7 are in Harmonic progression then the value of x is
- a) b) 5 c) d)
- A die is thrown once. The probability of getting a number 3 or 4 is
- a) b) c) 0 d) 1
- If the standard deviation of the scores 1, 2, 3, 4, 5 is then variance is
- a) b) c) 2 d) 3
- If x = 1 is a zero of the polynomial f(x) =x
^{3}– 2x^{2}+ 4x + k, then the value of K is - a) -3 b) 3 c) 4 d) -4

- In the figure, If PA and PB are tangents and AB = AP, then is :

- a) 30° b) 90° c) 45° d) 60°
- The length of a diagonal of a square of side 5 cm is
- a) 5cm b) cm c) 10 cm d) cm
- The distance of the point (-4, -7) from the y – axis is :
- a) 4 units b) 7 units c) 11 units d) units

**Answer the following 6****´****1 = 6**- If A = {2, 4, 6, 8 } and B = { x : x is an even natural number < 5}; then find A/B.
- What is the HCF of the smallest composite number and the smallest prime number.
- For the polynomial x
^{2}– 5x + 6 ; find the sum of zeroes. - Find the value of sin
^{2}60° – sin^{2}30°. - Find the surface area of a sphere having radius is 7 cm
- Write the co-ordinates of midpoint of the line joining the points ( 2, 3) and (4, 5).

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

- If A = { 3, 4, 5, 9}; B = { 4, 5, 6, 8} and C = { 5, 7, 8, 9}.

Show that intersection of sets is associative.

- Find the sum of all natural numbers between 1 and 201 which are divisible by 5.
- If
^{n}P_{4}= 20.^{n}P_{2}; find the value of n. - Find the HCF of 305 and 793 by Euclid’s division algorithm.
- If A is an event of a random experiment such that P(A) : P= 6 : 15, then find

(i) P(A) (ii) P

- If then find the value of x.
- Simplify by rationalizing the denominator
**.** - What must be subtracted from (x
^{3}+ 5x^{2}+ 5x + 8) so that the resulting polynomial is exactly divisible by (x^{2}+ 3x – 2)? - Solve x
^{2}+ 6x – 7 = 0 by the method of completing the square. - Construct two tangents to a circle of radius is 3 cm. Such that angle between them is 40°.
- In DPQR, ; QS ^ PR. If PQ = a, QR = b; RP = c and QS = p show that pc = ab.
- Prove that Sin A. Cos A. tan A + Cos A. Sin A. Cot A = 1, where ‘A’ is an acute angle.
- A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find ‘a’
- A clown’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
- The diameter of a metallic sphere is 18 cm. It is melted and drawn into a wire having diameter of cross section 0.4 cm. Find the length of the wire.
- Draw a plan of a level ground using the information given below.

Metre to C | ||

To D 120
To E 180 |
220
210 120 80 |
200 to B |

From A |

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**Answer the following (THREE marks questions) 6****´****3 = 18**- How many (i) lines (ii) triangles can be drawn through 8 points on a circle?

**OR**

A sports team of 11 students is to be constituted choosing atleast 5 from class IX and atleast 5 from class X. If there are 8 students in each of these classes in how many ways can the team be constituted?

- The number of books bought by 200 students in a book exhibition is given below.

No. of books | 0 | 1 | 2 | 3 | 4 |

No. of students | 35 | 64 | 68 | 18 | 15 |

Find the variance and standard deviation.

**If ‘**m’ and ‘n’ are the roots of the equation : x^{2}– 6x + 2 = 0 find the value of

(i) ( m + n)mn (ii) (iii) m^{3}n^{2} + n^{3}m^{2}

**OR**

Find three consecutive positive integers such that the sum of the square of the first and the product of other two is 154.

- A pair of perpendicular tangents are drawn to a circle from an external point. Prove that length of each tangent is equal to the radius of the circle.
- In the ABCD, AO = 3x – 19 ; OC = x – 5 ‘ BO = x – 3 ; OD = 3. Find ‘x’.

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**OR**

ABCD is a rectangle. ‘P’ is any point outside it such that PA^{2} + PC^{2} = BA^{2} + AD^{2}. Prove that ÐAPC = 90°.

- Prove that

OR

The angle of elevation of the top of a flag post from a point on a horizontal ground is found to be 30°. On walking 6 m towards the post, the elevation increased by 15°. Find the height of the flag post.

**Answer the following (FOUR marks questions) 4****´****4 = 16**- Find four terms in an A.P. such that the sum of the 2
^{nd}and the 3^{rd}terms is 22 and the product of the 1^{st}and 4^{th}terms is 85.

**OR**

Find (i) S_{2} : S_{4} for the series 5 + 10+ 20 + …….

(ii) S_{4} : S_{8} for the series 4 + 12 + 36 +

- Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
- Two circles of radii 5.5 cm and 3.5 cm touch each other externally. Draw a direct common tangent and measure its length.
- Solve the quadratic equation y = x
^{2}– 2x + 5 graphically.

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