**MODEL QUESTION**

Subject: Compulsory Mathematics

Full Marks: 100

Time: 3 hrs

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**Candidates are required to answer in their own words as far as practicable. *

**Credit will be given to originality, not rote learning.*

** **

**Attempt ALL the questions.**

** **

**Group 'A' [9×(2+2)=36]**

**1. **a. Evaluate: \(\frac{2^x\times3-2^x}{2^{(x+2)}-2^{(x+1)}}\)

b. Simplify: \(\sqrt[3]{54}\) - \(\sqrt[3]{250}\) + \(\sqrt[3]{16}\)

**2. **a. Solve: \(\sqrt{9x^2 – 20}\) = 3x – 2

b. Find three consecutive numbers such that 6 times the

smallest number is equal to double the sum of the other two.

**3.** a. If the mean of a grouped data having fm = 300 is 18,

find the value of N.

b. Find the third quartile class from the given ogive.

**4.** a. A card is drawn from a well shuffled deck of 52 playing cards.

Find the probability that the card drawn is either a black card or a jack.

b. There are 5 black and 6 white balls of same shape and size in a box.

Two balls are drawn at random in succession without replacement from the box.

Show the probability of all possible outcomes in a tree diagram.

**5.** a. The area of the adjoining parallelogram ABCD is 20cm^{2}.

If CD = 5cm and AD = 8cm, find the value of BCD.

b. The base of a right prism is an equilateral triangle with a perimeter of 12 cm.

The height of the prism is 7\(\sqrt{3}\) cm. Calculate its volume.

**6.** a. The total surface area of a hemi-sphere is 462cm^{2}. Find its diameter.

b. Find the base area of the given cone.

**7.** a. The price of a shirt becomes Rs. 1485 including 10% VAT.

Calculate its marked price if a discount of 10% is given.

b. In how many years will the population of a town be 209475 from

190000 at the growth rate of 5% per annum?

**8.** a. In the given figure, PT // QR. Square PQRS and parallelogram SQRT

are on the same base QR. If the diagonal QS = 8cm, find the area of

parallelogram SQRT.

b. In the given figure, O is the centre of the circle.

If BAC = 44º, find the value of OBC.

**9.** a. Find the value of ‘x’ from the given figure.

b. In the given figure, O is the centre of the circle.

PM and PN are two tangents. If PS = 7cm and OS = 5cm,

find the length of PM and PN.

**Group 'B' [16×4 =64]**

**10.** In an examination, 40% students passed in Mathematics,

45% passed in Science and 55% passed in English. 10% passed in

Mathematics and Science, 20% in Science and English

and 15 % in English and Mathematics.

a. Find the percentage of students who passed in all the three subjects.

b. Draw a Venn- diagram to illustrate the information.

** **

**11.** Find the LCM: 2x^{3} + 16, x^{2} + 3x + 2 and x^{2} + 4x + 4.

**12. **Solve: 3^{2x} – 4 × 3^{x + 2} + 243 = 0

**13.** Simplify: \(\frac{1}{x-a}\) - \(\frac{2}{2x+a}\) + \(\frac{1}{x+a}\) - \(\frac{2}{2x-a}\)

**14. **A fast bus takes 2 hours less than a slow bus for a journey of 240km.

If the speed of the slow bus is 10 km/hr less than the speed of the fast bus,

find the speed of both the buses.

**15. **If the mean of the following data is 41.5, find the missing frequency a.

Class |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |

Frequency (f) |
3 |
4 |
a |
15 |
3 |
5 |

**16. **A tree was broken due to the storm and the broken part bends

so that the top of the tree touches the ground making an angle of 30°

with the ground at a distance of 24 metres from the foot of the tree.

Find the height of the tree before it was broken.

**17. **Calculate the total surface area of the given combined solid.

**18.** The lateral surface area of a square-based pyramid is 720cm^{2}

and its slant height is 30cm. Calculate the volume of the pyramid.

**19. **A, B and C can complete a piece of work in 30, 40 and 60 days

respectively. All of them started the work together but B left the

work after working for 8 days. In how many days A and C

complete the remaining work?

**20. **A computer is sold at Rs. 20700 after giving 10% discount

and adding 15% VAT. Calculate the VAT amount.

**21. **If a sum becomes Rs.13310 in three years and Rs.14641 in four

years,interest being compounded annually, calculate the sum and

the rate of interest.

**22. **QRT and parallelogram PQRS are on the same base QR and

between the same parallel lines QR // PS. Prove that area of

the parallelogram PQRS = 2 times the area of QRT.

**23. **In the given figure, PAR = QBS. Prove that PS // QR.

**24. **Verify experimentally that the opposite angles of a cyclic

quadrilateral are supplementary. (Two figures are needed.

The radii of the circles should be more than 3cm.)

**25. **Construct a triangle ADE equal in area with quadrilateral

ABCD in which AB = 5.6 cm, BC = 6.4 cm, CD = 6.6 cm,

DA = 7.2 cm and the diagonal BD = 6cm.

****Good Luck****

- 2017-03-16 16:03:40
- Kullabs Admin
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