A die has 6 faces marked by the given numbers as shown below:The

Subject

Mathematics

Class

ICSE Class 10

Pre Boards

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Sample Papers

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 Multiple Choice QuestionsShort Answer Type

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1.

A die has 6 faces marked by the given numbers as shown below:


The die is thrown once. What is the probability of getting
(i) a positive integer.
(ii) an integer greater than - 3.
(iii) the smallest integer.


Given that the die has 6 faces marked by the given numbers as below:

Total number of outcomes = 6

(i) For getting a positive integer, the favourable outcomes are 1, 2, 3

Number of favourable outcomes = 3

Required probability = 36 = 12
(ii) For getting an integer greater than - 3, the favourable outcomes
are  - 2 , - 1, 1, 2, 3

Number of favourable outcomes = - 5

Required probability = 56
(iii) For getting a smallest integer, the favourable outcome is - 3

Number of favourable outcomes = 1

Required probability = 16


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2.

Find x, y if -2031- 12x + 3- 21 = 2y3.


3.

Shahrukh opened a ‘Recurring Deposit’ account in a bank and deposited Rs. 800 per month for 1½ years. If he received Rs. 15,084 at the time of maturity, find the rate of interest per annum.


4.

Without using trigonometric tables, evaluate

sin234° + sin256° + 2tan18°tan72° - cot230°


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5.

Using the Remainder and Factor Theorem, factorise the following polynomial:
x3 + 10x2 - 37x + 26


6.

The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order.
If the mean of the observations is equal to the median, find the value of x.


7.

In the figure, m∠DBC = 58°. BD is the diameter of the circle. Calculate:

(i) m∠BDC

(ii) m∠BEC

(iii) m∠BAC


8.

Use graph paper to answer the following questions. (Take 2 cm = 1 unit on both axes)
(i) Plot the points A( - 4, 2) and B(2, 4)
(ii) A' is the image of A when reflected at the y-axis. Plot it on the graph paper and write
the co-ordinates of A'.
(iii) B' is the image of B when reflected on the line AA'. Write the co-ordinates of B'.
(iv) Write the geometric name of the figure ABA'B'.
(v) Name a line of symmetry of the figure formed.


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9.

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:
(i) the VAT paid by the shopkeeper.
(ii) the total amount that the consumer pays for the washing machine.


10.

If x2 + y2x2 - y2 = 178 then find the value of :

(i) x:y

(ii) x3 + y3x3 - y3


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