CBSE
SAMPLE PAPER-03
Class – XI
MATHEMATICS
Time allowed: 3 hours, Maximum Marks: 100
General Instructions:
a) All questions are compulsory.
b) The question paper consists of 26 questions divided into three sections A, B and C. Section
A comprises of 6 questions of one mark each, Section B comprises of 13 questions of four
marks each and Section C comprises of 7 questions of six marks each.
c) All questions in Section A are to be answered in one word, one sentence or as per the exact
requirement of the question.
d) Use of calculators is not permitted.
Section A
1. Find the domain of the function .
Sol: Domain of is in the open interval
2. If
Sol:
3. What is the maximum value of if.
Sol: Max value is 2.
4. Name the locus of points , the sum of whose distance from two given points is a
constant.
Sol: Ellipse
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5. Check whether the three points (2, 0), (5, 3), (2, 6) are collinear.
Sol: Condition for colinearity is not satisfied here since
6. Write the condition so that the equation represents a
circle.
Sol:
Section B
7. Find the inverse of the function
Sol:
8. Find the vertex, axis , Focus , Directrix and latus rectum of the parabola
.
Sol:
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9. Express in the form .
Sol:
10. Solve the inequality .
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Sol: Either both factors are negative or both factors are positive to have this in equality. if
both factors are negative and if both factors are positive. Hence the solution is
11. Find the general value of if .
Sol:
12. In a single throw of 2 dies what is the probability of getting a prime number on each
die.
Sol: Total number of occurrence =
On each die there are 3 prime numbers
Hence total number of favorable cases
Probability of getting a prime in each die =
13. If Find the value .
Sol:
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14. If prove that .
Sol:
15. If is defined as follows: Find
Sol:
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16. Prove that the equation is impossible if x is real
Sol : Use the inequality
17. Find the domain of the function for which
.
Sol:
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Hence f(x) and (x) are equal when the domain is in the set
18. Find the limit .
Sol:
19. Solve
Sol:
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Section C
20. Differentiate from the first principle w.r.t. x.
Sol:
Note: As
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21. Find the sum of terms of the series
Sol: The successive First order of difference is this is an AP.
The second order difference is(Difference of the first difference)
Third order difference (Difference of second order differences) is all
n th term
Sum =
22. Find the equation of a circle whose diameter is the line joining the points
.
Sol: Let the point A be and B be
Let the point C be a point be (x, y) on the circle
Then AC and BC are perpendicular
Product of Slopes of line AC and BC =-1
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23. Calculate the mean deviation about the mean from the following data
xi 5 7 9 10 12 15
fi 14 6 2 2 2 4
Sol:
5 14 70 4 56
7 6 42 2 12
9 2 18 0 0
10 2 20 1 2
12 2 24 3 6
15 4 60 6 24
Mean Deviation
24. How many numbers can be formed with the digits so that odd
digits are in odd places and even digits are in even places.
Sol: The odd digits can be arranged in their 4 places in ways
Even digits can be arranged in their 3 places in
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Hence the total number of arrangements = ways
25. Two engineers go for an interview for two vacancies in the same grade. The
probability of engineer 1 (E1) getting selected is and that of engineer 2 (E2) is .
Find the probability that only one of them will be selected.
Sol: Probability of one of them getting selected = 1- (Probability of both getting
selected + Probability of none getting selected)
26. How many numbers are there between 1 and 1000(both included) that are not
divisible by 2, 3, and 5?
Sol: Let A denote the set of numbers that are divisible by 2, B set of numbers that are
divisible by 3, C set of numbers that are divisible by 5, D set of numbers that are divisible by
both 2 and3 , E set of numbers that are divisible by both 2 and 5, F set of numbers that are
divisible by 3 and 5, G set of numbers that are divisible by all the three numbers
In this case , Hence
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Numbers that are divisible by 2, 3, 5 are
Numbers that are not divisible by 2, 3, 5 are
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