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Class 11
Sample Questions
Syllabus & Sample Questions
Class 11
Syllabus
Sets, Relation and function, Induction, Complex number, Sequence and Series, Permutation and Combination,
Binomial Theorem, Straight Line, Limits and Derivatives, Trigonometric Functions, Statistics, 3D geometry,
Vectors, Probability, Logarithm, Inequality, Applied Mathematics, Mathematical reasoning, Verbal and
Non verbal reasoning.
i
1.
(A) 1
(C) i
(E) None of these
2.
2i
3i
4i
i
A function is defined as Fn ()  en2  e n2  e n2  e n2    e n , Where n  N . Find the value of limFn () .
n
(B) –1
(D) –i
If Z is a complex number and all the roots of the equation given by Z³ + pZ² + qZ + r = 0 is of unit modulus
then which one of the following options is not correct?
(A) p  3
(B)
q 3
(C) r  3
(D) All of these
(E) None of these
3.
Identify the equation for which the real roots are 2 and 3 respectively.
(A) 5log5 (m2 4m5)  m  1
(B)
2
(C) 5log5 (2m2 4m5)  2m  1
(E) None of these
(D) 5log5 (2m2 4m5)  2m  1
5log5 (m 4m5)  2m  1
4.
An insect is trying to reach the top of the slope of the 15 cm long pavement which is connecting the first
floor of a house to the garden of the backyard. While doing so it takes every time a jump of 2 cm but slips
1 cm while trying to hold the grip. Find the number of jumps required to reach the top of the pavement.
(A) 13
(B) 14
(C) 15
(D) 12
(E) None of these
5.
A sequence is such that it consists of 4n + 1 terms in which the first 2n + 1 terms are in AP whose common
difference is found to be 2 and the last 2n + 1 terms are in GP whose common ratio is
1
. Find the middle
2
term of the sequence if the middle term of the both AP and GP are equal.
Class 11 - Page:1
Erudite Olympiad Foundation
(A)
IIOM'12
2n  22n
22n1
2n  22n1
22n
(E) None of these
(C)
(B)
2n  22n1
22n1
(D)
2n  22n
22n  1
6.
There are 8 passengers waiting to cross the river on a boat. There is only one boat to cross the river.
Only three passengers can cross the river as often as they can in one trip and no three same
passangers can cross together more than once. Find the number of trip the boat will have to make
to cross the river for all the passangers.
(A) 56
(B) 96
(C) 112
(D) 148
(E) None of these
7.
For the binomial expansion (1 + y) 21 , find the sum of last ten coefficients of the expansion of the given
binomial terms.
(A) 221
(B) 220
(C) 219
(D) 218
(E) None of these
8.
A box contains 15 oranges, 5 of which are rotten. There are three inspectors to inspect the box by taking
out one orange from it at random and replaces it. Similarly the other two inspectors also do the same
thing. The probability that at least one of the inspector finds the rotten orange is:
(A)
1
27
19
27
(E) None of these
(C)
9.
(B)
8
27
(D)
7
27
The circle represented by the equation x² + y² – 2x + 2y = 47 has two diametre 2x – 3y = 5 and 3x – 4y = 7.
The area of the circle is given by:
(A) 154 sq. unit
(B) 148 sq. unit
(C) 164 sq. unit
(D) 172 sq. unit
(E) None of these
10. If θ lies in the third quadrant and 5sin2θ + 3sinθ + 4cosθ = 0 then the value of 3tanθ - 4 is given by:
(A) 4
2
5
(B)
2
5
(C) 3
2
5
(D) 0
(E) None of these
Answer
1. (C)
6. (A)
Class 11 - Page:2
2. (C)
7. (B)
3.
8.
(A)
(C)
4.
9.
(B)
(A)
5. (D)
10. (A)