MOST IMPORTANT QUESTIONS FOR SUB INSPECTOR EXAM IN PDF, Widely repeated questions in all tests.
1. A cyclic group of order n is generated by
(A) n elements (B) (n-1) elements (C) 1 element (D) None of these
2. Let G be a group of order 13.
(A) G is not cyclic (B) G is Non abelian (C) G is commutative (D) None of these
3. Identity element in a cyclic group is
(A) Infinite (B) Unique (C) Prime number (D) None of these
4. Which of the following statement is correct.
(A) A group can have more than one identity element
(B) The Null set can be considered to be a group
(C) The set of all real numbers is a group under subtraction
(D) To each element of a group there corresponds only one inverse element.
5. The unit matrix of order n has rank:
(A) zero (B) N (C) 1 (D) None of these
6. If determinant |A|=2 then
(A) 12 (B) 32 (C) 60 (D) None of these
7. A homogeneous system of linear equations has a non trivial solution if:
(A) The number of unknowns exceeds the number of equations
(B) The number of equations exceeds the number of unknowns
(C) The number of unknowns proceeds the number of equations
(D) None of these
8. A Square matrix A such that A2=A is called
(A) Involutary (B) Idempotent (C) Nilpotent (D) Symmetric
9. A system of m homogeneous linear equations AX=O has a non trivial solution if and only if
(A) Rank A = n (B) Rank A ˂ n (C) Rank A ˃ n (D) None of these
10. The intersection of two infinite sets :
(A) Always infinite (B) Always finite (C) May not be infinite (D) None of these
11. Least upper bound of a set, if exists is:
(A) Infinite (B) Finite (C) Unique (D) Always in fraction
12. The greatest lower bound of a set:
(A) Always belong to set (B) Not belong to set
(B) May or may not belong to set (D) None of these
13. A convergent sequence converges to :
(A) A unique limit (B) Many limits (C) Any two limits (D) None of these
14. Every pair of real numbers a and b satisfies one and only one of the conditions:
a b ,a = b , b ˂ a. This property of real numbers is known as:
(A) Transitive law (B) Associative law (C) Trichotomy law (D) Commutative law
15. The degree of the differential equation of all tangent lines to the parabola y2
=4ax is
(A) 3 (B) 1 (C) 2 (D) 4
16. The order of differential equation is defined as :
(A) The highest degree of variable (B) The order of highest derivative
(C) The power of variable in the solution (D) None of these
17. The Vector equation of a line through a point with position vector ‘a’ and parallel to a vector ‘b’
is ( t is scalar) .
(A) r = ta + b (B) r = a + tb (C) r = (1-t)a + tb (D) None of these
18. The work done by the force F= 2i-j-k through a displacement r= 3i+2j-5k is
(A) 3 (B) 6 (C) 9 (D) 12
19. Any three vectors A,B,C are coplanar if and only if:
(A) A.(B (B) ) A (B (C) A.(B (D) A (B
20. The vectors 2i-j+k and 3i-4j-4k are:
(A) Parallel (B) Collinear (C) Coplaner (D) None of these
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