MEDIUM
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Which principle of organising emphasizes that a subordinate should receive orders from one superior only?

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Important Questions on Continuity and Differentiability

MEDIUM
The identical point charges, q each, are kept 2 m apart in air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.
EASY
For x ϵ (0,32), let fx=x,gx=tanx and hx=1-x21+x2 . If ϕx=(hof)og)(x), then ϕ π3 is equal to:
HARD

Four-point charges Q, q, Q and q are placed at the corners of a square of side'a'as shown in the figure.

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Find the resultant electric force on a charge Q.

MEDIUM
If A=01  -10 , then which one of the following statements is not correct?
EASY
A relation R in a set A is called _____, if a1,a2R implies a2,a1R, for all a1,a2A.
MEDIUM

If A=12221-2a2b is a matrix satisfying the equation AAT=9I , where I is 3×3 identity matrix, then the ordered pair a, b is equal to 

MEDIUM
If A is a square matrix such that A2=I, then (A-I)3+(A+I)3-7A is equal to
HARD
Let N be the set of natural numbers and R be the relation on N×N defined by (a,b)R(c,d) iff ad=bc for all a,b,c,dN. Show that R is an equivalence relation.
EASY
Check whether the relation R defined in the set 1,2,3,4,5,6 as R=a,b:b=a+1 is reflexive, symmetric or transitive.
MEDIUM

If B is a 3×3  matrix such that B2=0, then det. I+B50-50B is equal to :

MEDIUM
Show that the relation R on R is defined as R={(a,b):ab}, is reflexive and transitive but not symmetric.
MEDIUM
Let A=cosα-sinαsinαcosα, aR  such that A32=0-110. Then, a value of α is:
HARD

Three-point charges q, 4q and 2q are placed at the vertices of an equilateral triangle ABC of side l as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q.

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EASY
If A is a symmetric matrix and B is skew- symmetric matrix such that  A+B=235-1 , then AB is equal to:
EASY
Find a matrix A such that 2A-3B+5C=0, where B=-220314 and C=20-2716
MEDIUM
Let R be a relation defined on as a R b is 2a+3b is a multiple of 5,a,b. Then R is
HARD
Let A={xZ:0x12}. Show that R={(a,b):a,bA,|a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class 2.
EASY
Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is