A random variable X has the following probability distribution: Then is equal to:
Option: 1
Option: 2
Option: 3
Option: 4
Option 2
View Full Answer(10)Let be the n^{th} term of a G.P. of positive terms. If is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
150
View Full Answer(5)If be a complex number satisfying then cannot be :
Option: 1
Option: 2
Option: 3
Option: 4
Option d
View Full Answer(3)
The following system of linear equations has
Option: 1 infinitely many solutions, satisfying
Option: 2 infinitely many solutions, satisfying
Option: 3 no solution
Option: 4 only the trivial solution.
System of Homogeneous linear equations 
If ? ≠ 0, then x= 0, y = 0, z = 0 is the only solution of the above system. This solution is also known as a trivial solution.
If ? = 0, at least one of x, y and z are nonzero. This solution is called a nontrivial solution.
Explanation: using equation (ii) and (iii), we have
This is the condition for a system have Nontrivial solution.

so infinite nontrivial solution exist
now equation (1) + 3 equation (3)
10x  20z = 0
x = 2z
Correct Option 2
View Full Answer(1)Let If then :
Option: 1
Option: 2
Option: 3
Option: 4
Elementary row operations 
Elementary row operations
Row transformation: Following three types of operation (Transformation) on the rows of a given matrix are known as elementary row operation (transformation).
i) Interchange of i^{th} row with j^{th} row, this operation is denoted by
ii) The multiplication of ith row by a constant k (k≠0) is denoted by
iii) The addition of ith row to the elements of jth row multiplied by constant k (k≠0) is denoted by
In the same way, threecolumn operations can also be defined too.

Correct Option (3)
View Full Answer(1)Let denote the greatest integer and Then the function, is discontinuous, when x is equal to:
Option: 1
Option: 2
Option: 3
Option: 4
Correct Option (1)
View Full Answer(1)Let be such that the equation, has a repeated root , which is also a root of the equation, . If is the other root of this equation, then is equal to:
Option: 1
Option: 2
Option: 3
Option: 4
Nature of Roots 
Let the quadratic equation is ax^{2} + bx + c = 0
D is the discriminant of the equation.
iii) if roots D = 0, then roots will be real and equal, then

ax^{2} – 2bx + 5 = 0 having equal roots or and
Put in the second equation
Correct Option 2
View Full Answer(1)In the expansion of , if is the least value of the term independent of when and is the least value of the term independent of when , then the ratio is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
General Term of Binomial Expansion
Term independent of x: It means term containing x^{0},
Now,
Correct option 1
View Full Answer(1)Let and be differentiable functions on such that is the identity function. If for some then is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
Rules of Differentiation (Chain Rule) 
Rules of Differentiation (Chain Rule)
Chain Rule or Derivation of Composite Function:
The chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.
Let f and g be functions. For all x in the domain of g for which g is differentiable at x and f is differentiable at g(x), the derivative of the composite function
h(x) = (f?g)(x) = f (g(x)) Is given by
h′(x) = f’(g(x))?g’(x)
Composites of Three or More Functions
For all values of x for which the function is differentiable, if k(x) = h(f(g(x)))Then,

Correct Option 4
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