Let A and B denote the statements
If then
A is false and B is true
Both A and B are true
Both A and B are false
A is true and B is false
If are noncoplanar vectors and p,q,are real number, then the equality,
hold for
exactly two values of
more than two but not all values of
all values of
exactly one value of
The projections of a vector on the three coordinate axis are 6, 3, 2 respectively. The direction cosines of the vector are
The differential equation which represents the family of curves where are arbitrary constants, is
Let y be an implicit function of x defined by
then equals
Let the line lie in the plane
.Then equals to
Let a, b, c be such that .If
then the value of is
any even integer
any odd integer
any integer
zero
As we learnt in
Value of determinants of order 3 

So n is any odd integer.
Option 1)
any even integer
Incorrect Option
Option 2)
any odd integer
Correct Option
Option 3)
any integer
Incorrect Option
Option 4)
zero
Incorrect Option
Directions : Questions are Assertion Reason type questions. Each of these questions contains two statements :
Statement 1 (Assertion) and Statement  2 (Reason).
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
Question : Let be a 2 x 2 matrix
Statement1 :
Statement2 :
Statement1 is true,Statement2 is true; Statement2 is not a correct explanation for Statement1
Statement 1 is true, Statement2 is false
Statement1 is false, Statement2 is true
Statement1 is true, Statement2 is true; Statement2 is correct explanation for Statement1
As we learnt in
Property of adjoint of A 
 wherein
denotes adjoint of and denotes determinant of and is the order of the matrix
Statement 2 is true
Statement 1 is true
Option 1)
Statement1 is true,Statement2 is true; Statement2 is not a correct explanation for Statement1
Correct Option
Option 2)
Statement 1 is true, Statement2 is false
Incorrect Option
Option 3)
Statement1 is false, Statement2 is true
Incorrect Option
Option 4)
Statement1 is true, Statement2 is true; Statement2 is correct explanation for Statement1
Incorrect Option
Given such that x = 0 is the only real root of .If P(1) < P(1) then in the interval :
P(1) is not minimum but P(1) is the maxmium of P
P(1) is minimum but P(1) is not the maxmium of P
neither P(1) is the minimum nor P(1) is the maxmium of P
P(1) is minimum and P(1) is the maxmium of P
Directions : Questions are Assertion Reason type questions. Each of these questions contains two statements :
Statement 1 (Assertion) and Statement  2 (Reason).
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
Question :
Statement 1 : is equivalent to
Statement 2 : is a tautology.
Statement1 is true,Statement2 is true; Statement2 is not a correct explanation for Statement1
Statement 1 is true, Statement2 is false
Statement1 is false, Statement2 is true
Statement1 is true, Statement2 is true; Statement2 is correct explanation for Statement1
If P and Q are the points of intersection of the circles
and , then there is a circle passing through P, Q and (1,1)for
all except one value of p
all except two values of p
exactly one value of p
all values of p
The ellipse is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is
Three distinct points A,B and C are given in the 2dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( –1, 0) is equal to 1/3. Then the circumcentre of the triangle ABC is at the point
The lines and
are perpendicular to a common line for .
exactly one value of p
exactly two value of p
more than two value of p
No value of p
The shortest distance between the line and the curve is
In a binomial distribution if the probability of at least one success is greater than or equal to ,then n is greater than
One ticket is selected at random from 50 tickets numbered 00, 01, 02, ...., 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals
For real x,let then
is onto but not oneone
is oneone and onto
is neither oneone nor onto
is oneone but not onto
As we learnt in
Onto function 
If f:AB is such that each & every element in B is the image of atleast one element in A.Then it is Onto function.
 wherein
The range of f is equal to codomain of f.
One  One or Injective function 
A line parallel to x  axis cut the curve at most one point.

f(x) = x^{3} + 5x + 1
f'(x) = 3x^{2} + 5 > 0
Which is strictly increasing function so that it is one  one function.
For
So it is onto function.
Correct option is 2.
Option 1)
is onto but not oneone
This is an incorrect option.
Option 2)
is oneone and onto
This is the correct option.
Option 3)
is neither oneone nor onto
This is an incorrect option.
Option 4)
is oneone but not onto
This is an incorrect option.
If A,B and C are three sets such that
then
As we learnt in
UNION OF SETS 
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used to denote the union.
 wherein
Symbolically, we write A U B = {x: x ∈ A or x ∈ B}.
INTERSECTION OF SETS 
The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol ‘∩ ‘is used to denote the intersection.
 wherein
Symbolically, we write A ∩ B = {x: x ∈ A and x ∈ B}.
and then B = C
Let
and or
So and and or
Both will be equal only and only if B = C
Correct option is 2.
Option 1)
This is an incorrect option.
Option 2)
This is the correct option.
Option 3)
This is an incorrect option.
Option 4)
This is an incorrect option.
Let
Statement  1 : The set
Statement  2 : is a bijection.
Statement  1 (Assertion) and Statement  2 (Reason).
Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for Statement1
Statement 1 is true, Statement2 is false
Statement1 is false, Statement2 is true
Statement1 is true, Statement2 is true; Statement2 is correct explanation for Statement1
As we learnt in
Bijective Function 
The function which is both oneone and onto is Bijective Function.

f(x) = (x + 1)^{2}  1
Let y = (x + 1)^{2}  1
Correct option is 2.
Option 1)
Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for Statement1
This is an incorrect option.
Option 2)
Statement 1 is true, Statement2 is false
This is the correct option.
Option 3)
Statement1 is false, Statement2 is true
This is an incorrect option.
Option 4)
Statement1 is true, Statement2 is true; Statement2 is correct explanation for Statement1
This is an incorrect option.