For a regular polygon, let be the radii of the inscribed and the circumscribed circles. A false statement among the following is
there is a regular polygon with
there is a regular polygon with
there is a regular polygon with
there is a regular polygon with
Let and let , where Then
Let Then the vector satisfying
If the vectors and are mutually orthogonal, then
( 3, 2 )
( 2, 3 )
( 2, 3 )
( 3, 2 )
Directions : Question are Assertion Reason type questions. Each of these questions contains two statements. Statement1 (Assertion) and Statement2 (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:
Statement1 : The point (3, 1, 6) is the mirror image of the point (1, 3, 4) in the plane
Statement2 : The plane bisects the line segment joining (3, 1, 6) and (1, 3, 4).
Statement 1 is true, statement 2 is true ; statement 2 is a correct explanation of statement1.
Statement 1 is true, statement 2 is true ; statement 2 is not a correct explanation of statement1.
Statement 1 is true, statement 2 is false.
Statement 1 is false, statement 2 is true.
A line AB in threedimensional space makes angles 45^{0} and 120^{0 } with the positive axis and the positive axis respectively. If AB makes an acute angle with the positive axis , than equals
30^{0}
45^{0}
60^{0}
75^{0}
Directions : Question are Assertion Reason type questions. Each of these questions contains two statements. Statement1 (Assertion) and Statement2 (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 × 2 matrix with nonzero entries and let where is 2 × 2 identity matrix. Define sum of diagonal elements of and = determinant of matrix .
Statement1 : 0
Statement2 : = 1
Statement 1 is true, statement 2 is true ; statement 2 is a correct explanation of statement1.
Statement 1 is true, statement 2 is true ; statement 2 is not a correct explanation of statement1.
Statement 1 is true, statement 2 is false.
Statement 1 is false, statement 2 is true.
As we learnt in
Multiplication of matrices 

Option 1)
Statement 1 is true, statement 2 is true ; statement 2 is a correct explanation of statement1.
Incorrect Option
Option 2)
Statement 1 is true, statement 2 is true ; statement 2 is not a correct explanation of statement1.
Incorrect Option
Option 3)
Statement 1 is true, statement 2 is false.
Correct Option
Option 4)
Statement 1 is false, statement 2 is true.
Incorrect Option
The number of 3 x 3 nonsingular matrices, with four entries as 1 and all other entries as 0, is
less than 4
5
6
at least 7
As we learnt in
Defination of Matrix 
A rectangular array of symbols (which could be real or complex numbers) along rows and columns is a matrix.

Use combination method and 4 entries for 1 and others for zero. Then atleast 7 number of nonsingular matrices
Option 1)
less than 4
Incorrect Option
Option 2)
5
Incorrect Option
Option 3)
6
Incorrect Option
Option 4)
at least 7
Correct Option
Consider the system of linear equations
The system has
infinite number of solutions
exactly 3 solutions
a unique solution
no solution
As we learnt in
Cramer's rule for solving system of linear equations 
When and atleast one of is nonzero , system of equations has no solution
 wherein
and
Option 1)
infinite number of solutions
Incorrect Option
Option 2)
exactly 3 solutions
Incorrect Option
Option 3)
a unique solution
Incorrect Option
Option 4)
no solution
Correct Option
Let be defined by
If has a local minimum at , then a possible value of is
1
0
–1/2
–1
The equation of the tangent to the curve that is parallel to the axis, is
Let be a positive increasing function with
1
2/3
3/2
3
Let S be a nonempty subset of R. Consider the following statement:
P : There is a rational number such that
Which of the following statements is the negation of the statement P ?
There is a rational number such that .
There is no rational number such that .
Every rational number satisfies .
and is not rational.
The line L given by passes through the point (13, 32). The line K is parallel to L and has the equation Then the distance between L and K is
If two tangents drawn from a point P to the parabola are at right angles, then the locus of P is
The circle intersects the line at two distinct points if
The correct sequence which shows decreasing order of the ionic radii of the element is
The main product of the following reaction is
From amongst the following alcohols the one that would react fastest with conc .HCl and anhydrous ZnCl_{2}, is
1Butanol
2Butanol
2Methylpropan2ol
2Methylpropanol
The reagent, conc.HCl and anhydrous ZnCl2 is Lucas reagent, which is used to distinguish between 1°, 2° and 3° alcohols.
3° alcohol + Lucas reagent → Immediate turbidity.
2° alcohol + Lucas reagent → Turbidity after 5 mins.
1° alcohol + Lucas reagent → No reaction.
Thus, the required alcohol is 2methylpropan2 ol, i.e.
The polymer containing strong intermolecular forces e.g., hydrogen bonding is
natural rubber
teflon
nylon6,6
polystyren