If then for all real
If then the value of
5
3
-5
-3
The vectors are not perpendicular and are two vectors satisfying : and . Then the vector is equal to
Let be the purchase value of an equipment and be the value after it has been used for years. The value depreciates at a rate given by differential equation where is a constant and is the total life in years of the equipment. Then the scrap value of the equipment is
If is equal to
13
– 2
7
5
Statement-1 : The point (1,0,7) is the mirror image of the point (1,6,3) in the line
Statement-2 : The line : bisects the line segment joining (1,0,7) and (1,6,3).
Statement-1 is true, Statement-2 is false.
Statement-1 is false, Statement-2 is true.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
If the angle between the line and the plane
2/5
5/3
2/3
3/2
The number of values of for which the linear equations
possess a non-zero solution is
1
zero
3
2
As we learnt in
Cramer's rule for solving system of linear equations -
When and atleast one of is non-zero , system of equations has no solution
- wherein
and
Option 1)
1
Incorrect Option
Option 2)
zero
Incorrect Option
Option 3)
3
Incorrect Option
Option 4)
2
Correct Option
Let A and B be two symmetric matrices of order 3 .
Statement -1 : and are symmetric matrices.
Statement -2 : is symmetric matrix if matrix multiplication of A and B is commutative.
Statement-1 is true, Statement-2 is false.
Statement-1 is false, Statement-2 is true.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 .
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
As we learnt in
Property of Transpose Conjugate -
- wherein
is the conjugate matrix of
Given that
Then
Similarly
AB is symmmetric matrix.
If AB is commulative.
Option 1)
Statement-1 is true, Statement-2 is false.
Incorrect Option
Option 2)
Statement-1 is false, Statement-2 is true.
Incorrect Option
Option 3)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 .
Incorrect Option
Option 4)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Correct Option
does not exist
For define
local minimum at and local maximum at
local maximum at and local minimum at
local maximum at and
local minimum at and
equals to
The values of for which the function
is continuous for all in R,are
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (–3, 1) and has eccentricity is
The shortest distance between line
The lines intersect the line at respectively. The bisector of the acute angle between
Statement-1 : The ratio
Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.
Statement-1 is true, Statement-2 is false.
Statement-1 is false, Statement-2 is true.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
The two circles touch each other if
Which one of the following orders presents the correct sequence of the increasing basic nature of the given oxides ?
Phenol is heated with a solution of mixture of KBr and KBrO_{3 }. The major product obtained in the above reaction is
2-bromophenol
3-bromophenol
4-bromophenol
2, 4, 6-tribromophenol
Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium trichloroacetate ion and another compound. The other compound is
2,2,2-trichloroethanol
trichloromethanol
2,2,2-trichloropropanol
chloroform