Which one of the following complexes shows optical isomerism ?
[Co(NH_{3})_{3}Cl_{3}]
cis[Co(en)_{2}Cl_{2}]Cl
trans[Co(en)_{2}Cl_{2}]Cl
[Co(NH_{3})_{4}Cl_{2}]Cl
(en=ethylenediamine)
If 0 ≤ x < 2 π, then the number of real values of x, which satisfy the equation
cos x + cos 2x + cos 3x + cos 4x = 0, is :
A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30^{0}. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^{0}. Then the time taken (in minutes) by him, from B to reach the pillar, is :
6
10
20
5
Let be three unit vectors such that
is not parallel to then the angle between
In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively
then the point (p, q) lies on a line :
parallel to x-axis.
parallel to y-axis.
making an acute angle with the positive direction of x-axis.
making an obtuse angle with the positive direction of x-axis
If a curve passes through the point and satisfies the differential
equation, then
is equal to :
If the line, lies in
the plane,then is equal to:
26
18
5
2
The distance of the point (1, −5, 9) from the plane x − y + z = 5 measured along the
line x = y = z is :
The number of distinct real values of λ for which the lines
and
are coplanar is :
4
1
2
3
ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, µ). If the median through A is equally inclined to the coordinate axes, then the value of (λ^{3}+µ^{3}+5) is :
1130
1348
676
1077
The distance of the point (1, −2, 4) from the plane passing through the point (1, 2, 2) and perpendicular to the planes x − y + 2z = 3 and 2x −2y + z + 12=0, is :
The shortest distance between the lines
and
lies in the interval :
[0, 1)
[1, 2)
(2, 3]
(3, 4]
The system of linear equations
x +λy −z = 0
λx − y − z = 0
x + y − λz = 0
has a non-trivial solution for :
infinitely many values of λ.
exactly one value of λ.
exactly two values of λ.
exactly three values of λ.
Solution Video
If and A adj A=A A^{T}, then
5 a + b is equal to :
-1
5
4
13
As we learnt in
Adjoint of a square matrix -
Transpose of the matrix of co-factors of elements of is called the adjoint of
- wherein
Transpose of a Matrix -
The matrix obtained from any given matrix , by interchanging its rows and columns.
- wherein
so that 15a - 2b = 0
and 10a + 3b =13
Option 1)
-1
This option is incorrect.
Option 2)
5
This option is correct.
Option 3)
4
This option is incorrect.
Option 4)
13
This option is incorrect.
The number of distinct real roots of the
equation,in the
interval is
4
3
2
1
Let then log p
is equal to :
If m and M are the minimum and the maximum values of
then M−m is equal to :
If is a differentiable function in the interval (0, ∞) such that = 1 and for each , then is equal to :
If the function is differentiable at x = 1, then
is equal to :
If , then 'a' is equal to :
2
Option 2