Suppose in the plane 10 pairwise
nonparallel lines intersect one another.
What is the maximum possible number
of polygons (with finite areas) that can
be formed?
The values of ′k′ for which the equation
∣x∣^2 (∣x∣^2 − 2k + 1) = 1 − k^2 , has
repeated roots, when k belongs to
(1) {1, −1}
(2) {0, 1}
(3) {0, −1}
(4) {2, 3}
Let us consider an equation f(x) = x^3
− 3x + k = 0. Then the values of k for
which the equation has
1. Exactly one root which is positive,
then k belongs to
2. Exactly one root which is negative,
then k belongs to
3. One negative and two positive root
if k belongs to
A spring with one end attached to a
mass and the other to a rigid support is
stretched and released.
(a) Magnitude of acceleration, when
just released is maximum.
(b) Magnitude of acceleration, when
at equilibrium position, is maximum.
(c) Speed is maximum when mass is at
equilibrium position.
(d) Magnitude of displacement is
always maximum whenever speed is
minimum.
Let z_1 and z_2 be two distinct complex
numbers and let z = (1 − t)z_1 + tz_2 for
some real number t with 0 < t < 1. If
arg(w) denotes the principal argument
of a non-zero complex number w, then
(1) ∣z − z_1 ∣ + ∣z − z_2 ∣ = ∣z_1 − z_2 ∣
(2) Arg (z − z_1 ) = Arg (z − z_2 )
(3) determinant (((z − z_1 ),(z^ − z_1 ^ )),((z_2 − z_1 ),(z_2 ^ − z_1 ^ ))) = 0
(4) Arg (z − z_1 ) = Arg (z_2 − z_1 )
If z_1 = a + ib and z_2 = c + id are complex
numbers such that ∣z_1 ∣ = ∣z_2 ∣ = 1 and
Re(z_1 z_2 ^ ) = 0, then the pair of complex
numbers ω_1 = a + ic and ω_2 = b + id
satisfy
(1) ∣ω_1 ∣ = 1
(2) ∣ω_2 ∣ = 1
(3) Re(ω_1 ω_2 ^ ) = 0
(4) ∣ω_1 ∣ = 2∣ω_2 ∣
In the figure shown below, the block of
mass 2 kg is at rest. If the spring constant
of both the springs A and B is 100 N/m
and spring B is cut at t = 0, then
magnitude of acceleration of block
immediately is