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Question Number 21070 Answers: 1 Comments: 2

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

$Let us consider an equation f (x) = x^{3}$ $- 3 x + k = 0 . Then the values of k for$ $which the equation has$ $1 . Exactly one root which is positive,$ $then k belongs to$ $2 . Exactly one root which is negative,$ $then k belongs to$ $3 . One negative and two positive root$ $if k belongs to$

Question Number 21067 Answers: 2 Comments: 0

∀n∈N, prove 9∣[n^3 +(n+1)^3 +(n+2)^3 ]

$\forall n \in N, p r o v e 9 ∣ [n^{3} + {(n + 1)}^{3} + {(n + 2)}^{3}]$

Question Number 21076 Answers: 1 Comments: 0

integrate with respect to x ∫x^(sinx)

$i n t e g r a t e w i t h r e s p e c t t o x$ $\int x^{s i n x}$

Question Number 21060 Answers: 0 Comments: 8

write sin 1° in surd form please show workings.

$write \sin 1 ° in surd form$ $please show workings .$

Question Number 21140 Answers: 1 Comments: 1

if tan β=((2sin αsin γ)/(sin (α+γ))) so proof cot γ+cot α=2cot β

$i f \tan β = \frac{2 \sin α \sin γ}{\sin (α + γ)}$ $s o p r o o f \cot γ + \cot α = 2 \cot β$

Question Number 21053 Answers: 0 Comments: 0

Question Number 21050 Answers: 1 Comments: 0

The most general solution of the equation sinx + cosx = min_(a∈R) {1, a^2 − 4a + 6} is

$The most general solution of the$ $equation \sin x + \cos x = \min_{a \in R} {1, a^{2} - 4 a + 6}$ $is$

Question Number 21048 Answers: 0 Comments: 0

If the equation 2cos2x − (a + 7)cosx + 3a − 13 = 0 possesses atleast one real solution, then the maximum integral value of ′a′ can be

$If the equation 2 \cos 2 x - (a + 7) \cos x +$ $3 a - 13 = 0 possesses atleast one real$ $solution, then the maximum integral$ $value of^{'} a^{'} can be$

Question Number 21038 Answers: 1 Comments: 1

Question Number 21031 Answers: 0 Comments: 0

if :∀ε>0, ∀(a,b)∈R^2 ,a<b+ε prove: a≤b

$i f : \forall ϵ > 0, \forall (a, b) \in R^{2}, a < b + ϵ$ $p r o v e : a ⩽ b$

Question Number 21029 Answers: 0 Comments: 0

Question Number 21021 Answers: 1 Comments: 2

Question Number 21015 Answers: 0 Comments: 0

Question Number 21013 Answers: 1 Comments: 1

Question Number 21012 Answers: 1 Comments: 3

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.

$A spring with one end attached to a$ $mass and the other to a rigid support is$ $stretched and released .$ $(a) Magnitude of acceleration, when$ $just released is maximum .$ $(b) Magnitude of acceleration, when$ $at equilibrium position, is maximum .$ $(c) Speed is maximum when mass is at$ $equilibrium position .$ $(d) Magnitude of displacement is$ $always maximum whenever speed is$ $minimum .$

Question Number 21009 Answers: 1 Comments: 0

Question Number 21006 Answers: 0 Comments: 0

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 )

$Let z_{1} and z_{2} be two distinct complex$ $numbers and let z = (1 - t) z_{1} + {t z}_{2} for$ $some real number t with 0 < t < 1 . If$ $\arg (w) denotes the principal argument$ $of a non - zero complex number w, then$ $(1) ∣ z - z_{1} ∣ + ∣ z - z_{2} ∣ = ∣ z_{1} - z_{2} ∣$ $(2) Arg (z - z_{1}) = Arg (z - z_{2})$ $(3) | \begin{matrix} z - z_{1} & \bar{z} - {\bar{z}}_{1} \\ z_{2} - z_{1} & {\bar{z}}_{2} - {\bar{z}}_{1} \end{matrix} | = 0$ $(4) Arg (z - z_{1}) = Arg (z_{2} - z_{1})$

Question Number 21005 Answers: 0 Comments: 0

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 ∣

$If z_{1} = a + i b and z_{2} = c + i d are complex$ $numbers such that ∣ z_{1} ∣ = ∣ z_{2} ∣ = 1 and$ $Re (z_{1} {\bar{z}}_{2}) = 0, then the pair of complex$ $numbers ω_{1} = a + i c and ω_{2} = b + i d$ $satisfy$ $(1) ∣ ω_{1} ∣ = 1$ $(2) ∣ ω_{2} ∣ = 1$ $(3) Re (ω_{1} {\bar{ω}}_{2}) = 0$ $(4) ∣ ω_{1} ∣ = 2 ∣ ω_{2} ∣$

Question Number 21001 Answers: 0 Comments: 0

determinant (((a 1 1)),((1 b 1)),((1 1 c)))>0 then showthat abc>−8−99

$| \begin{matrix} a 1 1 \\ 1 b 1 \\ 1 1 c \end{matrix} | > 0 t h e n s h o w t h a t a b c > - 8 - 99$

Question Number 20989 Answers: 1 Comments: 1

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

$In the figure shown below, the block of$ $mass 2 kg is at rest . If the spring constant$ $of both the springs A and B is 100 N / m$ $and spring B is cut at t = 0, then$ $magnitude of acceleration of block$ $immediately is$

Question Number 20988 Answers: 0 Comments: 1

Question Number 20991 Answers: 0 Comments: 1

x^3 −12x

$x^{3} - 12 x$

Question Number 20992 Answers: 3 Comments: 1

Question Number 20986 Answers: 1 Comments: 1

A 50 kg log rest on the smooth horizontal surface. A motor deliver a towing force T as shown below. The momentum of the particle at t = 5 s is

$A 50 kg \log rest on the smooth horizontal$ $surface . A motor deliver a towing force$ $T as shown below . The momentum of$ $the particle at t = 5 s is$

Question Number 20984 Answers: 1 Comments: 1

A ball of mass m is moving with a velocity u rebounds from a wall with same speed. The collision is assumed to be elastic and the force of interaction between the ball and the wall varies as shown in the figure given below. The value of F_m is

$A ball of mass m is moving with a$ $velocity u rebounds from a wall with$ $same speed . The collision is assumed$ $to be elastic and the force of interaction$ $between the ball and the wall varies as$ $shown in the figure given below . The$ $value of F_{m} is$

Question Number 20983 Answers: 1 Comments: 0

Find the number of ordered triples (a, b, c) of positive integers such that abc = 108.

$Find the number of ordered triples$ $(a, b, c) of positive integers such that$ $a b c = 108 .$

Pg 1818 Pg 1819 Pg 1820 Pg 1821 Pg 1822 Pg 1823 Pg 1824 Pg 1825 Pg 1826 Pg 1827

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