If \(f(x)=2 x^3-15 x^2+36 x+1, x \in[1,5]\), then the absolute minimum value of \(f(x)\) is:

The largest interval, in which the function \(f(x)=x^3+2 x^2-1\) is increasing, is:

500 g of jaggery syrup has 30% jaggery in it.
The quantity of jaggery that should be added to make it 50% of syrup is:

If a line makes angles \(\alpha, \beta\) and \(\gamma\) with positive \(x\)-axis, \(y\)-axis and \(z\)-axis respectively, then the value of \(\sin ^2 \frac{\alpha}{2} \cos ^2 \frac{\alpha}{2}+\sin ^2 \frac{\beta}{2} \cos ^2 \frac{\beta}{2}+\sin ^2 \frac{\gamma}{2} \cos ^2 \frac{\gamma}{2}\) is

The equation of the normal to the curve \(y=\sin x\) at \((0,0)\) is :

Let A = {1,2,3}.
The number of relations on A containing (1, 2) and (2, 3),
which is reflexive and transitive but not symmetric, is:

The corner points of the feasible region determined by the set of constraints (linear inequations) are P(0,5), Q(3, 5), R(5, 0) and S(4, 1) and the objective function z = ax + 2by where a, b > 0 The condition on a and b such that maximum z occurs at Q and S is :

The resistance of 1N solution of four different electrolytes are given below. Arrange them in increasing order of their equivalent conductance values if the same conductivity cell was used to measure the resistance of all the electrolytic solutions:
(A) 250 ohm
(B) 150 ohm
(C) 50 ohm
(D) 280 ohm
Choose the correct answer from the options given below:

Identify the species which is not invasive:

In Octahedral coordination entities :

In RNA interference (RNAi) genes are silenced using :

Read the given paragraph and answer the given question :
Parasitism has evolved in many taxonomic groups from plants to higher vertebrates. Many parasites have evolved to be host specific in such a way that both host and the parasite tend to co-evolve. In accordance with their life styles, parasite evolve special adaptations and complex life cycle. Identify the statements which are not correct regarding host–parasite relationship:
(A) Host and parasite co-evolve.
(B) Parasite develops a main nervous system to survive.
(C) If host rejects parasite, parasite evolves counter-mechanisms to neutralize host defenses.
(D) If host rejects parasite, parasite succeeds by shifting to another host.
Choose the correct answer from the options given below:

Two concentric coils, each of radius \( 2\pi \, \text{cm} \), are placed at right angles to each other. Currents of 3 A and 4 A respectively are flowing through the two coils. The magnetic induction at the center of the coils will be: