If \(\left|\begin{array}{lll}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{array}\right|=0\), then the values of \(x\) are:

The probability that A speaks the truth is \(4 / 5\). A coin is tossed and A reports 'Heads'. The probability that it actually showed 'Heads' is :

The solution set of the inequality \(\frac{2 x+3}{x-1}<0\) is:

The value of \(k\) for which the function \(f(x)=\left\{\begin{array}{ll}\frac{1-\cos 8 x}{16 x^2} & , \text { if } x \neq 0 \\ k & , \text { if } x=0\end{array}\right.\) is continuous at \(x=0\) is :

Let \(y=138.86+7.64(x-2021)\) be a straight line of best fit by using least square method.

\(YEAR(X)\)	2018	2019	2020	2021	2022	2023	2024
\(PROFIT(y)\)	144	130	126	144	138	156	164

Then the trend value for the year 2024 is :

The solution set of the linear inequation \(|4 x-3| \leq \frac{3}{4}\) is :

The points on the ellipse \(\frac{x^2}{9}+\frac{y^2}{25}=1\) at which the tangents are parallel to the \(x\)-axis are:

A parallel plate capacitor having area A and separated by distance d is filled by copper plate of thickness b. The new capacitance is:

The function \(f(x)=x^3, x \in R\), has:

Primary Endosperm Nucleus is the product of :

Arrange the following compounds in the decreasing order of reactivity towards Sn1 reaction
(A) (Ph)3C-1
(B) (Ph)3C-Br
(C) (Ph)3C-Cl
(D) (Ph)3C-F
Choose the correct answer from the options given below:

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:

A 25 cm long solenoid with 100 turns carries a current of 3 A. The flux density at the center of the solenoid is