An unbiased coin is tossed 6 times. The Probability of getting at least one head is:

If the objective function for an L.P.P. is \(z=3 x-4 y\) and the corner points for the bounded feasible region are \((0,0),(5,0),(6,5),(6,8),(4,10)\) and \((0,8)\), then the minimum value of \(z\) occurs at :

The inverse of the matrix \(A=\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8}\end{array}\right]\) is

The particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y(0)=1\) is :

If \(K\) is such that the area of triangle \(A B C\) is 3 , where \(A(1,3), B(0,0)\) and \(C(K, 0)\), then the value(s) of \(K\) is/are:

The marginal cost (MC) and marginal revenue (MR) functions of a product are \(M C=20+\frac{x}{20}\) and \(M R=30\) respectively. If the fixed cost is 200 , then the maximum value of the profit is :

Consider the LPP: Minimize \(Z=x+2 y\) subject to \(2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0\). The optimal feasible solution occurs at:

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of k/4 is

Which one of the followings cells are attacked by HIV?

The maximum value of \(z=4 x+3 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

Eight identical spherical drops, each having a potential of 9 V are combined together to form a single large drop. The potential of this large drop will be :

"The correct statement regarding the basicity of arylamines is :
A. Arylamines are generally more basic than alkylamines because of aryl group.
B. Aryl amines are generally more basic than alkylamines because the nitrogen atom in arylamines is 𝑠⁢𝑝 hybridised.
C. Aryl amines are generally less basic than alkylamines because the lone pair of electrons of nitrogen are delocalised by interaction with the pi electrons of the aromatic ring.
D. Aryl amines are generally more basic than alkylamines because the lone pair of electron of nitrogen are not delocalised by interaction with the pi electrons of aromatic ring.
E. Aryl amines are generally weaker bases than alkylamines due to electron withdrawing nature shown by aryl group.
Choose the correct answer from the options given below:"

Which of the following is NOT a cause of biodiversity loss due to human activities?