If \(\int_0^a 3 x^2 d x=27\), then value of \(a\) is :

Let R be the feasible region for a Linear Programming Problem and let \(z=a x+b y\) be the objective function. If R is bounded, then the objective function z has :

The function \(f(x)=\tan x-x\):

Kavya takes a personal loan of ₹ 10,00,000 at the rate of 12% per annum for 5 years, then the EMI by using flat rate method is:

The value of the determinant \(\left|\begin{array}{ccc}66 & 18 & 36 \\ 1 & 3 & 4 \\ 11 & 3 & 6\end{array}\right|\) is:

Consider the following hypothesis test:
\(H _0: \mu \leq 3432\)
\(H _{ a }: \mu>3432\)
A sample of 96 provided a sample mean \(\bar{x}\) = 3648 and sample standard deviation s = 802 then the degree of freedom of t-distribution is:

If the relation \(R: A \rightarrow B\), where \(A=\{2,3,4\}\) and \(B=\{3,4,5\}\) is defined by \(R=\{(x, y): x < y, x \in A, y \in B\}\), then

The corner points of the feasible region determined by a system of linear constraints are (0,0), (0, 40), (20, 40), (60, 20), (60, 0). If the objective function is \(Z = 4x + 3y\) then which one of the following is true?

The first isolated restriction endonuclease was:

The area of the region (in square units) bounded by \(x=1, x=2\) and the curve \(y^2=4 x\) in the first quadrant is:

If \(A=\left[\begin{array}{ccc}2 & -2 & 1 \\ 0 & 4 & 2\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 & -2 & 7 \\ 2 & 0 & 6\end{array}\right]\) are two matrices such that 3A - 2B + 4C = O, then matrix C is equal to:

Identify the correct statement(s) among the following:
(A) If three electrical cells each of emf, E and internal resistance r are connected in series to a resistance R, the current drawn from them is 3E/(R+3r).
(B) If these three cells are connected in parallel combination, across resistance R then the current drawn will be E/(3R+r).
(C) If the two cells are connected in series and then one in parallel which are then connected across resistance R, then the current drawn will be 2E/(2R+2r).
(D) In a mixed grouping of cells, current will be maximum when total external resistance is equal to total equivalent internal resistance.
Choose the correct answer from the options given below :

The equation of normal at the point (1, 1) on the curve \(2y + x^3 = 3\) is: