If matrix \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j}=\left\{\begin{array}{l}1, i \neq j \\ 0, i=j\end{array}\right.\) then \(A^3\) is equal to :

\(\int_0^2 x(2-x)^n d x\) is equal to

Which of the following statements are correct ?
(A) Determinant is a square matrix
(B) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{21}+a_{13} c_{31}\left(a_{i j}=\right.\) element, \(c_{i j}=\) cofactor \()\)
(C) Determinant is a number associated with a matrix
(D) Determinant is a number associated with a square matrix
(E) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{12}+a_{13} c_{13}\), where \(a_{i j}\) is the element, while \(c_{i j}\) is its corresponding cofactor
Choose the correct answer from the options given below :

The demand function for a certain product is represented by the equation: p = 20 + 5x - \(3 x^2\), where \(x\) is the number of units demanded and p is the price per unit (in Rs.), then the marginal revenue when 2 units are sold, is:

Let the matrix \(A=\left[a_{i j}\right]_{3 \times 3}\) be defined by
\(a_{i j}=\left\{\begin{array}{ll}2 i+3 j, & i<j \\5, & i=j \\3 i-2 j, & i>j\end{array}\right.\)
The number of elements in the matrix \(A\) which are greater than 7 , is:

If \(x \cos (a+y)+\cos a \sin (a+y)=0\), then \(\frac{d y}{d x}\) is equal to

If \(A\) be a square matrix of order 3 such that \(|A|=2\), then \(|\operatorname{adj}(2 A)|\) is equal to

The conductivity of 0.001 mol \(\text{L}^{-1}\) acetic acid is \(5.01 \times 10^{-5} \text{ S cm}^{-1}\).
Calculate its dissociation constant if \(\Lambda_m^{\circ}\) for acetic acid is
390.5 \(\text{S cm}^2 \text{mol}^{-1}\).

Development of fruits without fertilization is known as -

The finches found on Galapagos Islands were originally ___________ .

MONOHYBRID CROSS
The inheritance of flower color in the dog flower (Snapdragon or Antirrhinum sp.) can be understood by crossbreeding between true-breeding red-flowered (RR) and true-breeding white-flowered plants (rr). When they were crossed, F₁ (Rr) was pink. When F₁ was self-pollinated, the F₂ results were Red, Pink and White. Here the genotype ratios were exactly as expected, but the phenotype ratios have been changed. What happened was that R was not completely dominant over r and this made it possible to distinguish Rr as pink from RR (Red) and rr (White).
In the above passage, the inheritance is an example of:

A Wheatstone bridge has four resistors: R1= R2 = R3 = 1 \( \Omega \) and R4 = 2 \( \Omega \). In order to balance the bridge, resistor R4 has to be shunted by resistance of

Read the Passage below and answer the question:
Aldehydes and Ketones, having atleast one methyl group linked to the carbonyl carbon atom (methyl Ketones), are oxidised by sodium hypohalite to sodium salts of corresponding carboxylic acids having one carbon atom less than that of carbonyl compound is converted to haloform. This oxidation does not affect a carbon - carbon double bond, if present in a molecule.
Arrange in decreasing order of nucleophilic addition :
A. \(CH_3CHO\)
B. \(C_2H_5COCH_3\)
C. \(CH_3COCH_3\)
D. \(HCHO\)
Choose the correct answer from the options given below :