If \(A=\left[\begin{array}{ccc}2 & 0 & 3 \\ -1 & 1 & 3 \\ 0 & -4 & 0\end{array}\right]\), then the value of \(\operatorname{det}(2 A)\) is

The value of \(\left|\begin{array}{lll}1 & b & c+a \\ 1 & c & a+b\end{array}\right|\) is

A person has an initial investment of \(25000\) in an investment plan. After \(2\), years it has grown \(30000\), then the rate of return on his investment is:

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(\sin |x|+\cos |x|) d x\) is

The sum of order and degree of the differential equation \(\left(x^2 \frac{d^2 y}{d x^2}\right)^{\frac{3}{4}}=5\left(\frac{d y}{d x}\right)^2-3\) is equal to :

The real valued function \(f(x)=12 x^{\frac{4}{3}}-6 x^{\frac{1}{3}}, x \in[-8,8]\) has absolute maximum value equal to

The area of the region bounded by the curves \(y=x^2+2, y=-x, x=0\) and x = 1 is :

The electric field E associated with an electromagnetic wave is given by \( E = E_0 \sin(kx - \omega t) \). The speed of the wave is

Match List-l with List-ll

List-l (Birth control methods)	List-II (Features)
(A) Diaphragms	(I) Removal of vas deferens
(B) Lactational amenorrhea	(II) Increase phagocytosis of sperms
(C) Vasectomy	(III) Absence of menstrual cycle and ovulation following parturition
(D) IUDs	(IV) Cover the cervix and blocks the entry of sperm

Choose the correct answer from the options given below:

Evaluate the integral \(\int\left(x^4+x^2+1\right) d\left(x^2\right)\), where C is the constant of integration

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
Which of the following compounds will undergo nucleophilic addition readily?

The brain capacity of Homo habilis was around ______ cc.

Arrange the steps of biopsy and histopathology of tissue involved in detection of cancer.
(A) A thin section of tissue is stained
(B) Freezing of tissue in liquid nitrogen
(C) A piece of the suspected tissue cut into thin sections
(D) Examination under microscope
Choose the correct answer from the options given below: