The area (in square units) bounded by the curve \(y=\cos x\) between \(x=0\) and \(x=2 \pi\) in first quadrant is equal to :

The minimum value of \(Z = 2x + y\) subjected to \(x + y ≥ 10, 2x + 3y ≤ 26, x, y ≥ 0\) is

Ajesh has set up a sinking fund in order to have ₹ 10,00,000 after 10 years for his son's education. The amount should be set aside at the end of every 6 months into an account paying \(5\%\) per annum compounded half yearly is : [given \((1.025)^{20}=1.6386\) ]

If \(f: R \rightarrow R\) is defined by \(f(x)=x^2-3 x+2\) then \(f(f(x))\) is :

In the following matrix equation, the value of \(x\) is :
\(\left[\begin{array}{cc}x+y & 4 \\ -5 & 3 y\end{array}\right]=\left[\begin{array}{cc}3 & 4 \\ -5 & 6\end{array}\right]\)

The value of integral \(\int_0^1 \sqrt{1-x^2} d x\) is :

\(y=x(x-3)^2\) decreases for the value of \(x\) given by

Which one of the following codons performs a dual function?

Identify the incorrect statement(s) among the following:
when a dielectric medium is introduced between the plates of a charged capacitor:
(A) If a plate of dielectric constant k, thickness t is placed between the plates of a charged capacitor of area A and distance d, then the new capacitance will be \( \frac{A\varepsilon_0}{d - t(1 - 1/k)} \)
(B) The electric field between plates of the charged capacitor when the dielectric is introduced will be \( E = (E_0 - E_p) \)
(C) Dielectric constant of the dielectric placed between plates of charged capacitor will be \( k = \frac{E_0}{E_0 - E_p} \)
(D) Dielectric strength of the dielectric is the maximum value of the electric field which may be applied before its breakdown.
Choose the correct answer from the options given below :

A die is thrown again and again until three sixes are obtained. The probability of obtaining third six in sixth throw of the die is:

Grignard reagent should be prepared under anhydrous condition because

When a ray of light enters a glass slab from air :

Match List I with List II

LIST I	LIST II
A. Wheat	I. Perisperm
B. Black pepper	II. Polyembryony
C. Cashew	III. Albuminous seed
D. Citrus	IV. False fruits

Choose the correct answer from the options given below: