The area of the region enclosed between the parabolas \(y^2 = x + 1\) and \(y^2 = -x + 1\) is:

If the present value for a sequence of payments made at the end of each 6 months and continuing forever is ₹6000. If the money is worth 4% compounded semi-annually, then, the value of sequence of payment made is:

If \(A\) is a square matrix such that \(A^2=A\), then the value of \((I-A)^2-(I+A)^3\) is :

If \(x=4 t^2, y=8 t\), then \(\frac{d^2 y}{d x^2}\) is:

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 3 with \(|A|=2\) and let \(C=\left[C_{i j}\right]\), where \(C_{i j}\) is the cofactor of \(a_{i j}\) in \(A\). Then \(|C|\) is equal to :

The relation \(R\) on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is

The direction ratios of the perpendicular from the point \((1,0,1)\) to the plane \(x-y+z=0\) are :

Answer the question on the basis of passage given below :
Formaldehyde is the first member of the aldehydic series. It is present in green leaves of plants where its presence is supposed to be due to the reaction of \(CO_2\) with water in the presence of sunlight and chlorophyll. Commercially, formaldehyde is obtained by the controlled oxidation of methane in the presence of molybdenum oxide (\(MoO\)) acting as a catalyst. Formaldehyde is a constituent of a number of polymers also called resins. These are non volatile solids or semi solids which are obtained directly from certain plants and can be synthesized in the laboratory.
Match List I with List II

LIST I	LIST II
A. Bakelite formaldehyde resin	I. Condensation polymers
B. Melamine formaldehyde resin	II. Phenol and formaldehyde
C. Urea formaldehyde resin	III. Melamine and formaldehyde
D. Bakelite \(\&\) Melamine formaldehyde resin	IV. Unbreakable cups and laminated sheets

Choose the correct answer from the options given below:

If \(A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}\) and \(I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\), then the value of k so that \(A^2 = 6A + kI\) is given by:

The transfer of integral number of ___________ is one of the evidence of quantization of electric charge.

If the vectors \(\vec{a}=3 \hat{i}-p \hat{j}+5 \hat{k}\) and \(\vec{b}=-6 \hat{i}+14 \hat{j}+q \hat{k}\) are collinear, then the value of \(p\) and \(q\) are :

Find the least non-negative remainder obtained when \(3^{128}\) is divided by \(7\) .

Common oxidation state of lanthanoids is: