If the area bounded by the curve \(y^2 = 16x\) and the line \(y = mx\) is \(\frac{2}{3}\) sq. units, then the value of m is:

The value of which of the following integrals is zero?
(A) \(\int_0^1 x d x\)
(B) \(\int_{-1}^1 x d x\)
(C) \(\int_{-1}^1 x^2 d x\)
(D) \(\int_0^1 \log \left(\frac{x}{1-x}\right) d x\)
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Given equation of the plane is \(5x + 2y - 3z = 17\). Then,
A. A point \((2, 2, -1)\) lies on the plane
B. The direction cosines of normal to plane are \((2, 2, -1)\)
C. Coordinates of foot of perpendicular from origin are \((5, 2, -3)\)
D. The plane does not pass through the origin
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Area of the region bounded by the curve \(x^2=4 y, x\)-axis and \(x=3\) is:

The degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\) is :

The function \(f(x)=\left\{\begin{array}{ll}\frac{|x|}{x}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0\end{array}\right.\) is:

A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is:
[Given that (1.6) \({ }^{\frac{1}{5}}=1.098\) ]

Exine of pollen grains has prominent apertures where sporopollenin is absent are known as:

Spin free complex among the following is :

Roman numbers in the names of restriction enzymes indicate -

Match List-I with List-II

List-I (Name of Compound)	List-II (Application)
(A) Neutral Ferric Chloride	(I) Anaesthetic
(B) Methanol	(II) Detection of Phenolic group
(C) Diethylether	(III) Wood Spirit
(D) Acetylsalicylic acid	(IV) Analgesic

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The statements are not true for allergy :
(A) Allergy is due to release of chemicals like histamine and serotonin
(B) Allergens are the subtances which cause allergy
(C) The antibodies produced due to allergens are IgA type
(D) Adrenalin and steroids quickly enhance the symptoms of allergy
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Answer the question on basis of passage given below :
Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.

List - I	List - II
A. Mn2+	I. Yellow
B. \(F e 3+\)	II. Green
C. \(N i 2+\)	III. Blue
D. \(Cu 2+\)	IV. Pink

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