The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x\right) d x\) is:

Let A = {1, 2, 3} Consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} Then R is:

If \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 5\end{array}\right]\) then
Match List-I with List-II

List-I	List-II
(A) \(\operatorname{det}(A)\)	(I) \(-\frac{1}{3}\)
(B) \(\operatorname{det}\left(A^{-1}\right)\)	(II) \(- 12\)
(C) \(\operatorname{det}(2 A)\)	(III) \(- 3\)
(D) \(\operatorname{det}\left( 3 A ^T\right)\)	(IV) \(- 27\)

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The least positive integer \(x\) satisfying \(29 \equiv x(\bmod 5)\) is

Let \(A, B, C\) be matrices of order \(p \times k, 3 \times k\) and \(n \times 3\) respectively, then the conditions on \(n, k\) and \(p\) so that \(A B+C B\) will be defined are :

If \(\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|\), then \(x\) is equal to:

The differential equation representing the family of curves \(y=a \sin (x+b)\), where \(a\) and \(b\) are arbitrary constants is

Question based on the following passage :
P-Block elements are placed in group 13 to 18 in the periodic table. Group 15 is nitrogen family.
Nitrogen can react with hydrogen, oxygen, halogens etc. It shows multiple oxidation states in its various oxides i.e. \(N_2O, N_2O_3, N_2O_5\) etc. Important allotropic forms of phosphorus are white, red and black phosporus. Various compounds of phosphorus are phosphine, \(PCl_3, PCl_5\) and oxoacids of phosphorus. Oxidation states \(+1\) to \(+5\) are seen in various oxoacids of phosphorus. Group 17 elements are collectively known as halogens. Bond dissociation enthalpy of \(F_2\) is smaller than \(Cl_2\).
The gases present in group 18 are chemically unreactive, they form only few compounds. Neil Bartlett (in 1962) observed the reaction of a noble gas. Since then, many noble gas compounds have been synthesised.
The bond angle in \(PH_3\) is less than \(PH_4^+\) due to :

Match List-l with List-II

LIST-I	LIST-II
A. Planck's constant	(I) \(\left[M L^2 T^{-2}\right]\)
B. Work function	(II) \([L]\)
C. Stopping potential	(III) \(\left[M L^2 T^{-3} A^{-1}\right]\)
D. de Broglie wavelength	(IV) \(\left[M L^2 T^{-1}\right]\)

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Select the correct statement.

Light with an energy flux of \( 18 \text{ W/cm}^2 \) falls at normal incidence on a non-reflecting surface of area \( 20 \text{ cm}^2 \). If the light falls for 30 minutes on the surface, find the total momentum delivered to the surface.

If \(x^2-y^2=1\), then which of the following is correct?
(A) \(\left(x^2-1\right)\left(\frac{d y}{d x}\right)^2=x^2\)
(B) \(\left(x^2-1\right)\left(\frac{d^2 y}{d x^2}\right)^2=x^2\)
(C) \(\left(x^2-1\right)^3\left(\frac{d^2 y}{d x^2}\right)^2=x^2\)
(D) \(\left(x^2-1\right)^3\left(\frac{d^2 y}{d x^2}\right)^2=1\)
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What is not true regarding compound \(\text{[B]}\) ?
(A) They are higher boiling liquids than aldehydes and ketones due to extensive H Bonding
(B) They are soluble in Benzene
(C) They produce alkane when heated with soda lime
(D) Produces \(\text{CO}_2\) when treated with \(\text{NaHCO}_3\)
Choose the correct answer from the options given below :