Let \(A=\left[\begin{array}{cc}3 & -1 \\ 2 & 4\end{array}\right]\), then \(\operatorname{adjoint}(A)\) is:

\(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\) is equal to

Let \(\Delta = \begin{vmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{vmatrix}\), then \(\Delta\) lies in the interval

General solution of \(\frac{dy}{dx} + \frac{\sqrt{1-y^2}}{\sqrt{1-x^2}} = 0\) is:

Value of \(\int_{-4}^4|x+2| d x\) is :

If \(, A=\left[\begin{array}{ll}x & 3 \\ 2 & 4\end{array}\right], B=\left[\begin{array}{ll}2 & 3 \\ y & 3\end{array}\right]\) and,\(C=\left[\begin{array}{ll}z & 1 \\ 8 & 2\end{array}\right]\) are singular matrices then :
(A) \(x>y\)
(B) \(y>z\)
(C) \(z>x\)
(D) \(x \neq y \neq z\)
Choose the correct answer from the options given below :

If \(x=\frac{1-t}{1+t}\) and \(y=\frac{2 t}{1+t}\), then \(\frac{d^2 y}{d x^2}\) is equal to :

In an AC generator, a coil of 20 turns each with area \( 2 \times 10^{-2} \text{ m}^2 \) is rotated at 50 revolutions per sec in a uniform magnetic field of 2.5 T. The maximum induced emf produced is:

About ______ the first cellular forms of life appeared on earth.

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number. The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
Atomic number of \(\mathrm{V}, \mathrm{Mn}, \mathrm{Cu}\) and Zn is \(23,25,29\) and 30 respectively. Which of them shows a positive value for the standard electrode potential \(E^{\circ}\left(M^{2+} / M\right)\) ?

1. An electron of mass m is moving with kinetic energy k and momentum p. The de-Broglie wavelength associated will be :
(A) \( \lambda = \frac{\sqrt{2mk}}{p} \)
(B) \( \lambda = \frac{p}{h} \)
(C) \( \lambda = \frac{h}{p} \)
(D) \( \lambda = \frac{h}{\sqrt{2mk}} \)
Choose the correct answer from the options given below :

Interstitial transition metal compounds
(A) have higher melting points than those of pure metals.
(B) have more reactivity than those of pure metals.
(C) are non-stoichiometric compounds.
(D) formed when small atoms like H, C or N are trapped inside the crystal lattice of the metals.
Choose the correct answer from the options given below:

Photoelectric current depends on
(A) the intensity of incident light
(B) the potential difference applied between the two electrodes
(C) the nature of the emitter material
(D) the conductivity of the emitter material
Choose the correct answer from the options given below: