The angle between the planes whose equations are \(4 x+8 y+z=8\) and \(y+z=4\) is:

If \(95 \%\) confidence interval for the population mean was reported to be 140 to 150 and \(\sigma=25\), then the size of the sample used in this study is:
[Given: \(Z_{0.025}=1.96\) ]

For \(x \in\left(0, \frac{\pi}{2}\right), \int \frac{\sin x+\cos x}{\sqrt{\sin 2 x}} d x\) is equal to

Match List-I with List-II

List I (Function)	List II (Derivative with respect to ' x ')
(A) \(f(x)=x^x\)	(I) \(a x^{a-1}\)
(B) \(f(x)=a^x\)	(II) 0
(C) \(f(x)=a^a\)	(III) \(a^x \log _e a\)
(D) \(f(x)=x^a\)	(IV) \(x^x\left(1+\log _e x\right)\)

Choose the correct answer from the options given below:

The feasible region represented by the constraints \(x+2 y \geq 100,2 x-y \leq 0.2 x+y \leq 200, x \geq 0, y \geq 0\) of an LPP is

If A and B are two matrices of order 2 × 2 such that A is a symmetric matrix and B is a skew-symmetric matrix, then:

The effective rate that is equivalent to a nominal rate of \(12 \%\) compounded quarterly is :

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

Answer the question on the basis of passage given below :
All transition elements display typical metallic properties like high melting point, boiling point, tensile strength, high malleability and ductility, luster, etc. Their metallic character increases down the group and elements of \(4 d\) and 5d series exhibit higher metallic characters. They show variable oxidation states and forms a number of coloured compounds due to the presence of unpaired electrons which shows d-d transitions and makes them paramagnetic.
Which of the following will be coloured in aqueous medium?

A \(\beta\)-particle is moving perpendicular to the uniform electric field created by a potential difference of \( 6 \times 10^3 \text{ V} \) across parallel metal plates separated by a distance of 6 cm. What is the acceleration of the beta particle between the plates? (Mass of electron = \( 9.1 \times 10^{-31} \text{ kg} \))

Answer the question on the basis of passage given below :
Strong oxidising agents oxidise toluene and its derivatives to benzoic acid. However, it is possible to stop the oxidation at the aldehyde stage with suitable reagents that convert the methyl group to an intermediate that is difficult to oxidise further.
Conversions that can be done by same reagent are:
(A) Benzaldehyde to 2-nitrobenzaldehyde
(B) Propan-1-ol to propanal
(C) Pent-3-en-2-ol to pent-3en-2-one
(D) Butanal to Butan-1-ol
(E) Methanal to Ethanol
Choose the correct answer from the options given below :

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, \(3 d\) series ( \(S c\) to Zn), \(4 d\) series (Y to Cd), \(5 d\) series ( La and Hf to Hg ) and 6d series which has \(A c\) and elements from \(R f\) to \(C n\). The two series of the inner transition metals; \(4 f\) (Ce to Lu) and \(5 f\) (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of \(s\) and \(p\)-block elements. 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. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
The highest oxidation states shown by V , Fe and Ni respectively are __________ .

Identify the correct statements:
(A) A magnetic field exerts force on a moving charge and not on a stationary charge.
(B) A moving charge produces a magnetic field.
(C) The magnetic field at a point on the axis of a current element is zero.
(D) Magnetic field \( \vec{B} \) is tangential to a magnetic field line.
Choose the correct answer from the options given below: