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 :

A machine costing Rs. \(2,00,000\) has a useful life of 5 years. The estimated scrap value is Rs. 20,000 . By using straight line method, the annual depreciation is

Ravish rowed 40 km downstream in 2 hrs 30 min and returned to the starting point in 5 hrs . What is the speed of the current ?

On 1st April 2024, person ' \(X\) ' purchased a machinery costing ₹ 65000 and spent ₹ 10000 on its installation. The estimated effective life of the machinery is 5 years with a scrap value of ₹ 10000 . The annual depreciation using the straight-line method with the accounting year ending on 31st March 2025 is :

Let \(y=\log _z 5\), then \(\frac{d y}{d x}=\)

If the lines \(\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{\lambda}\) and \(\frac{x}{1}=\frac{y}{2 \lambda}=\frac{z}{3}\) are perpendicular to each other, then \(\lambda\) is equal to

For the problem \(\max Z=a x+b y, x \geq 0, y \geq 0\), which of the following is NOT a valid constraint to make it a linear programming problem?

The probability that in a year of the 22nd century chosen at random, there will be 53 Sundays is:

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) be vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=3,|\vec{b}|=5\) and \(|\vec{c}|=7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is

If \(y=\log _2\left(\log _2 x\right)\), then \(\frac{d y}{d x}\) is equal to :

The unit digit of \(12^{12}\) is :

The major product formed when acetanilide undergoes bromination in presence of acetic acid is:

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.
Metallic radii of some transition elements are as follows:
Fe: 126 pm; Co: 125 pm; Ni: 125 pm; Cu: 128 pm
Which of these elements will have highest density?