The value of \(\tan ^{-1} 5+\tan ^{-1} 3-\cot ^{-1} \frac{4}{7}\) is :

A mobile phone costing ₹ 50000 has a useful life of 5 years. If the annual depreciation is ₹ 5000, then by using a linear method, its scrap value is

The value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos ^2 x d x\) is:

Ram can row a boat in still water at the rate of 6 km/hr. He finds that it takes him twice as long to row upstream of a river as to row downstream of the same river, then the speed of the current of the river is

If \(a , b , c\) are the lengths of the sides of a triangle and \(\left|\begin{array}{ccc}a^2 & b^2 & c^2 \\ (a+1)^2 & (b+1)^2 & (c+1)^2 \\ (a-1)^2 & (b-1)^2 & (c-1)^2\end{array}\right|=0\) then :

A spherical ice ball is melting at the rate of \(100 \pi \mathrm{~cm}^3 / \mathrm{min}\). The rate at which its radius is decreasing when its radius is 15 cm, is

Function \(f(x)=x^x, x>0\) decreases on the interval

In the Cell reaction :
\(Mg ( s )+2 Ag ^{+}( aq ) \rightarrow Mg ^{2+}( aq )+2 Ag ( s )\)
\(E _{\text {cell }}^{\circ}=3.17 V\). By doubling the concentration of \(Mg ^{2+}, E _{\text {cell }}\) is :

The adaptive radiation is represented by which of the following?
(A) Darwin's finches
(B) Koala and Wombat
(C) Tiger cat and Sugar glider
(D) Spotted cuscus and lemur
(E) Anteater and Numbat
Choose the correct answer from the options given below :

Read the given passage and answer the question given below.
The sex linked recessive disease, which shows its transmission from unaffected carrier female to some of the male progeny has been widely studied. In this disease, a single protein that is a part of the cascade of proteins involved in the clotting of blood is affected. Due to this in an affected individual a simple cut will result in non-stop bleeding. The heterozygous female (carrier) for the disease may transmit it to sons. The possibility of a female becoming a sufferer of disease is extremely rare because mother of such a female has to be at least carrier and the father should be sufferer. The family pedigree of Queen Victoria shows a number of suffering descendents as she was a carrier of the disease.
Man who is sufferer of the disease marries a woman who is a carrier of this disease. What percentage of children born as carrier of this disease?

Select the correct statements regarding the menstrual cycle in females:
(A) The first menstruation begins at puberty and is called menopause.
(B) Ovulation occurs mid-cycle (around day 14) when progesterone level is maximum.
(C) In absence of fertilization, corpus luteum degenerates and causes breakdown of endometrium, starting a new cycle.
(D) In humans, menstrual cycle stops around the age of 50 years.
Select the correct answer from the options given below:

Which of the following is helpful in removing oil stains from the clothes ?

The reagent involved in Lucas test is