The area of the region bounded by \(y=|x-5|, x=0\) and \(x=1\) is :

The maximum value of \(\frac{\log x}{x}\) for \(x\) in \([2, \infty)\) is :

The order of \(\sqrt{1+\left(\frac{d y}{d x}\right)^2}=\left[a \frac{d^2 y}{d x^2}\right]^{\frac{1}{3}}\) is

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

Maximum value of \(z=5 x+4 y\) subject to the constraints \(x-y \leq 0, x+y \leq 4, x \geq 0, y \geq 0\) occurs at the point \((a, b)\). Then \(4 a+5 b=\) \(\_\_\_\_\) ,

A die is tossed 6 times and getting 1 or 5 is considered a success.
The probability of getting at least one success in six tosses is:

If the events A and B are independent, then which of the following statements are true?
(A) \(P\left(A^{\prime} \cap B\right)=[1-P(A)] P(B)\)
(B) A and B are mutually exclusive
(C) P(A) = P(B)
(D) \(P\left(A^{\prime} \cap B^{\prime}\right)=[1-P(A)][1-P(B)]\)
Choose the correct answer from the options given below:

An element \( \Delta \vec{l} = 0.5 \hat{j} \text{ cm} \) is placed at the origin and carries a large current \( I = 10 \text{ A} \). The magnetic field at point (50 cm, 0) is

Choose the most appropriate option about the presence of nitrogenous bases; Cytosine, 5-methyl uracil and Uracil.

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.
The two strongest oxidising agents among the oxides will be :
A. \(MoO _3\)
B. \(CrO _3\)
C. \(Mn _2 O _7\)
D. \(WO _3\)
E. \(VO _2\)
Choose the correct answer from the options given below:

The maximum value of the \(f(x)=\frac{1}{4 x^2+2 x+1}\) is :

The solution set of the inequality \(3 x+5 y<15\) is :

What will be the number of genotypes and phenotypes obtained in \(F _2\) generation when male parent RRyy is crossed with female parent rrYY?