The relationship between \(a\) and \(b\) making \(f(x)\) continuous at \(x=3\), where \(f(x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is:

Let \(f(x)=[x]\) and \(g(x)=|x|\). Then gof \(\left(\frac{-5}{3}\right)\) - fog \(\left(\frac{-5}{3}\right)\) where [x] is greatest integer valued function and |x| is modulus function.

\(\int_{-5}^{5} (3x^5 + \sqrt{5} x^3) e^x dx\) is equal to:

If the area of the triangle with vertices \(A(1,3), B(2,0), C(k, 2 k)\) is \(\frac{k^2}{2}\) sq. units, then the value(s) of \(k\) is/are:

If \(A=\left[\begin{array}{ll}x & 3 \\ 2 & y\end{array}\right], \quad B=\left[\begin{array}{cc}2 y & 1 \\ 3 & x\end{array}\right]\) and \(A+2 B=\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]\), then the value of \((x, y)\) is:

Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}\) and \(\vec{b}=-2 \hat{i}+3 \hat{j}-4 \hat{k}\), then which of the following statements are correct?
(A) \(|\vec{a}|=\sqrt{14}\)
(B) \(|\vec{b}|=29\)
(C) \(\vec{a} \cdot \vec{b}=8\)
(D) Angle between \(\vec{a}\) and \(\vec{b}\) is \(\cos ^{-1}\left(\frac{-8}{\sqrt{406}}\right)\)
Choose the correct answert from the option given below :

Area of the region bounded by the curve \(y=\cos x\) between \(x=0, x=\pi\) and \(x\)-axis is :

Arrange the following electrodes in increasing order of strength as an oxidizing agent.
(A) \(Ni ^{2+}+2 e^{-} \rightarrow Ni (s) \quad E^0=-0.25 V\)
(B) \(Cu ^{2+}+2 e^{-} \rightarrow Cu (s) \quad E^0=0.34 V\)
(C) \(Br _2+2 e^{-} \rightarrow 2 Br ^{-} \quad E^0=1.09 V\)
(D) \(O _2(g)+2 H ^{+}+2 e^{-} \rightarrow H _2 O _2 \quad E^0=0.68 V\)
Choose the correct answer from the options given below :

The speed of light in a material medium is given by :

Identify the important features of the semiconductor devices from the following
1. Semiconductor devices require cathode heating for the production of charge carriers.
2. They have long life and high reliability.
3. They are small in size and consume low power.
4. They operate at high voltage.
Choose the correct answer from the options given below:

Which of the following reactions are given by Phenols?
(A) Nitration
(B) Halogenation
(C) Oxidation
(D) Acetylation
Choose the correct answer from the options given above:

Read the given passage carefully and answer the questions
Antibiotics have greatly improved our capacity to treat deadly diseases such as plague, whooping cough (kali khansi), diphtheria (gal ghotu) and leprosy (kusht rog), which used to kill millions all over the globe.
Streptokinase produced by the bacterium Streptococcus and modified by genetic engineering is used as a 'clot buster' for removing clots from the blood vessels of patients who have undergone myocardial infarction leading to heart attack. Microbes are diverse-protozoa, bacteria, fungi and microscopic animal and plant viruses, viroids and also prions that are proteinacious infectious agents. The puffed-up appearance of dough is due to the production of CO₂ gas. Similarly the dough, which is used for making bread, is fermented using baker's yeast (Saccharomyces cerevisiae). Primary sewage treatment basically involve physical removal of particles - large and small from the sewage through filtration and sedimentation. These are removed in stages; initially, floating debris is removed by sequential filtration. Then the grit (soil and small pebbles) are removed by sedimentation. All solids that settle form the primary sludge, and the supernatant forms the effluent. The effluent from the primary settling tank is taken for secondary treatment. The primary effluent is passed into large aeration tanks, where it is constantly agitated mechanically and air is pumped into it. This allows vigorous growth of useful aerobic microbes into flocs. While growing, these microbes consume the major part of the organic matter in the effluent.
Prions are made up of :

In alcohols, C-O-H bond angle is: