The slope of the normal to the curve \(y=x^3-4 \sin x\) at \(x=0\) is:

Area of the triangle formed by the points (-2, 1), (-3, 2) and (-4, 3) is:

The value of \(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal to (where \(C\) is an arbitrary constant) :

The value of derivative of the function \(\cot ^{-1}\left\{(\cos 2 x)^{1 / 2}\right\}\) at \(x=\frac{\pi}{6}\) is

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

If \(f(x)=\cos 3 x, 0 \leq x \leq \frac{\pi}{2}\), then :
(A) \(f\) is strictly increasing on \(\left[0, \frac{\pi}{3}\right]\)
(B) \(f\) is strictly decreasing on \(\left(\frac{\pi}{3}, \frac{\pi}{2}\right]\)
(C)\(f\) is strictly increasing on \(\left(\frac{\pi}{3}, \frac{\pi}{2}\right]\)
(D) \(f\) is strictly decreasing on \(\left[0, \frac{\pi}{3}\right]\)
(E) \(f\) is strictly increasing on \(\left[0, \frac{\pi}{2}\right]\)
Choose the correct answerfrom the ptions given below:

\(y=e^{x+e^{\infty+e^{x+\cdots \infty}}}\) then \(\frac{d y}{d x}=\) ______________

Read the passage carefully and answer the questions
Many halogen containing organic compounds are present in nature and some of them are clinically useful. These classes of organic compounds find a wide range of applications in our daily life as well as in industries. Many of the polyhalogen compounds are useful too in agriculture. However, some of these compounds cannot be easily decomposed and are thus considered to be environmental hazards. These halo compounds are prepared via different synthetic routes where a variety of organic compounds can be used as substrates such as amines, hydrocarbons etc. They are used as solvents for relatively non-polar compounds. These compounds exhibit substitution and elimination reactions, in addition to their reactions with different metals, which leads to the formation of a versatile starting material for others organic compounds.
The reaction of aryl halide with sodium and dry ether is known as

Which of the following statements are correct:
A. In semiconductor diodes carriers are generated by photo-excitation.
B. When the photo diode is illuminated with light with energy (E) > Energy gap (Eg) of the semiconductor, then electron-holepairs are generated.
C. Photovoltaic devices convert electricity into optical radiation.
D. Photodiode can be used as a photodetector to detect optical signal.
E. Zener diode specification should be taken as per the required output voltage.
Choose the correct answer from the following options given below:

Aspartame is not used in hot drinks as sweetener because :

In a double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then, in the interference pattern:

The electric field at 20 cm from the center of a conducting sphere of radius 2 cm is \( 4.5 \times 10^3 \, \text{N C}^{-1} \). The magnitude of charge on the sphere is:

Which of the following are not involved in intra uterine devices?
(A) Lippes Loop
(B) LNG-20
(C) Saheli
(D) Implants
Choose the correct answer from the options given below: