In an intrinsic semiconductor, the relation between the number of holes \( (n_h) \) and conduction electrons \( (n_e) \) will be:

Resonant frequency of a LCR series circuit is 16 kHz. If the capacitance is increased to 16 times, then the new resonant frequency will become

The radius of a wire having resistance R is made half and its length reduced to one - fourth of its original length. The new resistance of the wire will be

A glass prism of angle 60° has an angle of minimum deviation of 30° for a given colour of light. The refractive index of glass for that colour of light is :

Match List-I with List-I

List-I	List-II
A. Electric field outside a uniformly charged thin spherical shell	(I) zero
B. Electric field inside a uniformly charged thin spherical shell	(II) \(\frac{\lambda}{2 \pi \epsilon_0 r} \vec{n}\)
C. Electric field due to an infinitely long straight uniformly charged wire	(III) \(\frac{\sigma}{2 \epsilon_0} \vec{n}\)
D. Electric field due to a uniformly charged infinite plane sheet	(IV) \(\frac{k q}{r^2} \vec{r}\)

Choose the correct answer from the options given below:

Two polaroid \( P_1 \) and \( P_3 \) are placed such that their pass-axis are mutually perpendicular. Another polaroid \( P_2 \) is rotated between \( P_1 \) and \( P_3 \). For what angle \( \theta \) between \( P_1 \) and \( P_2 \) the intensity of light emerging from \( P_3 \) will be maximum ?

Two coaxial solenoids having number of turns per unit length 50 and 200, respectively, have same length 50 cm. The area of cross-section of the two solenoids are \( 4 \, \text{cm}^2 \) and \( 6 \, \text{cm}^2 \), respectively. The mutual inductance of the two solenoids is:

The integral \(I=\int \frac{e^{5 \log _0 x}-e^{4 \log _0 x}}{e^{3 \log _0 x}-e^{2 \log _0 x}} d x\) is equal to:

The interval in which \(f(x)=x^2 e^{-x}+7\) is increasing is :

Arrange the given organisms involved in a food chain in correct sequence ?
(A) Fish
(B) Phytoplankton
(C) Man
(D) Zooplankton
Choose the correct answer from the options given below:

Replacement of Cl of \(C _6 H _5 Cl\) to give \(C _6 H _5 OH\) occurs only in drastic conditions, but Cl of 2,4-dinitrochlorobenzene is readily replaced. This is because:

A reaction takes 30 minutes to complete 50\(\%\) of the reaction and takes 45 minutes to complete 75\(\%\) of the reaction. The order of the reaction is :

Read the given passage carefully and answer the questions
Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
Widal test is used to diagnose