In series LCR circuit, the rms potential drop across R, L and C are V, 2 V and 2 V volts respectively. The source voltage is:

What is the de Broglie wavelength associated with an electron accelerated through a potential difference of 144 V?

The repetitive use of which of the following logic gate/s separately can be used to prepare an AND gate ?
(A) OR gate
(B) NOT gate
(C) NOR gate
(D) NAND gate
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A small charged water drop with charge \( q = 1.5 \times 10^{-6} \text{ C} \) and mass m = 10 g is suspended in air in electric field E. The value of E is given by (Take acceleration due to gravity \( g = 10 \text{ m s}^{-2} \))

Match List-I with List-II

List-I (Electric Field)	List-II (Expression)
(A) Field due to an infinitely long straight uniformly charged wire	(I) \(\sigma\left(2 \varepsilon_0\right)^{-1}\)
(B) Field due to a uniformly charged thin spherical shell (inside the shell)	(II)\(q\left(4 \pi \varepsilon_0 r^2\right)^{-1}\)
(C) Field due to a uniformly charged infinite plane sheet	(III) \(\lambda\left(2 \pi \varepsilon_0 r\right)^{-1}\)
(D) Field due to a uniformly charged thin spherical shell (outside the shell)	(IV) zero

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A cube of side \( a \) has a charge \( Q \) at each of its vertices. What is the potential due to this charge array at the centre of the cube?

In a semiconductor:
A. there are no free electrons at any temperature
B. there are no free electrons at 0 K (zero Kelvin)
C. the number of free electrons is less than that in a conductor
D. the number of free electrons increases with temperature
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Read the passage carefully to answer the questions given below
Some strains of `Bacillus thuringiensis` produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). In `Bacillus thuringiensis` the toxin is coded by a gene `crylAc` named cry. There are a number of them, for example, the proteins encoded by the genes `crylAc` and `cryllAb` control the cotton bollworms, that of `crylAb` controls corn borer. Using conventional methods of diagnosis (serum and urine analysis, etc.) early detection is not possible. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. The disorder is caused due to the deletion of the gene for adenosine deaminase. `RNAi` takes place in all eukaryotic organisms as a method of cellular defense. This method involves silencing of a specific `mRNA` due to a complementary `dsRNA` molecule that binds to and prevents translation of the `mRNA`.
Which of the following Bt toxin gene controls the corn borer?

If we take \(8\) identical slips of paper and write the number \(0\) on one of them, the number \(1\) on three of the slips, the number \(2\) on three of the slips and the number \(3\) on one of the slips. These slips are folded, put in a box and roughly mixed. One slip is drawn at random from the box. If \(X\) is the random variable denoting the number written on the drawn slip, the variance of \(X\) is:

The sum of order and degree of the differential equation \(\frac{\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2 y}{d x^2}}= p\) is :

Let \(A=\left[a_{i j}\right]_{n \times n}\) and \(B=\left[b_{i j}\right]_{n \times n}\).
Then which of the following is/are true?
(A) \(A B=B A\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=B^T A^T\)
(D) \(A B=0 \Rightarrow A=0\) or \(B=0\)
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Which of the following does not belong to the first transition series ?

Which of the following statements are correct?
(A) On dilution, conductivity of all the electrolytes decreases.
(B) On dilution, the number of ions per unit volume decreases.
(C) Molar conductivity increases with dilution.
(D) Limiting molar conductivity is the conductivity at a very high concentration.
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