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Percentage of free space in cubic close packed structure and in body centred packed structure are respectively

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In a binomial distribution $B(n,p=41 )$, if the probability of at least one success is greater than or equal to $109 $, then n is greater than

Which of the following statements is incorrect regarding physissorptions ?

A capillary tube (A) is drooped in water. Another identical tube (B) is dipped in a soap water solution which of the following shows the relative nature of the liquid columns in the two tubes ?

A body of mass m = 3.513 kg is moving along the x-axis with a speed of $5.00ms_{−1}$. The magnitude of its momentum is recorded as

Consider a uniform sqare plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

The value of $cot(cosec_{−1}35 +3tan_{−1}2 )$is:

Let $I=∫_{0}x sin dxandJ=∫_{0}x cosx dx$Then which one of the following is true?

In an experiment the angles are required to be measured using an instrument 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree $(=0.5_{∘})$, then the least count of the instrument is