The number of proper divisors of . . 15^r is-

If have a common factor then 'a' is equal to

A block C of mass is moving with velocity and collides elastically with block of mass  and connected to another block of mass  through spring constant .What is  if  is compression of spring when velocity of  is same ?

If  then ascending order of A, B, C.

The number of different seven digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is-

We know that there is not much difference between permutation and combination. Permutation is the way or method of arranging numbers from a given set of numbers such that the order of arrangement matters. Whereas combination is the way of selecting items from a given set of items where order of selection doesn’t matter. Both the word combination and permutation is the way of arrangement. Here, we will not use permutation because the order of toys is not necessary.

The centre and radius of the circle are respectively

The centre of the circle is

The equation of the circle with centre at , which passes through the point is

The foot of the perpendicular from on the line is

The foot of the perpendicular from the pole on the line is

The equation of the line parallel to and passing through is

The line passing through the points , (3,0) is

So here we used the concept of the equation of the line passing through two points. Here we also used the trigonometric terms to find the answer using the formulas. So the final solution is .

Statement-I : If  then A=
Statement-II : If  then 

Which of the above statements is true

If b > a , then the equation, (x - a) (x - b) - 1 = 0, has:

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, one of the roots will be in the interval of $\left(-\alpha ,a\right)$ and the other root will be in the interval $\left(b,\alpha \right)$.

If  be that roots  where ,  such that  and  then the number of integral solutions of λ is

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the number of integral solutions of λ is in between 

If α,β then the equation with roots will be

Here we used the concept of quadratic equations and solved the problem. We found the sum and product of the roots first and then proceeded for the final answer. Therefore,  will be the equation for the roots  .