The length of the perpendicular from (-1, π/6) to the line is

The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :

Alternatively, we can use the formula for the sum of numbers as
(n - 1)!  (sum of digits)  (11111 ............ntimes). We can also solve this problem by writing all the possible numbers and finding the sum of them which will be time taking and make us confused. We should know that the value of the digits is determined by the place where they were present. We should check whether there is zero in the given digits and whether there are any repetitions present in the numbers. Similarly, we can expect problems to find the sum of numbers formed by these digits with repetition allowed.

Total number of divisors of 480, that are of the form 4n + 2, n  0, is equal to :

We can also solve this question by writing 4n + 2 = 2(2n + 1) where 2n + 1 is always an odd number. So, when all odd divisors will be multiplied by 2, we will get the divisors that we require. Hence, we can say a number of divisors of 4n + 2 form is the same as the number of odd divisors for 480.

If ⁹P₅ + 5 ⁹P₄ = ¹⁰P_r , then r =

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 .