CONCEPT:

The equation of a line whose slope is m and which makes an intercept c on the Y-axis is given by: y = mx + c

CALCULATION:

Here, we have to find the equation of a line which intersects the y-axis at a distance of 3 units above the origin and makes an angle of 30° with the positive direction of the x-axis.

As we know that, equation of a line whose slope is m and which makes an intercept c on the Y-axis is given by: y = mx + c

CONCEPT:

Let us suppose a be the first term and d be the common difference of an AP. Then the nth term of an AP is given by:a_n = a + (n - 1) × d.

Note: If l is the last term of a sequence, then l = a_n = a + (n - 1) × d.

CALCULATION:

Here we have to find two digit numbers which are divisible by 7.

i.e 14, 21,............,98 is an AP sequence with first term a = 14, common difference d = 7 and the last term l = 98.

As we know that, if l is the last term of a sequence, then l = a_n = a + (n - 1) × d

⇒ 98 = 14 + (n - 1) × 7

⇒ 84 = 7(n - 1)

⇒ 12 = n - 1

⇒ n = 13

Concept:

tan (180 + θ) = tan θ

Calculation:

We have to find the value of tan 225°

⇒ tan 225° = tan (180 + 45)° = tan 45° = 1

We know that,

Mode refers to the most frequently occurring number in a set of numbers.

The given set of numbers is 3, 1, 4, 1, 1, 6, 6, 3, 3, 1, 1, 6

In the above set of numbers, 1 appears most frequently i.e. 5 times.

∴ 1 is the mode of the given set of numbers.