Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

An equilateral triangle is inscribed in the parabola y² = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Find `lim_(x -> 5) f(x)`, where f(x)  = |x| - 5

Suppose f(x)  = `{(a+bx, x < 1),(4, x = 1),(b-ax, x > 1):}`  and if `lim_(x -> 1) f(x) = f(1)` what are possible values of a and b?

Rewrite the following statement with “if-then” in five different ways conveying the same meaning.

If a natural number is odd, then its square is also odd.

Write the contrapositive and converse of the following statements.

If x is a prime number, then x is odd

Write the contrapositive and converse of the following statements.

It the two lines are parallel, then they do not intersect in the same plane.

Write the contrapositive and converse of the following statements.

Something is cold implies that it has low temperature.

Write the contrapositive and converse of the following statements.

You cannot comprehend geometry if you do not know how to reason deductively.

Write the contrapositive and converse of the following statements.

x is an even number implies that x is divisible by 4

Write each of the following statement in the form “if-then”.

You get a job implies that your credentials are good.

Write each of the following statement in the form “if-then”.

The Banana trees will bloom if it stays warm for a month.

Write each of the following statement in the form “if-then”.

A quadrilateral is a parallelogram if its diagonals bisect each other.

Write each of the following statement in the form “if-then”.

To get A⁺ in the class, it is necessary that you do the exercises of the book.

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.

(a) If you live in Delhi, then you have winter clothes.

(i) If you do not have winter clothes, then you do not live in Delhi.

(ii) If you have winter clothes, then you live in Delhi.

(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

State the converse and contrapositive of each of the following statements:

p: A positive integer is prime only if it has no divisors other than 1 and itself.

State the converse and contrapositive of each of the following statements:

q: I go to a beach whenever it is a sunny day.

State the converse and contrapositive of each of the following statements:

r: If it is hot outside, then you feel thirsty.

Write the statement in the form “if p, then q”.

r: You can access the website only if you pay a subscription fee.

Re write each of the following statements in the form “p if and only if q”.

p: If you watch television, then your mind is free and if your mind is free, then you watch television.