Explore topic-wise InterviewSolutions in Class 11.

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your Class 11 knowledge and support exam preparation. Choose a topic below to get started.

1.

Write the following statements in the form of "if -then". (i) you get a job implies your credibility are good. (ii) a quadrilateral is a prallelogram if its diagonals biset each other. (iii) to get a grade in the class, it is necessary that you do all the exercise of the book.

Answer» (3)(i) if you get a job, then your credibility are good.<br> (ii) if diagonals of a quadrilateral bisect each other, then it is a parallelogram.<br> (iii) if you get A grade in the class, then you do all the exercises in the book.
2.

Check the validity of the statements given below by the method given against it.(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).(ii) q: If n is a real number with `n &gt; 3`, then `n^2&gt;9

Answer» (i) True<br> (ii) True
3.

Write the contrapositive converse and inverse of the following statements: (i) if two lines are paralllel, then they do not interest in the same plane. (ii) something is hot implies that it has high temperature. (iii) if x is an odd number, then it is prime. (iv) if x is an even number, then it is divisible by 2. (iv) if the diagonals of a rectangle intersect at `90^@`, then it is a rhombus.

Answer» (2). Contrapositive statements :<br> (i) if two lines intersect in a plane , then they are not parallel.<br> (ii) if something has not high temperature, then it is not hot.<br> (iii) if x is not a prime number, then it is not odd.<br> (iv) if x is not divisible by 2 then it is not even.<br> (v) if a rectangle is not a rhomus, then its diagonal does not intersect at `90^@`.<br> Converse statements : (i) if two lines does not intersect in a plane, then they are parallel.<br> (ii) if something has not high temperature, then it is hot.<br> (iii) if x is not a prime number, then it is odd.<br> (iv) if x is not divisible by 2, then it is an even number.<br> (v) if a rectangle is a rhomus, then its diagonal intersect at `90^@`.<br> opposite statements :<br> (i) if two lines are not parallel, then they intersect in a plane.<br> (ii) if something is not hot, then its temperatureis not high.<br> (iii) if x is not an odd number,then it is not prime.<br> (iv ) if x is not an even number, then it is not divisible by 2.<br> (v) if the diagonals of a rectangle does not intersect at `90^@` then it is not a rhombus .
4.

Some statements are given 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 do not have winter clothes, then you do not live in delhi. (b) if a quadrilateral is a parallelogram, then its diagonals biset each other. (i) if the diagonals of a quadrilateral do not biset each other, then the quadrilateral is not a parallelogram. (ii) if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Answer» (4) (a) (i)contrapositive<br> (ii) converse<br> (b)(i) contropositive<br> (ii) converse
5.

Write the contrapositive of the following statements : (i) if you born in india, then you are a citizen of India. (ii) If a triangle is equilateral, then it is isosceles.

Answer» the contrapositive statements are :<br> (i) if you are not a citizen of india, then you were not born in india.<br> (ii) if a triangle is not isosceles, then it is not equilateral.
6.

Which of the following statements are true and whihc are false? In each case give a valid reason for saying so. (i) p: each radius of a circle is a chord of the circle. (ii) q: the centre of a circle bisects each chord of the circle. (iii) r: circles is a particular case of an ellipse.(iv) s : if x and y are integeres such that `xgty` , then `-xlarry`. (v) t: `sqrt(11)` is a rational number.

Answer» (i) Given statement : each radius of a circle is a chord of the circle.<br> `because` A chord meets the circle at two different points but the radius meets the circle at one point only .<br> `therefore` Any radius of the circle cannot be the chord of the circle .<br> Therefore, given statement is false.<br> (ii) Given statement : the centre of a circle bisects each chord of the circle.<br> `because` only the diameter of a circle is a circle is a chord at which the centre of the circle lie. centre does not lie on the other chords.<br> `therefore` centre does not bisect all chords.<br> therefore, given statement is false.<br> (iii) Given statement: circle is a particular case of an ellipse.<br> Equation of ellipse `: (x^2)/(a^2)+(y^2)/(b^2)=1`<br> If `a=b` then<br> `(x^2)/(a^2)+(y^2)/(a^2)=1rArrx^2+y^2=a^2`<br> which is the equation of a circle.<br> `rArr` circle is a particular case of ellipse.<br> (iv) Given statement : if x and y are integers such that `xgty` then `-xlarry`.<br> from the law of inequations `xgtyrArr-xlarry`<br> therefore , given statement is true.<br> (v) Given statement : `sqrt(11)` is a rational number. every rational number can be expressed in the form `(P)/(q)` where p and q are integers and `q ne 0`.<br> But `sqrt(11)` cannot be expressed in the form `(p)/(q)`.<br> `therefore` Given statement is false.
7.

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 clothes. (ii) if you have winter clothes, then you its 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 paralleogram.

Answer» (a) (i) Contrapositive (ii) Converse<br>(b) (i) Contrapositive (ii) Converse
8.

Which of the following is a statement ?A. x is a real numberB. Switch off the fanC. 6 is a natural numberD. Let me go

Answer» Correct Answer - C<br>As we know a statement is a sentence which is either true of false.<br> So, 6 is a natural number , which is true<br> Hence it is a statement .