 # ISC Class 11 Maths Important Questions

The purpose of learning mathematics goes much beyond the prevailing idea of improved proficiency in test scores. Mathematics provides us with the crucial ability to learn and think reasonably. A solid foundation in mathematics helps in developing the skills of interpreting data, identifying patterns, investigating proof and working out problems. ICSE class 11 Maths Important Questions is a very significant study material for students preparing for ICSE Class 11 examination. Question from important topics of the ICSE Class 11 syllabus is covered here.

### The Important Questions of ISC Class 11 Maths are given below:

1. If 𝛼 and 𝛽 are the roots of the equation , find
2. In how many ways can 12 books be arranged on a shelf if:
1. 4 particular books must always be together.
2. 2 particular books must occupy the first position and the last position.
3. An urn contains 60 blue pens and 40 red pens. Half of the pens of each one is defective. If one pen is chosen at random, what is the probability that it is a defective or a red pen?
4. Find the domain and range of: 2 – |x − 4|
5. Prove that
6. Using Mathematical induction, prove that is divisible by 9 for an nϵN.
7. If z = x + iy and |2z − 1| = |z + 2i|, find the locus of z and represent it in the argand diagram.
8. A Committee of 6 members has to be formed from 8 boys and 5 girls. In how many ways can this be done if the Committee consists of :
1. Exactly 3 girls
2. At least 3 girls
9. How many different words can be formed of the letter of word “GRANDMOTHER”, so that:
1. The word starts with G and end with R.
2. The letters A, N, D are always together.
3. All vowels never come together.
10. Find the equation of acute angled bisector of lines: 3x – 4y + 7 = 0 and 12x – 5y – 8 = 0
11. Find the equation of the circle which passes through the points (2, 3), (4, 5) and the centre lies on the line y – 4x + 3 = 0.
12. Differentiate the function Sin (2x – 3) by First Principle of differentiation.
13. The sum of three consecutive numbers of a G.P is 56. If we subtract 1, 7 and 21 from these numbers in the order, the resulting numbers form an A.P., find the numbers.
14. Find the mean, standard derivation for the following data:
 Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 Frequency 2 3 5 10 3 5 2
15. Find the coordinates of a point on =8x, whose focal distance is 4.
16. Prove that:

~(P⇒q) = P^(~q)

17. Write Converse and inverse of the given conditional statement: If a number n is even, then is even.
18. Find the centre, focus, eccentricity and latus rectum of the hyperbola 16 – 9 = 144.
19. In what ratio the point P(–2, y, z) divides the line joining the points A(2, 4, 3) and B(–4, 5, –6). Also, find the coordinates of point P.
20. If the origin is the centroid of the triangle with vertices (–4, 2, 6) (2a, 3b, 2c) and (8, 14, –10) find the values of a, b and c.