Ch3 PERMUTATION AND COMBINATION

JEE Question 07

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is


(A) 360 (B) 192 (C) 96 (D) 48
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JEE question

The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is

(A) 133 (B) 190 (C) 233 (D) 105

answer B
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Ch1 Theory Of Equations

The trinomial expression of the form ax2 + bx + c = 0, a ≠ 0 a, b, c are R is called quadratic equation, because the highest order term in it is of second degree. We can say… (a) ax2 + b x + c = 0, a ≠ 0 has exactly two roots which may be real or unequal or equal or complex. (b) If ax2 + b x + c = 0, a ≠ 0 can not have three or more roots & if it has, it becomes an identity. If ax2 + b x + c = 0 is an identity then a = b = c = 0. SOLUTION OF Q.E. Let α and β be the roots of the equation ax2 + b x + c = 0, a ≠ 0. then (a) x1 & x2 = [-b +-(b2 - 4ac)1/2] / 2a (b) b2 - 4ac= D is called Discriminant of the Q.E. (c) (i) Sum of the roots x1 + x2 = – b/a (ii) Product of roots x1.x2 = c/a (d) x2 – (sum of roots) x + (product of roots) = 0 NATURE OR TYPE OF ROOTS D and α , β are the roots of the ax2 + b x + c = 0, a ≠ 0 If D greater than; 0 then roots are real, distinct. If D = 0 then roots are real, equal. If D less than 0 then roots are imaginary. If p + iq is one root of equation, then the other root is p – iq(conjugate of each other). If D is perfect square then the roots are rational. If p + √q is one root of equation, then the other root is p – √q. SIGN OF ROOTS OF Q.E : conditions for sign of roots (a) For Both roots are +ive then (i) D greater than 0 (ii) sum of roots > 0 (iii) product of roots greater than 0 , these three conditions simultaneous true. (b) For Both roots are –ive (i) D greater than 0 (ii) sum of roots less than 0 (iii) product of roots greater than 0 , these three conditions simultaneous true. (c) For one root is +ive & one is –ive (i) D greater than 0 (ii) product of roots less than 0, these two conditions simultaneous true.

Ch2 Progression

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
The conceptual portion is very limited book. But the first problem in the examples itself is complicated. Every problem thereon is a complicated problem.
In Mathematics and Physics, the conceptual portion is going to be limited but the problems are going to be complicated. One has to sit down and do all the problems in examples and exercises to develop the sharp brain that can discover the structure in the problem given in the examination.