Mathematics Times – July 2019

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Introduction: Definition: Example: Example: Solution: Definition: Example: Introduction: The topic of our discussion is vieta’s ...

Example: Find two roots of the polynomial P(x) = x^2 - 1. What is the degree of P(x)? Solution: r 1 = 1, r 2 = -1. The degree is ...

the roots is n 1 n a a   . Now let’s look at the second equation. The left hand side is a sum of every possible product of a p ...

Example: Solution: Indeed, since both P (x) and G(x) have degree less than 3 (both have degree two), the Identity Theorem tells ...

SECTION- A line y = mx + 1 intersects the circle (x   3)^2 (y 2)^225 at points P and Q. If the midpoint of the line segmen ...

Rn:Rectangle of largest area, with sides parallel to the axes, inscribed in En, n >1. Then which of the following options is/ ...

SECTION- 13. 14. 15. 16. at random and a ball is chosen at random from the bag. Then which of the following options is/a ...

Let AP ( ; )a d denote the set of all the term of an infinite arithmetic progression with first term a and common difference d ...

 ( ) sin^4 cos^4  (6) and  ( ) sin^4  cos^4  2 sin^2  cos^2 (7) The problem is now reduced to minimising these f ...

SECTION- 5.Sol: meets the parabola y x^2 at twopoints B 1,1 and also at F  1,1. The region, say R 1 bounded by the three ...

common eccentricity e is given by 2 2 5 5 1 3 9 3         (5) From (3) and (5), the foci of E are at the points   1 5 ...

7.Sol: It is easy to check (A) by looking at the sign of f x'  for x  , 0. Note that f x x x x x'   54 20 3  30 2  ...

(as      1 n^1   n & n^1  n)      n( ) ( ) n n n            9.Sol: (a,b,d) Points on L 1 a ...

apply the Lagrange MVT to the interval   x,1,1 to get some c x 1  1 ,1 such that    1  1 , 0 ' 1 y x y c x    (4) ...

To find M^1 we use (1). As already noted,    2. Also adj M is given to us. Hence 1 1 1 1 1 1 8 6 2 2 2 5 3 1 M adjM    ...

vanish if the two zero entries are in the same row or the same column because then two columns (or rows) of A would be equal. In ...

^ / 4 2 4 1 1 2 (2 cos 1) I dx x       /4 2 2 4 1 sec 3sec 2 x dx x      put tanx t implies that sec^2 xdx dt ...