Recently Active Mathematics Questions

i feel that the question has some printing errors i am typing the question as given in the book consider \ the \ sequence \ x_n \ defined \ by \ \\ x_1 = \frac{1}{2} ,x_{n+1}=x_n^2 + x_n \\ define \ S = \frac{1}{x_1 +1}+\frac ...

Find the equation of a str line equally inclined to the axes and equidistant from points (1,-2) and (3,4) ...

1) limx→0 x2/sinx.tanx 2) limx→0[ x2/sinx.tanx ] 3) limx→0{ x2/sinx.tanx } 4)Find a,b i) limx→∞( x2+1/x+1 -ax-b)=0 ii) limx→∞( x2-x+1 -ax-b)≥0 ...

sum of the series \frac{1.2}{3!}+\frac{2.2^2}{4!}+\frac{3.2^3}{5!}+............\infty ...

Find the intervals of monotonicity of 1) sin\frac{\pi }{x} 2) (log_{3}x)^{2} + log_{3}x ...

let Zr,r=1,2,3.....n are n distinct roots of eq ^{n}C_{1}x+^{n}C_{2}x^{2}+^{n}C_{3}x^{3}+.......^{n}C_{n}x^{n}=0 in argand plane.If der exist exactly one Zr, rε{1,2....n} such that arg\left(\frac{Z_{r}-(-1+\sqrt{2}i}{(-1)-(- ...

let teh 3 sides of a triangle be integers l,m,n respect...satisfying l>m>n and \left\{\frac{3^{l}}{10^{4}} \right\}= \left\{\frac{3^{m}}{10^{4}} \right\}= \left\{\frac{3^{n}}{10^{4}} \right\} wer {x} is fractional part ...

If a1, a2, a3, a4,..........., a100 are the 100 roots of unity then find the value of \sum_{1\leq i \leq j \leq 100}^{}{} (aiaj)5 . ...

find the least positive integer m such that 22000 divides 2003m-1 ...

*Image* please explain the consequtive steps.... ...

find the product \frac{(1^4 +\frac{1}{4})(3^4 +\frac{1}{4})(5^4 +\frac{1}{4}).......(49^4 +\frac{1}{4})}{(2^4 +\frac{1}{4})(4^4 +\frac{1}{4})(6^4 +\frac{1}{4}).......(50^4 +\frac{1}{4})} ...

i was trying to practise maths but got 1 thing either the buks were 2 easy or it were 2 hard taking the case of trignometry and algebra i used sl loni and hall and knight but found there level easy when i saw arihant ofund it ...

n to the power p -n;divisible by p. p is a prime number. prove it ...

Let P(x)=x^5+ax^4+bx^3+cx^2+dx+e . If the graph of y = P(x) cuts the x-axis at five distinct points and P(0)=0, then which of the coefficients cannot be zero? ...

A sequence is obtained by deleting all the perfect squares from set of natural numbers . Find the remainder when 2003rd term of new sequence is divided by 2048 ?? ...

Q1 A point chosen from 1st quadrant x,y ε[0,4] ,the probablity that it satisfies [x]+[y]=3 is ?? I am getting 1/16 Q2 3 points P,Q,R are selected at random from circumference of circle.Find probablity that they lie on semici ...

prove that \sqrt{(x_1-x_2)^2+ (y_1-y_2)^2}\le \sqrt{x^2_1+y^2_1}+ \sqrt{x^2_2+y^2_2} for all real numbers x_1,y_1,x_2,y_2 HINT: proceed by forming a triangle with suitable coordinates ...

if p and q are the roots of the equation x^2 + px + q =0 then a)--- p=1 b)--- p = 1 or 0 c)--- p = -2 d)--- p = -2 or 0 ...

let S={1,2,3,.......,100} the number of unordered pairs (A,B)of subsets of S such that A and B have no ekements in common , where A or B both may be φ(null set) is ? answer : \frac{3^{100} + 1}{2} the no.of order pair is 310 ...

if \ a+b+c =1 ,; a,b, c \rightarrow R^+ \\ prove \ that \ \\ \\ \sum_{cyclic}{} {\frac{a}{1+bc}}\geq \frac{9}{10} ...

If the number of 5 digit numbers in which each of the digits 2 and 5 occur only once is 64k . Then find the value of k . options --- 150 , 148 , 248 , 128 . ...

sin2 nx ------------------ dx sin2 x ...

A triangle the lengths of whose sides are a,b&c is placed such that the mid points of its sides are on the coordinate axes , if the equation of the plane of the triangle be x/α + y/β + z/γ=1 then (A) α = 1/2 (a2+b2+c2)/2 ...

If x can be any real number, then find the value of \frac{(x-a)(x-b)(x-c)}{(d-a)(d-b)(d-c)}+\frac{(x-b)(x-c)(x-d)}{(a-b)(a-c)(a-d)}+\frac{(x-c)(x-d)(x-a)}{(b-c)(b-d)(b-a)}+\frac{(x-d)(x-a)(x-b)}{(c-d)(c-a)(c-b)} - 1 ...

If the orthocentre of ΔABC formed by the intersection of lines 2x + 3y - 1 = 0, x + 2y - 1 = 0 & ax + by - 1 = 0 is origin, find a, b. ...

Q1 limx→0[ ex-1/x ] Q2 limx→0 { ln(1+x)/x } where [.] =GINT and {.} is fract part ...

a circle is inscribed in a equilateral triangle of side a.find the area of any square inscribed in the circle. ...

FIITJEE HCT-6 Qsn..... If a central conic is represented by the std form ax^2+2hxy+by^2=0 with the condition that tangents at any point have a constant area (=k) of the triangle that they form with the co-ordinate axes, then ...

what are many-many maps......plz give definiton and an example!!!!!! ...

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