-
a gas is contained in a metallic container fited with a piston. the piston is suddenly moved in to compress the gas and is maintained at this positon. as time passes the pressure of the gas in the cylinder : 1) increases 2) d ...
-
NCERT question number 36. chapter - laws of motion. ...
-
6x + 8y = 48 intersects the coordinate axis at A and B respectively. a line L bisects the area and the perimeter of the triangle AOB. where O is the origin. the number of such lines possible is - (a) 1 (b) 2 (c) 3 (d) more th ...
-
find the largest and the smallest 7 digit number formed by the digits from 1 to 9 such that there is no repetition of digits and the number is divisible by all the digits. ...
-
find the number of points (x,y) with positive integral coordinates satisfying the x^2 + y^2 + 2xy - 2005x - 2005y - 2006 = 0. ...
-
Call a set of integers "spacy" if it contains no more than one out of any three consecutive integers. How many subsets of {1, 2, 3, ....... 12}, including the empty set, are spacy? ...
-
find the number of solutions of |[x]-2x| = 4 here [.] denotes the floor function... and |.| denotes modulus.. ...
-
find the solutions to 2x+ 2y + 2z = 2336. here x , y and z are positive integers.. ...
-
A polynomial f(x) has integer coefficients such that f(0) and f(1) are both odd numbers. Prove that f(x) = 0 has no integer solutions. ...
-
Show that the area of a right-angled triangle with all side lengths integers is an integer divisible by 6. ...
-
Show that there is no in finite arithmetic progression consisting of distinct integers all of which are squares. ...
-
if b is a real number satisfying b^4 + (1/b)^4 = 6 find the value of (b+ i/b )^16 where i is iota or √(-1). ...
-
if x+y+z = 1 and 2xy - z^2 = 1 solve for x, y ,z. here x, y, z are real numbers... ...
-
If any 7 numbers( not necessarily distinct ) are chosen from 2 to 12, prove that among those 7 numbers we can get three which form the sides of a triangle. ...
-
In triangle ABC, we are given that 3sin{A}+4cos{B}=6 and 4sin{B}+3cos{A}=1 then find angle C. ...
-
Suppose n be a natural number such that |i+2i2 + 3i3+...+nin|=18√2. find n. ...
-
prove that the tens digit of every power integral power of 3 is an even number. like 3^5 = 243. here it is 4. ...
-
prove that for all odd k (1k + 2k + 3k + ... + nk) is divisible by n(n+1)/2. you may use principal of mathematical induction. ...
-
consider 5-digit numbers formed using the digits 0,1,2,3,4,5 without repetition of digits. Q) the number of numbers divisible by 4 is ? Q) the number of numbers divisible by 12 is? Q) the number of numbers divisible by 15 is ...
-
prove that for a , b , c in [0,infinty) (a - 1/b)(b - 1/c)(c- 1/a) ≥ (a - 1/a)(b - 1/b)( c-1/c). here (a - 1/b) means a/1 - 1/b ...
-
Find all (x, y) where x and y are positive integers such that x^{2007} = y^{2007} − y^{1338} − y^{669} + 2. i found one pair to be (1,1) also 2007 = 3(669) and 1338 = 2(669). don't know but it might help. ...
-
Let a, b, c be positive reals such that a + b + c = 1. Prove that ( a/1 + 1/b )( b/1 + 1/c )( c/1 + 1/a ) ≥ (10/3)3 ...
-
Solve the equation (x^4 + 5x^3 + 8x^2 + 7x + 5)^4 + (x^4 + 5x^3 + 8x^2 + 7x + 3)^4 = 16 in the set of real numbers. ...
-
prove that - tan 2pi/13 + 4sin 6pi/13 = √(13+2√13) ...
-
two arithmetic progressions are a1, a1, a1 ........ and b1, b2 , b3 ......... such that a1 + b1 = 100. also a22 - b21 = b99 - b100. find the sum of 100 terms of the progression (a1 + b1) , (a2 + b2) .......... ...
-
The minimum value of x2 + 2xy + 3y2 – 6x – 2y, where x, y are Real , is equal to (a) –9 (b) –11 (c) –12 (d) –10 ...
-
if (a+2)sinx + (2a-1)cosx = (2a+1) find tanx. the options were (a) 3/4 (B) 4/3 (C) 2a/(a2+1) (D) 2a/(a2-1) well we can see that option B holds. i want the solution. ...
-
find the maximum and minimum value of sinx(sinx+cosx). i got the minimum value as [1-√2]/2 and the maximum value as [1+√2]/2. want to confirm it. ...
-
find all integers a such that (x+a)(x+1991) + 1 can be written as (x+b)(x+c) where b and c are integers themselves. it implies that we have to find all integers a , b and c such that 1991 + a = b + c and 1 + 1991a = bc for so ...
-
Find all primes p and q ,and even numbers n > 2 , satisfying the equation pn + pn-1 + · · · + p + 1 = q2 + q + 1. ...
