Recently Active Mathematics Questions

Q1 let f:R→R be defined as f(x)= x2+ax+1/x2+x+1 .the set of all exhasutive values of a for which f(X) is onto ans given is φ..it is wrong naa ?? Q2 whats min value of (sin-1(sin(x)))2-sin-1(sin(x)) Q3 if f(x)=x(2-x), 0≤x ...

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1-\frac{1}{4}+\frac{1}{7}-\frac{1}{10}+\frac{1}{13}-\frac{1}{16}............. not a doubt[4] hint-think DI ...

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not a doubt: find the no. of non-negative integral solutions of the equation where N is a whole number x+y+z+w ≤ N give the shortest method ...

it was a simple sum but its aftermath wa too much d/dx of under root 1-cos2x/1=cos2x (means whole function under root) easily solved it to tan^x now under root means tan x so answer sec^2 x simple but not the right answer ans ...

Discuss continuity of e[log{l{x2}l2}] and draw its graph where all brackets have their usual meaning... dont hesitate to tell me if it is not solvable at our level ...

Out of (m+1) given integers two of them can always be chosen such that there (a) difference is divisible by m (b) Sum is divisible by m (c) Product is divisible by m (d)none of these ...

If AB = a, AD = b, AC = 2b+ 3c & the area of quadrialteral ABCD is β times the area of ||gm whose adjacent sides are a, b. find the value of β. Here, a represents vector a, AC represents vector AC. ...

Is this solvable ?? Find no of ways by which we can stack 12 coins in a line so that each coin lies on table or on 2 coins ...

A stack of 2000 cards is labeled with the integers from 1 to 2000, with different integers on different cards. The cards in the stack are not in numerical order. The top card is removed from the stack and placed on the table, ...

If both product and sum of 2 positive reals are integers, are these reals necessarily integers individually? ...

f(x)=x2-4x g(x)=min f(t) ; x≤t≤x+1 ; 0≤x<4 i know this type ahs been discussed before...but i just need graph to check myself....no calculations....[1] ...

Is the function F(x) = x^3+C ; where C belongs to positive real numbers including 0 ; always strictly increasing at (0,0) ?? please explain !! ...

(Not a Doubt) [4] Find the no. of ways in which 5-A(s) & 6-B(s) can be arrranged in a row which reads the same Backwards. ...

limn→∞sin2(π (n!)2-n! ) ...

Q1 \int_{a}^{b}\frac{e^{x/a}-e^{b/x}}{x}dx Q2 \int_{0}^{1}\frac{lnx.ln(1-x)}{(1+x)^2}dx ...

The value of the definite integral I = ∫ [ 0 to Π][ x (1+l cos x l ) ] dx = ? (A) 2 2 Π(B) 2 Π(C) 2 Π(D) 4 Π...

Great question --- a must try , In how many parts an integer N >= 5 should be dissected so that the product of the parts is maximized ? Hint …….----- After getting the answer , you will immediately realize why the cond ...

Great question , specially Nishant sir very much liked it , I would ask him not to give the answer , unless and until everyone tries :) Find the total number of integers p , q , r such that the number , 2 p + 3 q + 5 r is a m ...

If set of values of 'a' for which f(x) = ax2 - (3+2a)x + 6 , a≠0 is positive for exactly 3 distinct negative integral values of x is (c,d] then the value of (c2 + 16 d2) is equal to ----------?? ...

not a doubt if a digit is removed frrom the left of a natural number n, the resultant is n/57 find the sum of digits of n ...

∫e^x(1+sinx)/(1+cosx) ...

MULTIPLE ANS QS 1) Lt x--->2 [(f(x) -9) / (x-2)] = 3 Then Ltx-->2f(x) is ? (A) 2 (b)5 (C) 9 (D)12 ...

Think its a A . Dasgupta question --- anyhow a good one --- there are two methods actually -- lets see Prove that the eqn . a0 x5 + a1 x4 + a2 x3 + a3 x2 + a4 x + a5 = 0 cannot have all real roots if 2 a12 - 5 a2 < 0. ...

f(x) = tan-1 [(x2 + 1) / (x2 + √3)] 1) Range contains NO natural no. 2) Range contains atleast one integer TRUE/FALSE ...

1) f(x) = i) Sin[x] ; [x] ≠0 [x] ii) 0 when ; [x] = 0 Find -- Lim (x→0) f(x). 2) Lim(x→∞) {(x+6)/(x+4)}x+4 = ? 3) If x>0, Lim(x→0) {(sinx)1/x +(1/x)sinx} = ? 4) Lim(x→ -∞) {x4 Sin(1/x) +x2}/{1+ lx3l } = ? ...

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plz solv ethese???? 1)if a,b ,c are real a+b+c=0,then quadratic equation 3a^2+2bx+cx=0 has- a)at lest 1 root in [0,1] b)at least one root in [1,2] ...