EASY
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Sum of all real values of x satisfying the equation logplog4x-2+px=x, p>2 is

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Important Questions on Fundamentals of Mathematics

HARD
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IMPORTANT

Let a denote the greatest integer less than or equal to 'a'. The set of all values of  'x' satisfying the inequality,

2x2-4x-7<1+12cosθcosθ2-sinθ22, -π2θ<π2 is

HARD
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IMPORTANT

S1:x+12=[x]  if {x}<12

S2:[nx]=n[x] if {x}<1n

where, · and ·  stands for greatest integer and fraction part functions respectively and n is a natural number

EASY
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IMPORTANT
If y=3[x]+1=4[x-1]-10, where · represents greatest integer function, then x+2y is
HARD
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IMPORTANT
If A, B, C are three decimal numbers and p=A+B+C and q=A+B+C (where · represents greatest integer function). Then maximum value of p-q is:
MEDIUM
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IMPORTANT
Number of solutions of the equation, y+y=2cosx is: (where y=13sinx+sinx+sinx and []=greatest integer function)
MEDIUM
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IMPORTANT
The number of solution of the equations 2x=x+1+x is / are:
MEDIUM
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IMPORTANT
The number of integral solutions of the equations x2-10x+21x2-12x+32=-x2-10x+21x2-12x+32 is/are 
MEDIUM
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If for all positive integers n, we are given that an=n2+20, nN and dn is the highest common factor (H.C.F.) of an+1 and an, then the value of 2n+1dn is (where {.} denotes fractional part function)