JEE Main & Advanced Mathematics Functions Question Bank

done Numerical Value Type Questions - Relations and Functions-I Total Questions - 15

• question_answer1)
  If \[A=\{2,4,5\},\,\,B=\{7,8,9\},\] then \[n(A\times B)\] is equal to
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• question_answer2)
  If the domain of the function \[f(x)={{\left[ {{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right) \right]}^{1/2}}\] is \[a\le x\le b,\] then \[a\,.\,b\] is
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• question_answer3)
  If \[{{e}^{f(x)}}=\frac{10+x}{10-x},\] \[x\in (-10,10)\] and \[f(x)=kf\left( \frac{200x}{100+{{x}^{2}}} \right),\] then k =
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• question_answer4)
  If \[A=\{1,2,3\},\,B=\{4,5,6\}\] and \[C=\{1,2\},\] then the number of elements in the set \[(A-B)\times (A\cap C)\] is
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• question_answer5)
  Sum of the number of elements in the domain and range of the relation R given by \[R=\{(x,y):y=x+\frac{6}{x};\] where \[x,\,\,y\in N\] and \[x<6\}\] is
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• question_answer6)
  Let R be a relation on N defined by \[x+2y=8\]. Then the number of elements in the domain of R is
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• question_answer7)
  The function f satisfies the functional equation \[3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30\] for all real \[x\ne 1\]The value of \[f(7)\] is
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• question_answer8)
  If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is
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• question_answer9)
  If \[2f(x+1)+f\left( \frac{1}{x+1} \right)=2x,\] then \[f(2)\]is equal to
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• question_answer10)
  If \[R=\{(x,y):x,y\in I\] and \[{{x}^{2}}+{{y}^{2}}\le 4\}\] is a relation in I, then the number of elements in the domain of R is
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• question_answer11)
  If \[n(A)=4,\,\,n(B)=3,\,\,n(A\times B\times C)=24,\] then \[n(C)=\]
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• question_answer12)
  The value of \[b-c\] for which the identity \[f(x+1)-f(x)=8x+3\] is satisfied, where \[f(x)-b{{x}^{2}}+cx+d,\] is
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• question_answer13)
  Let \[f(x)=a{{x}^{2}}+bx+c,\] \[g(x)=p{{x}^{2}}+qx+r,\] such that \[f(1)=g(1),\]\[f(2)=g(2)\] and \[f(3)-g(3)=2.\] Then \[f(4)-g(4)\] is
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• question_answer14)
  For a real number x, \[[x]\]denotes the integral part of x. The value of \[\left[ \frac{1}{2} \right]+\left[ \frac{1}{2}+\frac{1}{100} \right]+\left[ \frac{1}{2}+\frac{2}{100} \right]+....+\left[ \frac{1}{2}+\frac{99}{100} \right]\] is
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• question_answer15)
  Number of distinct element in the range of the function \[f(x)=\frac{x+2}{|x+2|}\] is
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