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Sets, Relations and Functions Mock Test for JEE

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Q1MathsUnit 1: Sets, Relations and Functions
If f:[0,∞)→[0,∞),\mathbf{f}:[\mathbf{0}, \infty) \rightarrow[\mathbf{0}, \infty), and f(x)=x1+x\mathbf{f}(\mathbf{x})=\frac{\mathbf{x}}{\mathbf{1}+\mathbf{x}} then f\boldsymbol{f} is
Q2MathsUnit 1: Sets, Relations and Functions
Let f:R→R\boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} where f(x)=2∣x∣−2−x\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2}^{|\boldsymbol{x}|}-\boldsymbol{2}^{-\boldsymbol{x}} then f(x)f(x) is
Q3MathsUnit 1: Sets, Relations and Functions
If X={4n−3n−1:n∈N}\boldsymbol{X}=\left\{4^{n}-3 n-1: n \in N\right\} and Y={9(n−1):n∈N},\boldsymbol{Y}=\{\mathbf{9}(\boldsymbol{n}-\mathbf{1}): \boldsymbol{n} \in \boldsymbol{N}\}, where N\mathrm{N} is the set of natural numbers, then X∪Y\boldsymbol{X} \cup \boldsymbol{Y} is equal to:
Q4MathsUnit 1: Sets, Relations and Functions
Which of the following is NOT equivalent to p→q?\boldsymbol{p} \rightarrow \boldsymbol{q} ?
Q5MathsUnit 1: Sets, Relations and Functions
The price of 357 mangoes is Rs.1517.25. What will be the approximate price of 49 dozens of such mangoes?
Q6MathsUnit 1: Sets, Relations and Functions
Indian cricket team won 4 more matches than it lost with New Zealand. If it won 35\frac{3}{5} of its matches, how many matches did India play?
Q7MathsUnit 1: Sets, Relations and Functions
Assertion The relation R\boldsymbol{R} given by R={(1,3),(4,2),(2,4),(2,3),(3,1)}\boldsymbol{R}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\} on a set A={1,2,3,4}A=\{1,2,3,4\} is not symmetric. Reason For symmetric relation R=R−1\boldsymbol{R}=\boldsymbol{R}^{-1}
Q8MathsUnit 1: Sets, Relations and Functions
Find the quantifier which best describes the variable of the open sentence x2+2≥0x^{2}+2 \geq 0
Q9MathsUnit 1: Sets, Relations and Functions
9/169 / 16 of a number is 51 greater than 50%50 \% of the number. Then, that number is
Q10MathsUnit 1: Sets, Relations and Functions
Let f(x)=2100x+1\boldsymbol{f}(\boldsymbol{x})=\mathbf{2}^{100} \boldsymbol{x}+\mathbf{1} g(x)=3100x+1\boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3}^{100} \boldsymbol{x}+\mathbf{1} Then the set of real numbers x such that f(g(x))=x\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=\boldsymbol{x} is
Q11MathsUnit 1: Sets, Relations and Functions
Let ff be a function such that f(3)=1f(3)=1 and f(3x)=x+f(3x−3)f(3 x)=x+f(3 x-3) for all xx Then find the value of f(300)\boldsymbol{f}(\boldsymbol{3 0 0})
Q12MathsUnit 1: Sets, Relations and Functions
Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.
Q13MathsUnit 1: Sets, Relations and Functions
Which of the following is a singleton set?
Q14MathsUnit 1: Sets, Relations and Functions
35 workers can build a house in 16 days. How many days will 28 workers working at the same rate take to build the same house?
Q15MathsUnit 1: Sets, Relations and Functions
0.86×0.86×0.86+0.14×0.14×0.10.86×0.86−0.86−0.14+0.14×0.1\frac{0.86 \times 0.86 \times 0.86+0.14 \times 0.14 \times 0.1}{0.86 \times 0.86-0.86-0.14+0.14 \times 0.1} is equal to

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