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Quantitative Ab...

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  • Question 1
    4 / -1

    Let \(A\) and \(B\) are two sets with two elements each, such that all the four elements are distinct.
    \(A \times B\) is defined as the set of all ordered pairs \((a, b)\) where, \(a \in A\) and \(b \in B\) that is \(A \times B=\{(a, b) \mid a \in A \text { and } b \in B\}\)
    How many subsets are there of the set \(A \times B\) with at least two elements?

  • Question 2
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    For what value of \(a,\) will the equation \(\left(a^{2}-9\right) x^{2}-\left(a^{2}+2 a-3\right) x+a^{2}+a-6=0\) have more than two solutions?

  • Question 3
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    How many positive integral values of \(x x\) are there for which \(_{1} x^{3}-3 x^{2}-10 x+24<0 ?\)

  • Question 4
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    What is the value of \(x x\) for which
    \(\log _{10}\left(2^{x}-x+41\right)=x\left(1-\log _{10} 5\right) ?\)

  • Question 5
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    A sequence \(T_{1}, T_{2}, T 3, \ldots\) is defined as such that \(T_{n}=T_{n-1}-T_{n-2}+T_{n-3}\) for all \(n \geq 4\). If \(T_{1}=16, T_{2}=22, T_{3}=29,\) then find out what will be the value of
    \(\left.T_{148}+T_{155}+T_{166}\right) ?\)

  • Question 6
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    A vessel contains milk and water in the ratio 7 : 3. 3 litres of this mixture is taken out and replaced with water. Again, 2 litres of the mixture is taken out and replaced with water. If the vessel contained 10 litres of milk-water solution initially, then what is the final ratio of milk and water in the vessel?

  • Question 7
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    In a triangle ABC, points P, Q and R lie on side AB, BC and CA respectively such that these points divide these sides in the ration of 1:2, 1:4 and 1:6 respectively. Find out the ratio of the area of triangle PQR to the area of triangle ABC?

  • Question 8
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    On selling 6 bats for Rs.600, a shopkeeper has a loss equal to the cost price of 2 bats. What should be the marked price of a bat if the shopkeeper has to gain a profit of 10% after giving a discount of 10%?

  • Question 9
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    \(\left(\log _{2} x\right)^{2}+3 \log _{2} x-4=0\)
    What is the sum of all the possible values of \(\log _{x} 2 ?\)

  • Question 10
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    Chintu distributed 75% of his birthday cake in the ratio 7 : 8 between his two friends and ate rest of the cake himself. Had he distributed the whole cake in the ratio 4 : 1: 3 among his friends and himself in that order, he would have received 187.5 g of cake extra. What was the total weight of the cake?

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