CBSE Questions for Class 12 Commerce Applied Mathematics Quantification And Numerical Applications Quiz 11 - MCQExams.com

Single Correct Answer Type
A swimmer wishes to cross a $$500$$-m river flowing at $$5$$ km h$$^{-1}$$. His speed with respect to water is 3 km h$$^{-1}$$. The shortest possible time to cross the river is:
  • 10 min
  • 20 min
  • 6 min
  • 7.5 min
The symbol $$\left| a \right| $$ means $$+a$$ if $$a$$ is greater than or equal to zero and $$-a$$ if $$a$$ is less than or equal to zero; the symbol M means "less than"; the symbol > means "greater than"
The set of values $$x$$ satisfying the inquality $$\left| 3-x \right| <4$$ consists of all $$x$$ such that:
  • $${ x }^{ 2 }<49$$
  • $${ x }^{ 2 }>1$$
  • $$1>{ x }^{ 2 }<49$$
  • $$-1< x< 7$$
  • $$-7< x< 1$$
Choose the correct answer from the alternatives given :
A sum of money is divided among A, B, C and D in the ratio of 3 : 7 : 9 : 13 respectively. If the share of B is Rs. 9180 more than the share of A. then what is the total amount of money of A and C together?
  • Rs. 27540
  • Rs. 26560
  • Rs.26680
  • Rs. 24740
If $$A:B=3:4$$ and $$B:C=2:3$$, then $$A:B:C$$ will be
  • $$3:4:6$$
  • $$3:4:12$$
  • $$4::6$$
  • $$6:4:3$$
Sameer can row certain distance downstream in 24 h and can come back covering the same distance in 36 h. If the stream flows at the rate of 12 km/h. find the speed of Sameer in still water.
  • 30 km/h
  • 15 km/h
  • 40 km/h
  • 60 km/h
A boat takes $$4$$ hours to move $$10\ km$$ and back to starting point in still water. If the river flow velocity is $$2\ km/hr$$, then time taken by the boat to move $$10\ km$$ upstream and back to starting point is approximately
  • $$4\ hours$$
  • $$5\ hours$$
  • $$6\ hours$$
  • $$7\ hours$$
A boat takes two hours to travel 8 km down and 8 km up the river when the water is still. How much time will the boat take to make the same trip when the river starts flowing at 4 kmph?
  • 2 hour
  • 2 hour 40 minute
  • 3 hour
  • 3 hour 40 minute
A boat takes $$2$$ hours to go $$8\ km$$ and come back in still water lake. The time taken for going $$8\ km$$ upstream and coming back with water velocity of $$4\ km/hr$$ is:
  • $$140\ min$$
  • $$150\ min$$
  • $$160\ min$$
  • $$170\ min$$
A motor boat going downstream overcomes a float at a point $$A$$. $$60$$ minutes later it turns and after some time passes the float at a distance of $$12\ km$$ from the point $$A$$. The velocity of the stream is (assuming constant velocity for the boat in still water)
  • $$6\ km\ h^{-1}$$
  • $$3\ km\ h^{-1}$$
  • $$4\ km\ h^{-1}$$
  • $$2\ km\ h^{-1}$$
The velocity of a motorboat with respect to still water is $$7 ms^{-1}$$ and speed of the stream is $$3 ms^{-1}$$. When the boat starts moving upstream a float was dropped from it. The boat travels $$4.2$$ km up stream turned about and caught up with the  float. The time is taken by the boat to reach the float is:
  • 25 mins
  • 30 mins
  • 35 mins
  • 48.125 mins
Solve inequality and show the graph of the solution, $$7x+3 < 5x+9$$ 
A boat covers certain distance between two spots on a river taking $$'t_1'$$ time, going down stream and $$'t_2'$$ time going upstream, what time will be taken by the boat to cover the same distance in still water :-
  • $$\dfrac{t_1 + t_2}{2}$$
  • $$\dfrac{t_1 }{2}$$ + $$\dfrac{3}{4}$$$$t_2$$
  • $$\dfrac{2t_1t_2}{t_1 + t_2}$$
  • $$\dfrac{t_1 + t_2}{2t_1t_2}$$
A boat crosses a river of width 200m in the shortest time and is found to experience a drift of 100m is reaching the opposite bank. The time taken now is 't'. If the same boat is to cross the river by shortest path, the time taken to cross will be:
  • $$2t$$
  • $$\sqrt 2t$$
  • $$3t$$
  • $$\dfrac{2t}{\sqrt 3}$$
A man swimming down stream overcome a flot at a point M. After travelling distance D he turned back and passed the float at a distance of D/2 from the point M. then the ratio of speed of swimmer with respect to still water to the speed of the speed of the river will be.
  • 2
  • 3
  • 4
  • 2.5
If $$x+ 10= y + 14$$, then $$x > y$$.
  • True
  • False
Area of the region {$$(x,y):{x}^{2}+{y}^{2}\le 1\le x+y$$} is
  • $$\dfrac{\pi}{4}+\dfrac{1}{2}$$
  • $$\dfrac{\pi}{4}-\dfrac{1}{2}$$
  • $$\dfrac{\pi}{4}+\dfrac{3}{4}$$
  • $$\pi+1$$
A, B and C are three rafts floating in a river such that they always form an equilateral triangle. A swimmer whose swimming speed is constant swims from A to B then from B to C and finally from C to A along straight lines. Time taken by the swimmer is maximum in swimming: 
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  • from A to B
  • from B to C
  • from C to A
  • it is same in all the parts.
A man rows upstream a distance of $$9\ km$$ or downstream a distance of $$18\ km$$ taking $$3$$ hours each time. The speed of the boat in still water is
  • $$7\dfrac {1}{2}km/h$$
  • $$6\dfrac {1}{2}km/h$$
  • $$5\dfrac {1}{2}km/h$$
  • $$4\dfrac {1}{2}km/h$$
Number of solutions to $$x+y+z=10$$ where $$1\le x,y,z\le 6$$ and $$x,y,z\in N$$.
  • $$35$$
  • $$36$$
  • $$27$$
  • $$66$$
Number of integral solutions of inequality $$|x + 3| > |2x - 1|$$ is 
  • $$3$$
  • $$4$$
  • $$5$$
  • $$2$$
If $$S$$ is the set of all real $$x$$ such that $$\dfrac{2x}{2x^2 + 5x + 2} > \dfrac{1}{x + 1}$$, then $$S$$ is equal to
  • $$(-\infty, \dfrac{-1}{2})$$
  • $$(-\infty, \dfrac{-2}{3})$$
  • $$(-\infty, \dfrac{2}{3})$$
  • $$( \dfrac{2}{3}, \infty)$$
A boat travels a distance of $$80 \ km$$ in $$4$$ hours upstream and same distance down stream in $$2$$ hours in a river. Then the velocities of boat and stream are (in Kmph)
  • $$20, 10$$
  • $$30, 10$$
  • $$30, 20$$
  • None of these
The solution of $$x$$ in the inequation, $$\dfrac{1}{x-3} < 0$$ if $$x \in R$$ is
  • $$x\in (-\infty,3]$$
  • $$x\in (-\infty,3)$$
  • $$x\in (-\infty,-3)$$ $$\cup  (3,\infty)$$
  • $$x\in (-\infty,-3)$$
The value of $$x$$, which satisfies the inequation,  $$\left (\log _{ (1/2) }{ x } \ge \log _{ (1/3) }{ x }\right ) $$ is
  • $$(0,1]$$
  • $$(0,1)$$
  • $$[0,1)$$
  • none
The largest interval among the following for which $${x}^{12}-{x}^{9}+{x}^{4}-x+1> 0$$ is
  • $$-4< x\le 0$$
  • $$0< x< 1$$
  • $$-100< x< 100$$
  • $$-\infty< x< \infty$$
$$x> \sqrt{(1-x)}$$ and $$x<0.5$$ have infinitely many solutions
  • True
  • False
the set of values of $$'x'$$ satisfying the inequation $$|x+5|\geq 10$$ are
  • $$x\in (-15, 5]$$
  • $$x\in (-5, 5]$$
  • $$x\in (-\infty, -15]\cup [5, \infty)$$
  • $$x\in [-\infty, -15]\cup [5, \infty)$$
A man rows a boat with a speed of 18 km/hr in north-west direction. The shoreline makes an angle  of $$15^o$$ south of west. Obtain the component of the velocity of the boat along the shoreline.
  • $$9 \ km/hr$$
  • $$18 \dfrac{\sqrt{3}}{2} \ km/hr$$
  • $$18 cos (15^o) \ km/hr$$
  • $$18 cos (75^o) \ km/hr$$
If z satisfies the inequality $$|z-1-2i| \leq 1$$ , then 
  • $$min (arg (z)) = tan^{-1} (\dfrac{3}{4})$$
  • $$max (arg (z)) =\dfrac{\pi}{6}$$
  • $$min ( |z|) = \sqrt{5}$$
  • $$max ( |z|) = \sqrt{5}$$
If $$|x - 2| + |x + 1| \ge 3$$, then complete solution set of this inequation is 
  • $$[1 , \infty)$$
  • $$(-\infty , -2]$$
  • $$R$$
  • $$[-2 , 1]$$
0:0:1


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