CBSE Questions for Class 12 Commerce Applied Mathematics Quantification And Numerical Applications Quiz 3 - MCQExams.com

Which of the following could be the graph of all values of $$x$$ that satisfy the inequality $$2-5x\le -\cfrac{6x-5}{3}$$
Solution set of inequality $$4x+3<5x+7$$ is $$(-4, \infty)$$.
  • True
  • False
If $$A : B: C = 2 : 3 : 4$$, then $$\dfrac {A}{B} :\dfrac {B}{C} : \dfrac {C}{A}$$ is equal to
  • $$4 :9 : 16$$
  • $$8 : 9 : 12$$
  • $$8 : 9 : 16$$
  • $$8 : 9 : 24$$
A man swims to and fro along the bank of a river with a velocity v relative to water. If the velocity of flow is u,the average speed of the man (for to and motion)is 
  • $$ \frac { v^2-u^2 }{ v } $$
  • $$ \sqrt { uv } $$
  • $$ \frac { u+v }{ 2 } $$
  • $$ \frac { v^2-u^2 }{ 2v } $$
The value of $$x$$ for which $$12 x - 6 < 0$$ and $$12 - 3 x < 0$$
  • $$\phi$$
  • $$R$$
  • $$R - \{ 0 \}$$
  • $$None$$
The ratio of coins of $$1\ Rs\ 50$$ paise and $$25$$ pasie in a bag is $$4 : 5 : 6$$. If total number ofcoins is $$ 120$$ then the number of coins of $$25$$ paise 
  • $$None\ of\ these$$
  • $$48$$
  • $$40$$
  • $$32$$
A diamond price is proportional to square of its weight it gets broken onto $$4$$ pices with its weight in the ratio $$1:2:3:4$$. The total price of diamond after breaking is $$70000$$ less than the diamond in original.What was the price of the original diamond?
  • $$70,000$$
  • $$1,00,000$$
  • $$1,40,000$$
  • $$none\ of\ these$$
A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body
  • It will slowly come back to its earlier position
  • It will remain submerged, where it is left.
  • It will sink
  • It will come out violently
A motor boat covers the distance between two places on a river and returns in $$14 \ hrs$$. If the velocity of the boat in still water is $$35 \ km/h$$ and velocity of water in the river is $$5 \ km/h$$, then the distance between the two places is
  • $$100 \ km$$
  • $$240 \ km$$
  • $$220\  km$$
  • $$180\  km$$
If $$\left | x-2 \right |=p$$, when x < 2, then $$x-p=$$
  • -2
  • 2
  • $$2-2p$$
  • $$2p-2$$
Wind is blowing from west to east along two parallel tracks. A train is moving on each track in opposite directions. They have same speed when no wind is blowing. Now, one train has speed double that of the other. The speed of each train is
  • Equal to that of wind
  • Double that of wind
  • Three times that of wind
  • Half of that of wind
The mean of 45, 38.5, 42.4, 44.3, 35.8, 39.1, 41.5, 39.4 is.
  • 44.3
  • 35
  • 40.7
  • 29.6
An aeroplane flies along a straight line from A to B with a speed $$v$$$$_{0}$$ and back again with the same speed $$v$$$$_{0}$$. A steady wind $$v$$ is blowing. If $$AB = l$$ then
  • total time for the trip is $$\dfrac{2v_{0}l}{v_{0}^{2}-v^{2}}$$ if wind blows along the line AB
  • total time for the trip is $$\dfrac{2l}{\sqrt{v_{0}^{2}-v^{2}}}$$, if wind blows perpendicular to the line AB
  • total time for the trip decrease because of the presence of wind
  • total time for the trip increase because of the presence of wind
A motor ship covers the distance of $$300 km$$ between two localities on a river in $$10$$ hours downstream and in $$12$$ hours upstream. Find the flow velocity of the river assuming that these velocities are constant.
  • 2.0 km/h
  • 2.5 km/h
  • 3 km/h
  • 3.5 km/h
A boat takes $$2 h$$ to travel $$8 km$$ and back in still water. In a lake with water velocity of $$4 km/h$$, the time taken for going upstream of $$8 km$$ and coming back is
  • $$120 min$$
  • $$160 min$$
  • $$200 min$$
  • none of these
The width of river is 1 km. The velocity of boatis 5 km/hr. The boat covered the width of riverwith shortest will possible path in 15 min. Thenthe velocity of river stream is :
  • 3 km/hr
  • 4 km/hr
  • $$\sqrt { 29 } km/hr$$
  • $$\sqrt { 41 } km/hr$$
Solve the linear inequations and represent the solution set on the number line.
(a) $$9\geq 7x-5\geq 5x-11,x\in R$$

(b) $$-2\le \cfrac{1}{2}-\cfrac{2x}{3}\leq 1\cfrac{5}{6},x\in N$$
  • (a) $$\left [ -3,1 \right ]$$

    (b) $$\dfrac{15}{4}\geq x\geq -2$$
  • (a) $$\left [ 0,2 \right ]$$

    (b) $$\dfrac{15}{4}\geq x\geq -2$$
  • (a) $$\left [ -3,2 \right ]$$

    (b) $$\dfrac{15}{4}\geq x\geq -2$$
  • (a) $$\left [ 0,5 \right ]$$

    (b) $$\dfrac{15}{4}\geq x\geq -2$$
The range of values of $$x$$ satisfying the following inequation, $$\dfrac{1}{2-\left | x \right |}\geq 1$$ is
  • $$x\in [-2,-1]\cup [1,2]$$
  • $$x\in (-2,-1)\cup (1,2)$$
  • $$x\in (-2,-1]\cup (1,2]$$
  • $$x\in (-2,-1]\cup [1,2)$$
Identify solution set for $$\left | 4-x \right |+1< 3$$
  • $$(2,3)$$
  • $$(2,6)$$
  • $$(3,6)$$
  • $$(4,3)$$
What is the solution set for $$\dfrac{\left | x-2 \right |}{x-2}> 0$$?
  • $$(2, \infty )$$
  • $$(-\infty ,-2)$$
  • $$(-\infty ,0)$$
  • (0,2)
What is the solution set for $$\left |\dfrac{2x-1}{x-1}  \right |> 2$$?
  • $$(\frac{-3}{4},1)\cup (1,\infty )$$
  • $$(\frac{3}{4},1)\cup (1,\infty )$$
  • $$(\frac{1}{4},1)\cup (1,\infty )$$
  • $$(\frac{5}{4},1)\cup (1,\infty )$$
7 - 3 (1 - y) = - 5 + 2x
  • Area of triangle: $$18\,\,sq.\,units$$ and co-ordinate axes:(1,-3)
  • Area of triangle: $$73\,\,sq.\,units$$ and co-ordinate axes:(1,-3)
  • Data insufficient
  • None of these
Represent the set of real values of x on the number line satisfying $$\dfrac{1}{2}(2x-1)\leq 2x+\dfrac{1}{2}\leq 5\dfrac{1}{2}+x$$. Also, find the greatest and the values of x satisfying the inequations.
  • $$x\in \left [ 1,5 \right ]$$
  • $$x\in \left [ -1,5 \right ]$$
  • $$x\in \left [ -4,3 \right ]$$
  • $$x\in \left [ 4 ,3 \right ]$$
Solve the following inequality:
 $$\dfrac{3x-1}{5}\leq 2-\dfrac{x+1}{3}$$
  • $$x\leq 2$$
  • $$x> 2$$
  • $$2$$
  • $$0$$
What is the solution set for $$\dfrac{2x+3}{3x-7} >0$$
  • $$\left(-\infty ,-\dfrac{1}{2}\right)\cup \left(\dfrac{2}{3},\infty \right)$$
  • $$\left(-\infty ,-\dfrac{3}{2}\right)\cup \left(\dfrac{7}{4},\infty \right)$$
  • $$\left(-\infty ,-\dfrac{3}{2}\right)\cup \left(\dfrac{7}{3},\infty \right)$$
  • $$\left(-\infty ,-\dfrac{1}{2}\right)\cup \left(\dfrac{7}{4},\infty \right)$$
Identify the solution set for $$\dfrac{1}{\left | x \right |-3}< \dfrac{1}{2}$$
  • (-3,2)
  • $$(-\infty ,-5)\cup (5,\infty )$$
  • $$(5,\infty )$$
  • $$(-\infty ,-5)\cup (-3,3)\cup (5,\infty )$$
Solve the following inequalities: $$\dfrac{1}{\left | x \right |-3}< \dfrac{1}{2}$$
  • $$(-\infty ,5)\cup (5,\infty )$$
  • $$(-\infty ,-5)\cup (5,\infty )$$
  • $$(\infty ,-5)\cup (5,\infty )$$
  • None of these
Identify the solution set for $$\dfrac{7x-5}{8x+3} >4.$$
  • $$\dfrac{-17}{25},\dfrac{-3}{8}$$
  • $$\dfrac{-5}{7},\dfrac{-3}{8}$$
  • $$\dfrac{-31}{28},\dfrac{-3}{8}$$
  • $$\dfrac{-13}{15},\dfrac{-3}{8}$$
The solution set for $$\left | x \right |> 7$$ is
  • $$(-\infty ,-7)$$
  • $$(7, \infty )$$
  • $$(-\infty ,-7)\cup (7, \infty )$$
  • $$(-\infty ,-7]\cup [7, \infty )$$
Solve the following inequalities: $$\dfrac{\left | x+2 \right |-x}{x}< 2$$
  • $$(1,\infty )$$
  • $$(-\infty,-1 )$$
  • $$(-\infty,-0 )$$
  • None of these
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