CBSE Questions for Class 12 Commerce Applied Mathematics Quantification And Numerical Applications Quiz 6 - MCQExams.com

If p : q = r : s = t : u = 2 : 3 then what is (mp + nr + ot) : (mq + ns + ou) equal to?
  • 2 : 3
  • 5 : 6
  • 7 : 9
  • 2 : 5
If x is an integer greater than-10, but less than 10 and $$\displaystyle \left | x-2 \right |<3,$$ then the values of x are 
  • $$\displaystyle -10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,$$
  • $$\displaystyle 0,1,2,3,4,5,6,7,8,9,10,$$
  • $$\displaystyle 0,1,2,3,4,$$
  • $$\displaystyle -1,0,1$$
If x : a = y : b = z : c then
$$\displaystyle \frac{ax-by}{\left ( a+b \right )\left ( x-y \right )}+\frac{by-cz}{\left ( b+c \right )\left ( y-z \right )}+\frac{cz-ax}{\left ( c+a \right )\left ( z-x \right )}$$ is equal to
  • 1
  • 2
  • 3
  • 0
A leak in the bottom of the tank can empty it in $$6$$ hr. A pipe fills the tank at $$4$$ ltr/min. When the tank is full the inlet is opened but due to the leak, the tank is emptied in $$8$$ hour. What is the capacity of the tank ?
  • $$5,260 L$$
  • $$5,760 L$$
  • $$5,846 L$$
  • $$6,970 L$$
The solution set of inequality $$\displaystyle 2 sin^2 x - 5 sin x + 2> 0 if x \varepsilon [0, 2 \pi] is
  • $$\displaystyle [0, \frac {\pi}{6}]$$
  • $$ \left[\dfrac {5 \pi}{6}, 2 \pi\right]$$
  • $$\displaystyle \left[0, \frac {\pi}{6} \right] \cup \left[\frac {5 \pi}{6}, 2 \pi\right]$$
  • None of these
A boat takes $$2$$ hours to go $$8 \;km$$ and come back in still water lake. With velocity of $$4\;km/hr$$, the time taken for going upstream of $$8\;km$$ and coming back is 
  • 140 minutes
  • 150 minutes
  • 160 minutes
  • 170 minutes
A boy is now $$a$$ years old, and his father is $$5a$$ years old. What will the father be when the boy is $$3a$$ years old? How old was the father when the boy was born?
  • $$7a, 4a$$ years
  • $$4a, 10a$$ years
  • $$12a , 3a $$ years
  • $$15a, 3a $$ years
The complete solution set of the inequation $$\displaystyle x-\frac{2(k-1)}{5}\leq \frac{2}{3k}(x+1)$$ given by 
  • $$\displaystyle (-\infty ,2)$$ if $$\displaystyle k>\frac{2}{3}$$
  • $$\displaystyle [-\infty ,2)$$ if $$\displaystyle k>\frac{2}{3}$$
  • $$\displaystyle (-\infty ,2]$$ if $$k < 0$$
  • All of these
If $$a, b, c, d$$ are positive real numbers, such that $$a + b + c + d = 2$$, then $$M = (a + b) (c + d)$$ satisfies the 
  • $$\displaystyle 0\leq M\leq 1 $$
  • $$\displaystyle 1\leq M\leq 2 $$
  • $$\displaystyle 2\leq M\leq 3 $$
  • $$\displaystyle 3\leq M\leq 4 $$
If $$p,q$$ and $$r$$ are positive real number, then the quantity $$\dfrac{( p + r )}{ ( q + r)}$$ is 
  • $$> \dfrac{p}{q}$$ if $$p > q$$
  • $$= \dfrac{p}{q}$$ if $$p > q$$
  • $$> \dfrac{p}{q}$$ if $$p < q$$
  • $$< \dfrac{p}{q}$$ if $$p >q$$
If $$\displaystyle l^{2}+m^{2}+n^{2}=5,$$ then $$( lm + mn + ln)$$ is 
  • $$\displaystyle \geq (-5/2)$$
  • $$\displaystyle \geq (-1)$$
  • $$\displaystyle \geq 5$$
  • Option A & C both
In $$\triangle ABC$$, if $$D$$ is a point in $$BC$$ and divides it in the ratio $$3:5$$ i.e., if $$BD:DC=3:5$$ then, $$ar(\triangle ADC) : ar(\triangle ABC) =?$$
  • $$3:5$$
  • $$3:8$$
  • $$5:8$$
  • $$8:3$$
Solve for $$\displaystyle x: \left | x + 4 \right |< 12$$
  • $$\displaystyle \left [ -16,7 \right ]$$
  • $$\displaystyle \left ( -16,4 \right ]$$
  • $$\displaystyle \left [ -16,3 \right )$$
  • $$\displaystyle \left ( -16,8 \right )$$
The speed of motor boat in still water $$20\ km/hr$$ and river flow is $$5\ km/hr$$. A float is dropped from the boat when it start moving upstream. After moving $$1.5\ km$$ the boat returns back. The boat will catch the float (from initial instant) after 
  • $$6\ min$$
  • $$12\ min$$
  • $$10\ min$$
  • $$15\ min$$
Let $$a, b, c, x, y, z$$ be positive real numbers such that $$a+b+c = x+y+z$$ and $$abc = xyz.$$ Further, suppose that $$a \leq x < y < z \leq c$$ and $$a < b < c.$$ then $$a = x, b = y,$$ and $$c = z$$
  • True
  • False
A motor ship covers the distance of 300 km between two localities on a river in 10 hrs downstream and in 12 hrs upstream. Find the flow velocity of the river assuming that these velocities are constant. 
  • 2.0 km/hr
  • 2.5 km/hr
  • 3 km/hr
  • 3.5 km/hr
Solve for $$x:$$ $$\displaystyle \left | 3x+2 \right |\geq 7 $$
  • $$\displaystyle \left ( -\infty  ,-3  \right ]\cup \left [ \frac{5}{3},\infty  \right )$$
  • $$\displaystyle \left ( -\infty  ,-\dfrac53  \right ]\cup \left [3,\infty  \right )$$
  • $$\displaystyle \left ( -3,0  \right ]\cup \left [ \frac{5}{3},\infty  \right )$$
  • $$\displaystyle \left ( -5 ,-3  \right ]\cup \left [ \frac{5}{3},\infty  \right )$$
solve for $$\displaystyle x:\left | x-3 \right |> 4$$
  • x < - 1
  • x > 7
  • x < 2
  • (1) or (2)
If $$\displaystyle \left | x + 7 \right |> -8$$  then find the solution set
  • Q
  • N
  • W
  • R
$$\displaystyle 12\frac{3}{10}=$$_________
  • 12.10
  • 10.3
  • 12.3
  • 123.10
What are the real values of x that satisfy the inequations $$6x + 9 < 3x +5$$ and  $$4x + 7 > 2x - 5$$?
  • $$\displaystyle \left ( -6,\frac{-4}{3} \right )$$
  • $$\displaystyle \left (\frac{-2}{3},5 \right )$$
  • $$\displaystyle \left (\frac{7}{3},10 \right )$$
  • $$\displaystyle \left (-5,\frac{2}{3}\right )$$
Which of the following number line represents the solution of the inequality
$$-6x + 12 > -7x + 17$$ ?
Solve the inequality. Write the solution set in interval notation.
$$\left|5-4x\right| > 8$$
  • $$\left( \displaystyle\frac { 3 }{ 4 } , -\displaystyle\frac { 13 }{ 4 } \right) $$
  • $$\left( -\infty ,-\displaystyle\frac { 3 }{ 4 } \right) \cup \left( \displaystyle\frac { 13 }{ 4 } ,\infty \right) $$
  • $$\left( -\infty ,\displaystyle\frac { 1 }{ 4 } \right) \cup \left( -\displaystyle\frac { 15 }{ 4 } ,\infty \right) $$
  • $$\left( -\displaystyle\frac { 13 }{ 4 } ,-\displaystyle\frac { 3 }{ 4 } \right) $$
Solve the rational inequality. Write the solution set in interval notation.
$$\displaystyle\frac{1}{x+10} > 0$$
  • $$\left( -\infty ,10 \right) $$
  • $$\left( 10,-\infty \right) $$
  • $$\left( -10,\infty \right) $$
  • $$\left[ 10,\infty \right] $$
Solve the polynomial inequality. Express the solution set in interval notation.
$$13x^2-5x\le 0$$
  • $$(-\infty,0)\cup\left(\dfrac{5}{13},\infty\right)$$
  • $$\left(0, -\dfrac{5}{13}\right)$$
  • $$(-\infty,0)\cup\left[-\dfrac{5}{13},\infty\right]$$
  • $$\left[0, \dfrac{5}{13}\right]$$
$$\displaystyle\frac { 5 }{ x } >3$$
  • $$(-\infty,\dfrac 53)$$
  • $$(-\infty,\dfrac 43)$$
  • $$(-\infty,\dfrac 57)$$
  • None of these
$$\displaystyle\frac { 5x-8 }{ x-5 } \ge 2$$
  • $$[-\dfrac 23,5] \cup [5,\infty]$$
  • $$(-\infty,-\dfrac 23]\cup(5,\infty)$$
  • $$[-\dfrac 23,5)$$
  • None of these
Solve the following inequality. $$\displaystyle \frac{x-1}{x+2}<0$$
  • $$-2< x < 1$$
  • $$-2< x < 7$$
  • $$-4< x < 1$$
  • None of these
The point which does not belong to the feasible region of the LPP:
Minimize: $$Z=60x+10y$$
subject to $$3x+y \ge 18$$
$$2x+2y \ge 12$$
$$x+2y\ge 10$$
$$x,y \ge 0$$ is
  • $$(0,8)$$
  • $$(4,2)$$
  • $$(6,2)$$
  • $$(10,0)$$
Solve the following inequality. $$\displaystyle \frac{a-1}{a}>0$$
  • $$a < 0$$ or $$a > 1$$
  • $$a < 0$$ or $$a > 5$$
  • $$a < 0$$ or $$a > 2$$
  • None of these
0:0:1


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