CBSE Questions for Class 12 Commerce Applied Mathematics Quantification And Numerical Applications Quiz 4 - MCQExams.com

The above diagram shows a number line.
The above number line represents the solution for
104653.png
  • $$-3\leq x$$ and $$x> 4$$
  • $$-3< x< 4$$
  • $$-3\leq x< 4$$
  • $$-3< x$$ and $$x\leq 4$$
Solve the system of inequalities: $$\displaystyle \frac{x+7}{x-8}> 2, \frac{2x+1}{7x-1} > 5$$
  • $$(-\dfrac{16}{7}, \dfrac{5}{7})$$
  • $$(-\dfrac{7}{8}, \dfrac{2}{7})$$
  • (2,5)
  • No solution
The solution set for: $$\dfrac{\left | x \right |-1}{\left | x \right |-2}, x\neq \pm 2$$
  • $$(-2, 2)$$
  • $$(-1, 2)\cup (3, \infty )$$
  • $$(-\infty , 2)\cup (2, \infty )$$
  • $$x\:\epsilon\:(-\infty,\infty)-\big\{-2,2\big\}$$
The solution set for: $$\displaystyle \left | 3x-2 \right |\leq \frac{1}{2}$$ is
  • $$\displaystyle \left [\frac{1}{2},\frac{5}{6} \right ]$$
  • $$\displaystyle \left [\frac{2}{3},\frac{1}{2} \right ]$$
  • $$\displaystyle \left [\frac{5}{6},\frac{1}{2} \right ]$$
  • $$\displaystyle \left [\frac{1}{2},\frac{2}{3} \right ]$$
State True or False.
Check whether the following half planes contain the corresponding point:
7x≥2y+x,7x≥2y+x, point (1, 0)
  • True
  • False
State True or False.
Check whether the following half planes contain origin (0,0) or not:
$$2x+5y\geq x+12$$
  • True
  • False
The solution set for: $$\left |\dfrac{2(3-x)}{5}  \right |< \dfrac{3}{5}$$
  • $$(\dfrac{1}{4}, \dfrac{3}{4})$$
  • $$(\dfrac{3}{2}, \dfrac{9}{2})$$
  • $$(\dfrac{1}{2}, \dfrac{3}{2})$$
  • $$(\dfrac{3}{2}, \dfrac{5}{2})$$
Solve: $$\left | 2x-5 \right |< 1$$
  • $$x\in (4, 5)$$
  • $$x\in (3, 5)$$
  • $$x\in (2, 3)$$
  • $$x\in (1, 2.5)$$
If $$\cos x-y^{2}-\sqrt{y-x^{2}-1} \geq 0,$$ then
  • $$ y \geq 1$$
  • $$x \in R$$
  • $$y=1$$
  • $$x=0$$
The range of the values of $$x$$ which satisfies the inequation $$\left(\dfrac{3x+2}{2x+3}\right )\geq 4$$  is
  • $$x\in \left [ -2, -\dfrac{3}{2} \right )$$
  • $$x\in \left ( -2, -\dfrac{3}{2} \right )$$
  • $$x\in \left [ -\dfrac{2}{3}, -\dfrac{3}{2} \right ]$$
  • $$x\in \left [ -2, \dfrac{3}{2} \right ]$$
Form a new inequality from the given inequality by performing the operation stated in brackets.
(a) $$4 >2\left [ \times 5 \right ]$$
(b) $$-4x\geq 32\left [ \div (-4) \right ]$$
  • $$(a)\quad 20 > 10$$
    $$(b)\quad x\le -8\quad $$
  • $$(a)\quad 20 < 10$$
    $$(b)\quad x > 8\quad $$
  • $$(a)\quad 20\le 10$$
    $$(b)\quad x\ge -8\quad $$
  • $$(a)\quad 20\ge 10$$
    $$(b)\quad x\ge -8\quad $$
$$\left |\dfrac{8-n}{3}  \right |\geq 12$$
  • $$28 >n >-28$$
  • $$-28\leq n\leq 28$$
  • $$n\leq -28$$
  • $$n\geq 44$$
Which region is described by the shade in the graph given above?
104766_00f78f632ef64e3bba828a66b7e6eb63.png
  • $$2x+3y=3$$
  • $$2x+3y< 3$$
  • $$2x+3y> 3$$
  • $$-2x+3y< 3$$
Identify the region described by the shaded part in the graph above.
104767.png
  • $$y=4x-6$$
  • $$y\neq 4x-6$$
  • $$y< 4x-6$$
  • $$y> 4x-6$$
For any positive real number 'a', the following results hold.
(i) $$\left | x \right |\leq a\Rightarrow -a\leq x\leq a$$
(ii) $$\left | x \right |\geq  a\Rightarrow x\geq a$$ or $$x\leq a$$
Using the above indentities, evaluate the following:
$$\left |\dfrac{4m-8}{2}\  \right |\leq  6$$
  • $$1\leq m\leq 5$$
  • $$-1\leq m\leq 5$$
  • $$1\leq m\leq -5$$
  • $$-1\leq m\leq -5$$
Given: $$A:B = 3:4$$ and $$B:C = 6:7$$, so $$A: C is 9: 14$$
State true or false.
  • True
  • False
If $$A : B = 3 : 4$$ and $$B : C = 6 : 7$$, then $$A : B : C $$ is $$9 : 12 : 14$$
State true or false.
  • True
  • False
A boat can go across a lake and return in time $${ t }_{ 0 }$$ at a speed $$u$$. On a rough day, there is uniform current at speed $$v$$ to help the onward journey and impede the return journey. If the time taken to go across and return on the rough day be $$t$$, then $$\dfrac{t}{{ t }_{ 0 }}$$ is equal to
  • $$1-\cfrac { { v }^{ 2 } }{ { u }^{ 2 } } $$
  • $$\cfrac { 1 }{ 1-\left( \cfrac { { v }^{ 2 } }{ { u }^{ 2 } } \right) } $$
  • $$1+\cfrac { { v }^{ 2 } }{ { u }^{ 2 } } $$
  • $$\cfrac { 1 }{ 1+\left( \cfrac { { v }^{ 2 } }{ { u }^{ 2 } } \right) } $$
A boat takes $$2$$ hours to travel $$8\ km$$ and back in still water lake. With water velocity of $$4\ { km }/{ h }$$, the time taken for going upstream of $$8\ km$$ and coming back is
  • $$160\ minutes$$
  • $$80\ minutes$$
  • $$100\ minutes$$
  • $$120\ minutes$$
In what ratio must two kinds of tea worth Rs 18 and Rs 28 per kg be mixed so that by selling the mixture at Rs 32 per kg, there may be a gain of 20%.
  • 2 : 13
  • 1 : 13
  • 3 : 14
  • 2 : 3
In an alloy, the ratio of copper to zinc is $$5\,\colon\,2$$. If $$1.250\:kg$$ of zinc is mixed in $$17.500\:kg$$ of alloy, then what will be the new ratio of copper to zinc?
  • $$\;2\,\colon\,1$$
  • $$\;2\,\colon\,3$$
  • $$\;3\,\colon\,2$$
  • $$\;1\,\colon\,2$$
Wind is blowing west to east along two parallel tracks. Two trains moving with same speed in opposite directions have the relative velocity with respect to wind in the ratio $$1 : 2$$. The speed of each train is
176754.png
  • equal to that of wind
  • double that of wind
  • three times that of wind
  • half that of wind
The ratio of the present ages of Sunita and Vinita is $$4\,\colon\,5$$. Six years hence, the ratio of their ages will be $$14\,\colon\,17$$. What will be the ratio of their age $$12$$ years hence?
  • $$\;15\,\colon\,19$$
  • $$\;13\,\colon\,15$$
  • $$\;16\,\colon\,19$$
  • $$\;17\,\colon\,19$$
If $$A : B : C = 2 : 3 : 4,$$ then what is $$\displaystyle \frac{A}{B} : \frac{B}{C} : \frac{C}{A} $$ equal to?
  • $$4 : 5 : 15$$
  • $$3 : 7 : 18$$
  • $$6 : 2 : 21$$
  • $$8 : 9 : 24$$
If $$a : b = 2 : 3$$ and $$b : c = 4 : 5$$, find $$a^2 : b^2 : bc$$.
  • $$4 : 9 : 45$$
  • $$16 : 36 : 45$$
  • $$16 : 36 : 20$$
  • $$4 : 36 : 20$$
Zinc and copper are in the ratio of $$5\,\colon\,3$$ in $$200\:$$ gm of an alloy. How much grams of copper must be added to make the ratio $$3\,\colon\,5$$?
  • $$\;\displaystyle\frac{400}{3}$$
  • $$\;\displaystyle\frac{1}{200}$$
  • $$\;72$$
  • $$\;66$$
If $$Rs.782$$ be divided into $$3$$ parts, proportional to $$\dfrac{1}{2}:\dfrac{2}{3}:\dfrac{3}4$$, then the first part is
  • $$Rs. 182$$
  • $$Rs. 190$$
  • $$Rs. 196$$
  • $$Rs. 204$$
There are $$90$$ multiple choice questions in a test. Suppose you get two marks for every correct answer and for every question you leave unattempted or answer wrongly one mark is deducted from your total score of correct answers. If you get $$60$$ marks in the test, then how many questions did you answer correctly?
  • $$40$$
  • $$60$$
  • $$50$$
  • $$48$$
If $$a\,\colon\,b=5\,\colon\,7$$ and $$c\,\colon\,d=2a\,\colon\,3b$$, then find $$ac\,\colon\,bd$$.
  • $$\;20\,\colon\,38$$
  • $$\;50\,\colon\,147$$
  • $$\;10\,\colon\,21$$
  • $$\;50\,\colon\,151$$
The ratio of a father's age to his son's age is $$4:1.$$ The product of their ages is $$196.$$ What is the ratio of their ages after 5 years?
  • $$11:4$$
  • $$5:3$$
  • $$3:8$$
  • $$6:7$$
0:0:1


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