CBSE Questions for Class 12 Commerce Applied Mathematics Quantification And Numerical Applications Quiz 15 - MCQExams.com

If for any real x, we have $$-1\leq\displaystyle  \frac{x^2+nx-2}{x^2-3x+4}\leq 2$$, then $$n$$ belongs to.
  • $$\left[-\sqrt{40}+6, -1\right]$$
  • $$\left[-\sqrt{40}+6, \sqrt{40}-6\right]$$
  • $$\left[-1, \sqrt{40}-6\right]$$
  • None of these
The acceleration experienced by a moving boat after its engine is cut-off, of given by: a = -kv$$^3$$ where k is a constant. If $$v_0$$ is the magnitude of velocity at cut-off, then the magnitude of the velocity at time t after the cut-off is :-
  • $$\cfrac { v_0 }{ 2ktv_0^2 }$$
  • $$\cfrac { v_0 }{ 1 + 2ktv_0^2 }$$
  • $$\cfrac { v_0 }{\sqrt { 1 - 2ktv_0^2 }}$$
  • $$\cfrac { v_0 }{\sqrt  {1 + 2ktv_0^2 }}$$
Rs. $$3200$$ is divided among $$A, B$$ and $$C$$ in the ratio of $$3:5:8$$ respectively. What is the difference (in Rs.) between the share of $$B$$ and $$C$$?
  • $$400$$
  • $$600$$
  • $$800$$
  • $$900$$
The set of values satisfying the inequation $$\left(x+3\right){\left(3x-2\right)}^{5}{\left(7-x\right)}^{5}{\left(5x+8\right)}^{2}\ge0$$
  • $$\left(-\infty,-3\right)\cup\left(\frac{2}{3},7\right)\cup\left\{-\frac{8}{5} \right\} $$
  • $$\left(-\infty,-3\right]\cup\left[\frac{2}{3},7\right]\cup\left\{-\frac{8}{5} \right\} $$
  • $$\left[-\infty,-3\right]\cup\left[\frac{2}{3},7\right]\cup\left\{-\frac{8}{5} \right\} $$
  • $$\left[-\infty,-3\right)\cup\left[\frac{2}{3},7\right)\cup\left\{-\frac{8}{5} \right\} $$
A man swimming downstream overcomes a float 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 river will be:
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
The ratio of the distance carried away by the water current, downstream, in crossing a river, by a person, making same angle with downstream and upstream is $$2 : 1$$. The ratio of the speed of person to the water current cannot be less than
  • $$1/3$$
  • $$4/5$$
  • $$2/5$$
  • $$4/3$$
A man can swim in still water with a speed of $$2\ ms^{-1}$$. If he wants to cross a river of water current speed $$\sqrt {3}\ ms^{-1}$$ along shortest possible path, then in which direction should he swim?
  • At an angle $$120^{\circ}$$ to the water current
  • At an angle $$150^{\circ}$$ to the water current
  • At an angle $$90^{\circ}$$ to the water current
  • None of these
A boat covers a certain distance between two spots in a river taking $$t_1$$ hrs going downstream and $$t_2$$ hrs going upstream. What time will be taken by boat to cover same distance in still water ? 
  • $$\dfrac{t_1+t_2}{2}$$
  • $$2(t_2=t_1)$$
  • $$\dfrac{2 t_1 t_2}{t_1+t_2}$$
  • $$\sqrt{t_1 t_2}$$
A swimmer crosses a flowing stream of width $$'\omega'$$ to and fro in time $$t_1$$. The time taken to cover the same distance up & down the stream is $$t_2$$. if $$t_3$$ is the time swimmer would take to swim a distance $$2\omega$$ in still water, then:
  • $$t^2_1 = t_2t_3$$
  • $$t^2_2 = t_1t_3$$
  • $$t^2_3 = t_1t_3$$
  • $$t_3 = t_1 + t_2$$
The boys and girls in a college are in the ratio $$3:2$$. If $$20\%$$ of the boys and $$25\%$$ of the girls are adults, the percentage of students who are not adults is?
  • $$58\%$$
  • $$67.5\%$$
  • $$78\%$$
  • $$82.5\%$$
The ratio of the incomes of $$A, B$$ and $$C$$ is $$3 : 7 : 4$$ and the ratio of their expenditure is $$4 : 3 : 5$$. If in the income of $$Rs. 2400$$, A saves $$Rs. 300$$ then the savings of $$B$$ and $$C$$ is respectively are
  • $$Rs. 4025$$ and $$Rs. 575$$
  • $$Rs. 1575$$ and $$2625$$
  • $$Rs. 2750$$ and $$Rs. 1025$$
  • $$Rs. 3725$$ and $$Rs. 1525$$
A man can swim with a speed of $$3m/s$$ in still water and river flows at the rate of $$5m/s$$. River width is $$500m$$
1075325_33c0544005f946f397177d3351dd7ca4.png
  • For shortest path journey $$\theta =\tan^{-1}\dfrac{4}{3}$$
  • For shortest path journey $$\theta =\tan^{-1}\dfrac{3}{4}$$
  • time taken for shortest path journey is $$3\dfrac{17}{36}\ min$$
  • time taken to cross river in shortest time is $$2\dfrac{28}{36}\ min$$
A boat moves along the flow of of river between two fixed points P and Q. It takes 40 minutes when going downstream and takes 120 minutes when going upstream between these two points. What time it will take in still water to cover the distance equal to PQ?
  • 50 minute
  • 100 minute
  • 60 minute
  • 90 minute
A motor boat travels a distance of 7.5km in a river in 3hrs down stream & 5hrs  upstream the velocity of boat in kmph is
  • $$2.0$$
  • $$0.5$$
  • $$2.5$$
  • $$1.5$$
A swimmer can swim with velocity a in still water. He jumps in a river flowing with speed b. The swimmer goes a distance d downstream and then returns to original position. The time consumed in the process will be
  • $$\dfrac{3ad}{a^{2}-b^{2}}$$
  • $$\dfrac{2ad}{a^{2}-b^{2}}$$
  • $$\dfrac{ad}{a^{2}-b^{2}}$$
  • $$\dfrac{4ad}{3a^{2}-b^{2}}$$
The sum of digits in $${ \left( { 10 }^{ { 2n }^{ 2 }+5n+1 }+1 \right)  }^{ 2 }$$, (where n is a positive integer), is
  • $$4$$
  • $$6n$$
  • $$6+n$$
  • $$24n$$
A boat of mass $$80\,kg$$ is floating on still water. A dog of mass $$20 \,kg$$ on the boat at a distance of $$10 \,m$$ from the shore. The dog moves on the boat by a distance of $$2 \,m$$ towards the shore. The distance of the dog from the shore is:
  • $$11.6 \,m$$
  • $$8.4 \,m$$
  • $$9.6 \,m$$
  • $$10.4 \,m$$
A river is following at $$3 m/s$$ towards East, a boat is steered toward North at $$4 m/s$$ and wind is blowing at $$5 m/s 53^{o}$$ North of East. Flag mounted on boat will flutter along
  • North-East
  • South-West
  • West
  • Stand still
Max. value of $$z = 10 x + 7 y$$ subject to $$x \leq 4 , y \leq 8 , x + y \leq 8 , x \geq 0 , y \geq 0$$ is 
  • $$82$$
  • $$65$$
  • $$68$$
  • $$56$$
If $$x$$ satisfies $$|x-1|+|x-2|+|x-3|\le 6$$, then
  • $$0\le x\le4$$
  • $$x\le-2$$ or $$x\ge4$$
  • $$x\le 0$$ or $$x\ge 4$$
  • $$None\ of\ these$$
if $$p, q, r$$ and $$s$$ are in proportion then $$p$$ and $$s$$ are
  • Middle terms
  • Extreme terms
  • In ratio
  • None of these
Find the range of values of $$x$$ which satisfies equation $$\left|5x-5 \right|+\left|3-2x \right|= \left|3x-2 \right|$$
  • $$\left (- \infty, 1 \right] \cup \left[\dfrac {3}{2}, \infty \right)$$
  • $$  \left (- \infty, 1 \right) \cup \left(\dfrac {3}{2}, \infty \right)$$
  • $$\left[1,\dfrac {3}{2}\right]$$
  • None of these
A boat covers the distance between two points in a river in $$6$$ hours downstream and $$8$$ hrs upstream. A floating body in the lakes crosses these two points in 
  • 48 hrs
  • 16 hrs
  • 18 hrs
  • 2 hrs
A vertex of common graph of inequalities $$zx+y\ge 2$$ and $$x-y\le 3$$ is
  • $$(0,0)$$
  • $$(5/3,\ -4/3)$$
  • $$(5/3,\ 4/3)$$
  • $$(-4/3,\ 5/3)$$
If $${ 2 }^{ \sin x }+{ 2 }^{ \cos x }\ge 2^{ 1-y }$$, then the value of $$y$$ is 
  • 1
  • $$\sqrt { 2 } $$
  • $$\frac{1}{\sqrt2}$$
  • $$0$$
A boat travels a distance in 4 hrs upstream and same distance downstream in 2 hrs.Then ratio of velocity of the boat to that of water is 
  • 1:3
  • 3:1
  • 1:$$\sqrt{3}$$
  • $$\sqrt{3}$$: 1
A steamer takes 10 minute to travel a distance d downstream and 15 minute in upstream for same distance. The steamer can travel the same distance in still water is
  • 12 minute
  • 10 minute
  • 6 minute
  • 15 minute
A boat is travelling with a speed of 27 kmph due east. an observer is situated at 30 m south of the line of travel. the angular velocity of boat relative to the observer in the position shown will be :-
1575611_f11bd587fdd147a79c677d99049737a9.png
  • 0.125 rad /sec
  • zero
  • 0.250 rad/sec
  • 0.67 rad/sec
Solve $$\dfrac {x}{x-9} \le \dfrac {1}{1-x}$$
Write your solution set in interval notation.
  • $$(-3 < x < 1)\cap (3 < x < 9)$$
  • $$(-3 \le x < 1)\cap (3 < x < 9)$$
  • $$(-3 \le x < 1)\cap (3 < x < 9)$$
  • $$(-3 \le x \le 1)\cap (3 \le x \le 9)$$
Graphical solution of $$2 x+y-2>0$$
0:0:1


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