CBSE Questions for Class 12 Commerce Applied Mathematics Quantification And Numerical Applications Quiz 13 - MCQExams.com

If $$x:y=1:1$$, then $$\cfrac{3x+4y}{5x+6y}=$$
  • $$\cfrac{7}{11}$$
  • $$\cfrac{17}{11}$$
  • $$\cfrac{17}{23}$$
  • $$\cfrac{4}{5}$$
A motot boat covers the distance between two spots on the river banks in $$t_1=8h$$ and $$t_2=12h$$ in down stream and upstream respectively. The time required for the boat to cover this distance in still water will be:
  • $$6.9$$ hr
  • $$9.6$$ hr
  • $$69$$ second
  • $$96$$ second
If $$p:q=2:5$$, then $$\cfrac{25p+14q}{5p+7q}=$$
  • $$8:5$$
  • $$5:8$$
  • $$8:3$$
  • $$3:8$$
Choose the most appropriate option.
$$60$$kg of an alloy X is mixed with $$100$$ kg of an alloy Y. If alloy X has lead and tin in the ratio of $$3:2$$ and alloy Y has tin and copper in the ratio of $$1:4$$, then the amount of tin in the new alloy is?
  • $$53$$ kgs
  • $$80$$ kgs
  • $$36$$ kgs
  • $$44$$ kgs
What least number is to be subtracted from each term of the ratio $$15:19$$ to make the ratio $$3:4$$?
  • $$3$$
  • $$5$$
  • $$6$$
  • $$9$$
A man swims relative to water with a velocity greater than river flow velocity. Then:
  • Man may cross the river along shortest path
  • Man cannot cross the river
  • Man cannot cross the river without drifting
  • None of the above
What must be added to each term of the ratio $$9:16$$ to make the ratio $$2:3$$?
  • $$5$$
  • $$3$$
  • $$4$$
  • $$6$$
A man rows directly cross a river in time t second and rows an equal distance down the stream in $$T$$ second. The ratio of man's speed in still water to the speed of river water is?
  • $$\dfrac{t^2-T^2}{t^2+T^2}$$
  • $$\dfrac{t^2+T^2}{t^2-T^2}$$
  • $$\dfrac{T^2-t^2}{T^2+t^2}$$
  • $$\dfrac{T^2+t^2}{T^2-t^2}$$
Consider the inequality $$9^x - a3^x - a + 3 \leq 0$$, where 'a' is a real parameter.

The given inequality has at least one real solution of $$a\space\epsilon$$
  • $$(-\infty, 3)$$
  • $$(2, \infty)$$
  • $$(3, \infty)$$
  • $$(-2, \infty)$$
A river is flowing from W to E with a speed of $$ 5 $$ m/min. A man can swim in still water with a velocity $$ 10 $$ m/min. In which direction should the man swim so as to take the shortest possible path to go to the south.
  • $$ 30^{\circ} $$ with downstream
  • $$ 60^{\circ} $$ with downstream
  • $$ 120^{\circ} $$ with downstream
  • South
When the pilot reverses the propeller in a boat moving north, the boat moves with an acceleration directed south. Assume the acceleration of the boat remains constant in magnitude and direction. What happens to the boat?
  • It eventually stops and remains stopped.
  • It eventually stops and then speeds up in the forward direction.
  • It eventually stops and then speeds up in the reverse direction.
  • It never stops but loses speed more and more slowly forever.
  • It never stops but continues to speed up in the forward direction.
A ball is thrown vertically upwards from the ground. If $$\displaystyle T_{1}$$ and $$\displaystyle T_{2}$$ are the respective time taken in going. up and coming down, and the air resistance is not ignored, then
  • $$\displaystyle T_{1}> T_{2}$$
  • $$\displaystyle T_{1}= T_{2}$$
  • $$\displaystyle T_{1}< T_{2}$$
  • Nothing can be said
Region represented by the inequation system
$$x + y \leq 3$$
$$y \leq 6$$
and $$x \geq 0,y \geq 0$$
is :
  • Unbounded in the first quadrant
  • Unbounded in the first and second quadrant
  • Bounded in the first quadrant
  • None of the above
When the square of a bigger number and the cube of a small number are added, the result is $$593$$. If the square of the smaller number exceeds the bigger number by $$55$$. Find the difference of two numbers. 
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
A woman sells to the first customer half of her stock of apples and half an apple, to the second customer she sells half her remaining stock and half an apple, and so on to the third and to the fourth customer. She finds that she has now $$15$$ apples left. How many apples did she have before she started selling?
  • $$422$$
  • $$375$$
  • $$255$$
  • $$182$$
A motor boat going downstream crosses a float at a point A. $$60$$ minutes later it turns back and after some time it again crosses the float, now the float is at a distance of $$12$$ km from the point A. The velocity of the stream is
  • $$8 \ km/h$$
  • $$4\  km/h$$
  • $$6 \ km/h$$
  • $$10\  km/h$$
A man can row a boat with $$4 km/h$$ in still water. If he is crossing a river where the current is $$2 km/h$$ and width of river is $$4 km$$. How long will it take him to row $$2 km$$ up the stream and then back to his starting point?
  • $$2 hrs$$
  • $$1 hr$$
  • $$\dfrac{4}{3} hrs$$
  • None of the above
If $$a$$ $$ \neq 0$$, then the inequation $$|x+ a| + |x + a| < b$$
  • has no solution, if $$b$$ $$\le 2 |a|$$
  • has a solution set $$\left(-\dfrac{b}{2},\dfrac{b}{2}\right)$$, if $$b > 2 |a|$$
  • has a solution set $$\left(-\dfrac{b}{2},\dfrac{b}{2}\right)$$, if $$b < 2 |a|$$
  • has no solution, if $$b > 2 |a|$$
The inequalities $$y(-1) \geq -4$$, $$y(1) \leq 0$$ and $$y(3) \geq 5$$ are known to hold for $$y=ax^2+bx+c$$ then the least value of 'a' is ____________.
  • $$\dfrac{-1}{4}$$
  • $$\dfrac{-1}{3}$$
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{8}$$
If $$ |r-6| = 11$$ and $$|2q - 12| = 8$$ then, the minimum value of $$\displaystyle \frac{q}{r}$$ 
  • $$-2$$
  • $$\displaystyle \frac{17}{10}$$
  • $$\displaystyle \frac{-1}{5}$$
  • $$\displaystyle \frac{2}{5}$$
If $$4x + 3y = 121$$ find how many positive integer solutions are possible?
  • $$10$$
  • $$1$$
  • $$0$$
  • Cannot be determined
Solve the following inequality. $$\displaystyle \frac{3}{x-4}\le -1$$
  • $$[1,4)$$
  • $$[-1,4)$$
  • $$[1,-4)$$
  • None of these
One year payment of the servant is  one shirt and $$Rs.200$$ . The servant leaves after $$9$$ months and receives $$Rs.120$$ and a shirt. What is the price of the shirt?
  • RS.$$80$$
  • Rs.$$100$$
  • Rs.$$120$$
  • Cannot be determined
The inequality $$(2n+7)<(n+3)^2$$ is true for
  • All negative numbers.
  • All whole numbers
  • All natural numbers
  • None of these
Cost of pure milk is Rs. $$16$$ per liter. On adding water, the mixture is sold at Rs. $$15$$ per liter. In this way, the milkman earns $$25\ %$$ profit. What is the ratio of milk and water in the mixture?
  • $$25 : 7$$
  • $$7 : 25$$
  • $$15 : 1$$
  • $$1 : 15$$
  • None of these
The population of a bacteria culture doubles in number every 12 minutes. the ratio of the number of bacteria at the end of 1 hour to the number of bacteria at the beginning of that hour is
  • 8 : 1
  • 16 : 1
  • 32 : 1
  • 60 : 1
If $$\displaystyle \left | 9-x \right |< 2-3x $$, then find the range of $$\displaystyle x\epsilon R $$
  • $$\displaystyle (-\infty,0 )$$
  • $$\displaystyle \left (-\infty,\frac{-7}{2} \right)$$
  • $$\displaystyle (-\infty,-3 )$$
  • $$\displaystyle \left ( -16,8 \right )$$
The minimum value of $$| \sin x + \cos x + \tan x + \sec x + \text{cosec} x + \cot x | $$ is
  • $$2\sqrt 2 -1$$
  • $$2\sqrt 2 +1$$
  • $$\sqrt 2 -1$$
  • $$\sqrt 2 +1$$
The least perimeter of a cyclic quadrilateral of a given area A square units is
  • $$\sqrt A$$
  • 2$$\sqrt A$$
  • 3$$\sqrt A$$
  • 4$$\sqrt A$$
If three numbers in the ratio $$3:2:5$$ be such that the sum of their squares is $$1862$$, the middle number will be
  • $$10$$
  • $$14$$
  • $$28$$
  • $$32$$
0:0:1


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