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

If $$a:b:c=3:4:7$$, then the ratio $$(a+b+c):c$$ is equal to
  • $$14:3$$
  • $$7:2$$
  • $$1:2$$
  • $$2:1$$
The Vertices of a triangle are $$A(1,0,1) \quad B(2,-1,4) $$ and $$C(3,-4,-1)$$ .Then The triangle is 
  • Acute Angled
  • Obtuse Angled
  • Equialteral 
  • Right angled
A person can swim in still water at $$5 \,m/s$$. He moves in river of velocity $$3 \,m/s$$, First down the stream next same distance up the steam the ratio of times takes are
  • $$1:1$$
  • $$1:2$$
  • $$1:4$$
  • $$4:1$$
Whether the given equation  $$x>\sin x > x -\dfrac{x^3}{6}$$ for all $$x>0$$. is ?
  • True
  • False
Solution set of the inequality, $$49^x + 7^{x + 1} - 98 < 0$$, is:
  • $$\left(-\infty, \dfrac{1}{2}\right)$$
  • $$\left(-1, \infty\right)$$
  • $$\left(-\infty, 1\right)$$
  • $$\left(-1, \dfrac{1}{2}\right)$$
The minimum value of $$P = 6 x + 16 y$$ subject to constraints $$x \leq 40 , y \geq 20$$ and  $$x , y \geq 0$$ is
  • $$240$$
  • $$320$$
  • $$0$$
  • $$280$$
The solution set of the in equation $$|x-1|\geq |x-3|$$, is
  • $$[-\alpha,2]$$
  • $$[2,\alpha]$$
  • $$[1,3]$$
  • none of these
If the sum of the upstream and downstream speed of a fish is 82 mph , and it travels 105 m upstream in 3hr. Find the time taken by boat to cover 126 m downstream 
  • $$2.4$$ hrs
  • $$2.8$$ hrs
  • $$2.5$$ hrs
  • $$2.68$$ hrs
If the sum of the upstream and downstream speed of a fish is $$82$$ mph, and it travels $$105$$ m. upstrem in $$3$$ hr. Find the time taken by a boat to cover $$126$$ m downstream.
  • $$2.7$$ hrs
  • $$2.8$$ hrs
  • $$2.5$$ hrs
  • $$2.68$$ hrs
Area of the region $$\left\{(x, y)/x^{2}+y^{2}\le 1\le x+y\right\}$$ is
  • $$\dfrac{\pi}{4}+\dfrac{1}{2}$$
  • $$\dfrac{\pi}{4}-\dfrac{1}{2}$$
  • $$\dfrac{\pi}{4}+\dfrac{3}{4}$$
  • $$\pi +1$$
Find the set of values of $$x$$ which satisfies the inequality  $${|  x+2|}\leq 2x+1.$$
  • $$(-1,\infty)$$
  • $$[1,\infty)$$
  • $$(-2,\infty)$$
  • None of these
Mark the correct alternative of the following.
If $$a=2b$$, then $$a : b=$$?
  • $$2 : 1$$
  • $$1 : 2$$
  • $$3 : 4$$
  • $$4 : 3$$
Mark the correct alternative of the following.
If $$57 : x=51 : 85$$, then the value of x is?
  • $$95$$
  • $$76$$
  • $$114$$
  • None of these
A boat takes $$4\ hr$$ upstream and $$2\ hr$$ down the stream for covering the same distance. The ratio of the velocity of boat to velocity of water in the river is 
  • $$1 : 3$$
  • $$3 : 1$$
  • $$1 : \sqrt{3}$$
  • $$\sqrt{3} : 1$$
In the given figure D is a point on BC such that BD : DC = $$1 : 3$$. If O is the midpoint of AD, then the ratio of areas of $$\Delta$$AOB and $$\Delta$$ ABC will be  
1225118_96725c11af2c4f42898167488f2e88c8.png
  • $$1 :8$$
  • $$1 :3$$
  • $$1 :4$$
  • $$1 :6$$
If a point (h,k) satisfies an inequation ax + by > 4, then the half plane represented by the inequation is 
  • The half plane contacting the point (h,k) but excluding the point on ax + by =4
  • The half plane contacting the point (h , k) and the points on ax +by =4
  • Whole xy-plane
  • None of these
The number of real values of $$\lambda$$ for which the system of linear equations
$$2x + 4y - \lambda z =0$$
$$4x +\lambda y + 2z =0$$
$$\lambda x + 2y +2z =0$$
has infinitely many solution is: 
  • 0
  • 1
  • 2
  • 3
$$\sin ^ { - 1 } ( x ) > \cos ^ { - 1 } ( x )$$ holds for
  • every $$x$$
  • $$x \in \left( 0 , \dfrac { 1 } { \sqrt { 2 } } \right)$$
  • $$x \in \left( \dfrac { 1 } { \sqrt { 2 } } , 1 \right]$$
  • not possible
Three numbers are in the ratio 4 : 5 : 6 and their average is 25.The largest number is :
  • $$30$$
  • $$32$$
  • $$36$$
  • $$42$$
A value of 't' satisfying the equation $$\dfrac { 7t+5 }{ 6 } \ge \dfrac { t-1 }{ 2 } $$
  • -1
  • -3
  • -4
  • -6
State true or false.
For any real value of "a"
$$4 a ^ { 4 } - 4 a ^ { 3 } + 5 a ^ { 2 } - 4 a + 1 \geq 0 $$ 
  • True
  • False
If $$A$$ and $$B$$ are in the ratio $$4 : 5$$ and the difference of their squares is $$81$$, what us the value of $$B$$ ?
  • $$15$$
  • $$12$$
  • $$36$$
  • $$45$$
Let $$\overline {AB} $$ be a diameter of a circle and $$C$$ be a point on $$\overline {AB} $$ with $$2AC = BC$$. Let $$D$$ and $$E$$ points on the circle, such that $$\overline {DC}  \bot \overline {AB} \,\,{\rm{and}}\,\,\overline {DE} $$ is second diameter, then the ratio of the area of $$\Delta DEC$$ to the area of $$\Delta ABD$$ is
1286113_17d48e0a1b4e492cbeab804d6564b344.png
  • 1 : 3
  • 2 : 3
  • 3 : 1
  • none of these
A steamer is going downstream overcome a raft point $$A$$. $$2\ hr$$ later it turned back and after some time passed the raft at a distance $$4\ km$$ from point $$A$$. The speed of the river is 
  • $$1\ km/h$$
  • $$2\ km/h$$
  • $$3\ km/h$$
  • $$4\ km/h$$
In what ratio is the line joining A(8,9) and B(-7,4) is divided by 
  • the point$$(2,7)$$
  • the x-axis
  • the y-axis
  • at the ratio $$2:3$$
A man can swim in still water at $$4m/s$$. River is flowing at $$2m/s$$. The angle with downstream at which he should swim wo cross the river with minimum drift is:
  • $$120^o$$
  • $$150^o$$
  • $$30^o$$
  • $$60^o$$
The sum $$1\cdot 3+3\cdot 5+5\cdot 7+\dots \dots +(2 n-1)(2 n+1)  $$ is equal to
  • $$\dfrac{n(4n^{2}+3n-2)}{3}$$
  • $$\dfrac{n(4n^{2}+6n-1)}{3}$$
  • $$\dfrac{(4n^{2}-6n-1)}{2}$$
  • None of these
Mark the correct alternative of the following.
The sides of a triangle are in the ratio $$2 : 3 : 5$$. If its perimeter is $$100$$ cm, the length of its smallest side is?
  • $$2$$ cm
  • $$20$$ cm
  • $$3$$ cm
  • $$5$$ cm
Mark the correct alternative of the following.
The angles of a triangle are in the ratio $$1 : 2 : 3$$. The measure of the largest angle is?
  • $$30^o$$
  • $$60^o$$
  • $$90^o$$
  • $$120^o$$
If $$a:b=2:5$$, then $$\cfrac{3a+2b}{4a+b}=$$
  • $$\cfrac{16}{13}$$
  • $$\cfrac{13}{16}$$
  • $$\cfrac{25}{22}$$
  • $$\cfrac{20}{21}$$
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