CBSE Questions for Class 12 Commerce Applied Mathematics Quantification And Numerical Applications Quiz 14 - MCQExams.com

If $$x : y = 5 : 2$$ and $$y : z = 3 : 2$$, what is the ratio of $$x : z$$?
  • $$3 : 1$$
  • $$3 : 5$$
  • $$5 : 3$$
  • $$8 : 4$$
  • $$15 : 4$$
Vinod recently opened a surfboard store at the beach. He buys each surfboard in wholesale for $$ $80$$ and has fixed monthly expenses of $$ $3,500$$. If he sells each surfboard at $$\$120$$ then how many surfboards does he need to sell in a month to get overall profit?
  • $$18$$
  • $$30$$
  • $$45$$
  • $$90$$
The minimum value of the sum of the lengths of diagonals of a cyclic quadrilateral of area $$a^2$$ square units is
  • $$\sqrt 2$$ a
  • 2$$\sqrt 2$$ a
  • 2a
  • none of these
The minimum value of $$4^x+4^{1-x} $$, $$x \epsilon R$$, is
  • 1
  • 2
  • 4
  • none of these
The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
  • $$\displaystyle 299m+261j\ge 1000$$
  • $$\displaystyle 299m+261j>1000$$
  • $$\displaystyle \frac { 299 }{ m } +\frac { 261 }{ j } \ge 1000$$
  • $$\displaystyle \frac { 299 }{ m } +\frac { 261 }{ j } >1000$$
Which of the following is a correct graph of $$x>1, x<4$$?
537662.PNG
  • Line A
  • Line B
  • Line C
  • Line D
  • Line E
Conclude from the following:
$$t = (2y \times 10^3)+(3y \times 10^3)$$
$$y > 0$$

A: $$t$$
B: $$5y\times 10^3$$
  • The quantity A is greater than B.
  • The quantity B is greater than A.
  • The two quantities are equal.
  • The relationship cannot be determined from the information given.
The number of ordered tuples $$(x,y,z,w)$$ where $$x,y,z,w \in [0,10]$$ which satisfies the inequality
$$2^{\sin ^2x}\times 3^{\cos ^2y}\times 4^{\sin ^2z}\times 5^{\cos ^2w}\geq 120$$, is
  • $$81$$
  • $$144$$
  • $$0$$
  • $$\infty$$
For $$\theta>\dfrac {\pi}3$$, the value of $$f(\theta)=\sec ^2 \theta+\cos ^2\theta$$  always lies in the interval
  • $$(0,2)$$
  • $$[0,1]$$
  • $$(1,2)$$
  • $$[2,\infty)$$
If $$0<x<\dfrac {\pi}2$$, then the minimum value of $$\dfrac {\cos ^4x}{\sin ^2x}+\dfrac {\sin ^4x}{\cos ^2x}$$ is
  • $$\sqrt 3$$
  • $$\dfrac 12$$
  • $$\dfrac 13$$
  • $$1$$
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Both Assertion and Reason are incorrect
If roots of the equation $$x^4-8x^3+bx^2+cx+16=0$$ are positive, then
  • $$b=c=8$$
  • $$b=-24,c=-32$$
  • $$b=24,c=-32$$
  • $$b=24,c=32$$
$$2^{\sin ^2x}+2^{\cos ^2x}$$ is
  • $$>2$$
  • $$\geq 2\sqrt 2$$
  • $$\leq 2$$
  • $$<1$$
The minimum value of the sum of the lengths of diagonals of a cyclic quadrilateral of area $$a^2$$ sq. units is
  • $$\sqrt 2 a$$
  • $$2a$$
  • $$2\sqrt 2 a$$
  • None of the above.
If $$p,q,r $$ be three distinct real numbers , then the value of $$(p+q)(q+r)(r+p)$$ is
  • $$> 8pqr$$
  • $$> 16pqr$$
  • $$8pqr$$
  • $$< 8pqr$$
The minimum value of $$|\sin x+\cos x+\tan x+\sec x+\mathrm{cosec} x+\cot x|$$ is
  • $$2\sqrt 2-1$$
  • $$2\sqrt 2+1$$
  • $$\sqrt 2-1$$
  • $$\sqrt 2+1$$
A stick of length $$20$$ units is to be divided into $$n$$ parts so that the product of the lengths of the parts is greater than unity.
The maximum possible value of $$n$$ is
  • $$20$$
  • $$19$$
  • $$18$$
  • $$21$$
Equation $$x^4+ax^3+bx^2+cx+1=0$$ has real roots ($$a,b,c $$ are non-negative). Maximum value  of $$a$$ is 
  • $$10$$
  • $$9$$
  • $$5$$
  • $$-4$$
$$f(x)=\dfrac {(x-2)(x-1)}{x-3}, \forall x>3$$. The minimum value of $$f(x)$$ is equal to
  • $$3+2\sqrt 2$$
  • $$3+2\sqrt 3$$
  • $$3\sqrt 2+2$$
  • $$3-2\sqrt 2$$
If positive numbers $$a,b,c$$ be in H.P, then the equation $$x^2-kx+2b^{101}-a^{101}-c^{101}=0$$ $$(k\in R)$$ has
  • Both roots positive
  • Both roots negative
  • One positive and one negative root
  • Both roots imaginary
If $$xy+yz+zx=12$$, where $$x,y,z$$ are positive values, then the greatest value of $$xyz$$ is
  • $$8$$
  • $$18$$
  • $$6$$
  • None of the above.
If $$0<a,b,c<1$$ and $$a+b+c=2$$, then the greatest value of $$\dfrac a{1-a}\times\dfrac b{1-b}\times\dfrac c{1-c}$$ is
  • $$7$$
  • $$4$$
  • $$8$$
  • $$12$$
Equation $$x^4+ax^3+bx^2+cx+1=0$$ has real roots ($$a,b,c $$ are non-negative). Minimum non-negative real value of $$b$$ is
  • $$12$$
  • $$15$$
  • $$6$$
  • $$10$$
In $$\Delta ABC$$, the least value of $$\mathrm{cosec} \dfrac A2+\mathrm{cosec} \dfrac B2+\mathrm{cosec} \dfrac C2$$ is
  • $$4\sqrt 2$$
  • $$0$$
  • $$\dfrac 3{\sqrt 2}$$
  • $$6$$
Equation $$x^4+ax^3+bx^2+cx+1=0$$ has real roots ($$a,b,ca,b,c$$ are non-negative). Maximum real value of $$c$$ is 
  • $$-10$$
  • $$-9$$
  • $$-6$$
  • $$-4$$
The least value of the expression $$2\log_{10}x-\log_x(0.01)$$, for $$x>1$$, is
  • $$1$$
  • $$2$$
  • $$4$$
  • $$8$$
If $$\frac{4\alpha}{\alpha^2+1}\geq 1$$ and $$\alpha+\frac{1}{\alpha}$$ is an odd integer then number of possible values of $$\alpha$$ is
  • 1
  • 2
  • 3
  • 4
The ratio of inradius and circumradius of a square is :
  • $$1\ :\ \sqrt { 2 }$$
  • $$\sqrt { 2 } \ :\ \sqrt { 3 }$$
  • $$1\ :\ 3$$
  • $$1\ :\ 2$$
Number of integers satisfying the inequalities $$\sqrt {\log_{3}x - 1} + \dfrac {\dfrac {1}{2} \log_{3}x^{3}}{\log_{3}\dfrac {1}{3}} + 2 > 0$$, is
  • $$5$$
  • $$6$$
  • $$7$$
  • $$8$$
On a linear escalator running between two points $$A$$ and $$B$$, a boy takes time $${t}_{1}$$, to move from $$A$$ to $$B$$, if the boy runs with a constant speed on the escalator. If the boy runs from $$B$$ to $$A$$, he takes time $${t}_{2}$$ to reach $$B$$ from $$A$$. The time taken by the boy to move from $$A$$ to $$B$$ if he stands still on the escalator will be (The escalator moves from $$A$$ to $$B$$)
  • $$\cfrac { { t }_{ 1 }{ t }_{ 2 } }{ { t }_{ 2 }-{ t }_{ 1 } } $$
  • $$\cfrac { { 2t }_{ 1 }{ t }_{ 2 } }{ { t }_{ 2 }-{ t }_{ 1 } } $$
  • $$\cfrac { { t }_{ 1 }^{ 2 }+{ t }_{ 2 }^{ 2 } }{ { t }_{ 1 }{ t }_{ 2 } } $$
  • $$\cfrac { { t }_{ 1 }^{ 2 }-{ t }_{ 2 }^{ 2 } }{ { t }_{ 1 }{ t }_{ 2 } } $$
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