Suppose that Q is a number and 0 1

The correct option is C Only III is possibleWe know, 0^∘ = 1 and 90^∘ = ∞ Hence, when 0 lt; Q lt; 90 then 1 lt; sec Q lt; ∞ Th ...

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Standard XII

Mathematics

Applications of Cross Product

Suppose that ...

Question

Suppose that Q is a number and $0 < Q < 90^{\circ}$ Consider the following statements and select the correct choice
I $sec (Q^{\circ}) < 1$
II $sec (Q^{\circ}) = 1$
III $sec (Q^{\circ}) > 1$

Only I is possible

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All are possible

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Only III is possible

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Only I is impossible

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Solution

The correct option is C Only III is possible
We know,
$sec 0^{\circ} = 1$ and $sec 90^{\circ} = \infty$
Hence, when $0 < Q < 90$ then $1 < s e c Q < \infty$
Thus, III is possible.

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Similar questions

Q. In the following question, the symbols

@, ©, %, $

and

⋆

are used with the following meaning as illustrated.

^{'} P © Q^{'}

means 'P is not greater than Q'.

^{'} P ⋆ Q^{'}

means 'P is not smaller than Q'.

^{'} P % Q^{'}

means 'P is neither greater than nor equal to Q'.

^{'} P $ Q^{'}

means 'P is neither smaller than nor greater than Q'.

^{'} P @ Q^{'}

means 'P is neither greater than nor smaller to Q'.
In each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given is/are definitely true.
©

\Rightarrow\leq

, @

\Rightarrow

⋆ \Rightarrow\geq

, %

\Rightarrow

$

\Rightarrow

>
Statements

Z © K

K % E

E @ R

Conclusions
I.

R $ K

II.

Z % E

III.

R $ Z

Q. A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and

\frac{1}{2}

, respectively. If the probability that the student is successful, is

\frac{1}{2}

, then

Q. Directions: In the following questions, the symbols @ copyright

% $

and

*

are used with the following meaning as illustrated.
'P copyright Q' means 'P is not greater than Q'.

^{'} P * Q^{'}

means 'P is not smaller than Q'.

^{'} P % Q^{'}

means 'P is neither greater than nor equal to Q'.

^{'} P $ Q^{'}

means 'P is neither smaller than nor equal to Q'.
'P @ Q' means 'P is neither greater than nor smaller than Q'.
Now in each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given below them is/are definitely true.
Statements: Z copyright K,

K % E

E @ R
Conclusions:
I.

R $ K

II.

Z % E

III.

R $ Z

Q. In the following question, the symbols

@, ©, %, $

and

⋆

are used with the following meaning as illustrated.

^{'} P © Q^{'}

means 'P is not greater than Q'.

^{'} P ⋆ Q^{'}

means 'P is not smaller than Q'.

^{'} P % Q^{'}

means 'P is neither greater than nor equal to Q'.

^{'} P $ Q^{'}

means 'P is neither smaller than nor greater than Q'.

^{'} P @ Q^{'}

\Rightarrow\leq

, @

\Rightarrow

⋆ \Rightarrow\geq

, %

\Rightarrow

$

\Rightarrow

>
Statements

B % H

H $ J

J ⋆ M

Conclusions:
I.

B % J

II.

M % B

III.

H $ M

Q. Suppose that

θ

is a number and 0 <

θ

< 90

^{\circ}

. Consider the following statements and select the correct choice:

I : sec (

θ^{\circ}

) < 1 ;

II : sec (

θ^{\circ}

)

=

1 ;

III : sec (

θ^{\circ}

) > 1 ;

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Suppose that Q is a number and 0<Q<90∘ Consider the following statements and select the correct choiceI sec(Q∘)<1II sec(Q∘)=1III sec(Q∘)>1

The correct option is C Only III is possibleWe know,sec0∘=1 and sec90∘=∞Hence, when 0<Q<90 then 1<secQ<∞Thus, III is possible.

Suppose that Q is a number and $0 < Q < 90^{\circ}$ Consider the following statements and select the correct choice
I $sec (Q^{\circ}) < 1$
II $sec (Q^{\circ}) = 1$
III $sec (Q^{\circ}) > 1$

The correct option is C Only III is possible
We know,
$sec 0^{\circ} = 1$ and $sec 90^{\circ} = \infty$
Hence, when $0 < Q < 90$ then $1 < s e c Q < \infty$
Thus, III is possible.