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Phrases Previous Year Questions (PYQs)

Phrases Properties Of Triangle PYQ

Phrases PYQ
List I List II
A. Dog : Rabies :: Mosquito : I. Bacteria
B. Amnesia : Memory :: Paralysis : II. Liver
C. Meningitis : Brain :: Cirrhosis : III. Movement
D. Influenza : Virus :: Typhoid : IV. Malaria






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Phrases Previous Year PYQPhrases CUET 2023 PYQ

Solution

Dog causes Rabies, Mosquito causes Malaria → A-IV
Amnesia affects Memory, Paralysis affects Movement → B-III
Meningitis affects Brain, Cirrhosis affects Liver → C-II
Influenza is caused by Virus, Typhoid is caused by Bacteria → D-I

Correct matching: A-IV, B-III, C-II, D-I
Phrases PYQ
The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is $60^\circ$. If the third side is 3, the remaining fourth side is





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

Opposite angles in a cyclic quadrilateral are supplementary. Using cosine rule in both triangles and equating, the fourth side comes out as 4.
Phrases PYQ
Which of the following is true
A. If $a\cos A=b\cos B$, then the triangle is isosceles or right angled.
B. If in a triangle $ABC$, $\cos A\cos B+\sin A\sin B\sin C=1$, then the triangle is isosceles right angled.
C. If the ex-radii $r_1,r_2,r_3$ of $\triangle ABC$ are in H.P., then its sides are not in A.P.

Choose the correct answer from the options given below:





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

A:
$a\cos A=b\cos B \Rightarrow \cos A\cos A=\cos B\cos B$
This holds when $A=B$ (isosceles) or one angle is $90^\circ$
✔ True

B:
Maximum value of $\cos A\cos B+\sin A\sin B\sin C$ is $1$
This occurs when $A=B=45^\circ,\ C=90^\circ$
✔ True

C:
If ex-radii are in H.P., sides cannot be in A.P.
✔ True
Phrases PYQ
The mean deviation from the mean of the A.P. $a, a+d, a+2d, \ldots, a+2nd$ is





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

The A.P. is symmetric with $2n+1$ terms. Mean deviation from mean for such A.P. is $\dfrac{n(n+1)d}{2n+1}$.

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