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**Q.1.****then x is equal to: (2019)****Ans. **(1)**Solution.**** ****Q.2. ****If x = sin ^{-1} (sin 10) and y = cos^{-1} (cos 10), then y - x is equal to: (2019)**

(1) 0

(2) 10

(3) 7 Ï€

(4) Ï€

**Q.3. (2019)****(1) 21/19****(2) 19/21****(3) 22/23****(4) 23/22****Ans. **(1)**Solution.****Q.4. ****All x-satisfying the inequality (cot ^{-1} x)^{2 }- 7(cot^{-1}x)+ 10 > 0, lie in the interval: (2019)**

(1) (-âˆž, cot 5) âˆª (cot 4, cot 2)

(2) (cot 2, âˆž)

(3) (-âˆž, cot 5) âˆª (cot 2, âˆž)

(4) (cot 5, cot 4)

â‡’ ...(1)

But cot

Now, from equation (1)

cot

Now, it is clear from the graph

x âˆˆ (cot 2, âˆž)

(2) contains more than two elements

(3) is a singleton

(4) is an empty set

Therefore, A is a singleton set.

**Q.7.where -1 â‰¤ x â‰¤ 1, -2 â‰¤ y â‰¤ 2, then for all x, y, 4x ^{2} -4xy cosÎ± +y^{2} is equal to: (2019)**

(2) 2 sin

(3) 4 sin

(d) 4 cos

Solution.

Solution.

(1)

(2)

(3)

(4)

Ans.

Solution.

â‡’

â‡’

x

Given that sin[cot

We know that,

Here, A = x + 1

or 1 + 2x = 0

or

A normal to y = f(x) at x = Ï€/6 also passes through the point: (2016)

(1) (0, 0)

(2) (0, 2Ï€/3)

(3) (Ï€/6, 0)

(4) (Ï€/4, 0)

Ans.

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