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 π
(4) π
Ans. (4)
Solution.
Q.3. (2019)
(1) 21/19
(2) 19/21
(3) 22/23
(4) 23/22
Ans. (1)
Solution.
Q.4. All xsatisfying the inequality (cot^{1} x)^{2 } 7(cot^{1}x)+ 10 > 0, lie in the interval: (2019)
(1) (∞, cot 5) ∪ (cot 4, cot 2)
(2) (cot 2, ∞)
(3) (∞, cot 5) ∪ (cot 2, ∞)
(4) (cot 5, cot 4)
Ans. (2)
Solution.
⇒ ...(1)
But cot^{1} x lies in (0, π)
Now, from equation (1)
cot^{1}x ∈ (0, 2)
Now, it is clear from the graph
x ∈ (cot 2, ∞)
Q.5. Considering only the principal values of inverse functions, the set (2019)
(1) contains two elements
(2) contains more than two elements
(3) is a singleton
(4) is an empty set
Ans. (3)
Solution.
Therefore, A is a singleton set.
Q.6.then α  β is equal to: (2019)
Ans. (4)
Solution.
Q.7.where 1 ≤ x ≤ 1, 2 ≤ y ≤ 2, then for all x, y, 4x^{2} 4xy cosα +y^{2} is equal to: (2019)
(1) 4 sin^{2}α
(2) 2 sin^{2}α
(3) 4 sin^{2}α  2x^{2}y^{2}
(d) 4 cos^{2} α + 2x^{2}y^{2}
Ans. (1)
Solution.
Q.8. The value of is equal to: (2019)
Ans. (2)
Solution.
Q.9. If for x∈ the derivative of tan^{1} is √x × g(x) , then g(x) equals (2017)
(1)
(2)
(3)
(4)
Ans. (2)
Solution.
⇒
⇒
Q.10. The value of is equal to: (2017)
Ans. (1)
Solution.
x^{2} = cos2θ ; θ =
=
=
=
Q.11. A value of x satisfying the equation sin[cot^{1}(1+x)]=cos[tan^{1}x], is: (2017)
(1)
(2) 0
(3) 1
(4) 1/2
Ans. (1)
Solution.
Given that sin[cot^{1} (x+1)] = cos (tan^{1}x) ......(i)
We know that,
Here, A = x + 1
or 1 + 2x = 0
or
Q.12. Consider
A normal to y = f(x) at x = π/6 also passes through the point: (2016)
(1) (0, 0)
(2) (0, 2π/3)
(3) (π/6, 0)
(4) (π/4, 0)
Ans. (2)
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