Only One Option Correct Type- The equation of the tangent to the curve y = e–|x| at the
point where the curve cuts the line x = 1 is
(a) x + y = e (b) e(x + y) = 1
(c) y + ex = 1 (d) none of these - The acute angles between the curves y = |x^2 – 1| and
y = |x^2 – 3| at their points of intersection is
(a) π
4(b) tan−⎛
⎝⎜⎞
⎠⎟1 42
7
(c) tan (−^147 ) (d) none of these- If f(x) = xα ln x and f(0) = 0, then the possible value of
α for which Rolle’s theorem can be applied in [0, 1] is
(a) –2 (b) –1
(c) 0 (d) none of these - If f : R → R is the function defined by
fx ee
ee
xx
xx()= −
+−
−22
22 , then
(a) f(x) is an increasing function
(b) f(x) is a decreasing function
(c) f(x) is onto (surjective)
(d) none of these- Let f (x) = tan x – tan 2x. Then
(a) f has no critical point
(b) f has minimum at x=cos (−^110 − 1 ) / 4
(c) f has minimum at x=cos (−^110 − 2 ) / 4
(d) f has maximum at x=cos (−^110 − 2 ) / 4
6. The diagonal of a square is changing at the rate of
0.5 cm/sec. Then the rate of change of area, when
the area is 400 cm^2 , is equal to
(a) 20 2 cm /sec^2 (b) 10 2 cm /sec^2
(c)1
10 2cm^2 /sec (d)^10
2cm /sec^2One or More Than One Option(s) Correct Type- A point on the ellipse 4x^2 + 9y^2 = 36, where the
tangent is equally inclined to the axes is
(a)^9
13
4
13⎛ ,
⎝⎜⎞
⎠⎟(b) ⎛⎝⎜− ⎞⎠⎟9
134
13,(c)9
134
13⎛ ,−
⎝⎜⎞
⎠⎟^ (d) none of these- The extreme values of the function
fx
xx
()
sin cos=
+−
−1
41
4 where x^ ∈^ R is(a)4
82 −(b)22
82 −(c)22
42 1+(d)^42
82 +- If fx
xx x
xx(),
,= ,then+ −−≤≤
− < ≤⎧
⎨⎪
⎩⎪3121 1 2
37 2 32(a) f (x) is increasing on [–1, 2]
(b) f (x) is continuous on [–1, 3]
(c) f ′(2) does not exist
(d) f (x) has the maximum value at x = 2Application of Derivatives
T
his specially designed column enables students to self analyse their
extent of understanding of specified chapters. Give yourself four
marks for correct answer and deduct one mark for wrong answer.
Self check table given at the end will help you to check your
readiness.Total Marks : 80 Time Taken : 60 Min.
Class XII