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Differential Calculus Test Paper Solutions
Solution 1:- (c)
(L Hospital Rule)
Solution 2:- (c)
Here f (x) is continuous at x = 0 when,
k = e2 Solution 3:- (c)
For x 0, we have
because, as h 0, h is a negative number, so that
Here f is not differentiable at x = 0. Thus the points of
differentiability are ( , ) ~ {0}.
Solution 4:- (d)
Here,
When parametric coordinates are given by;
Equation of tangent,
x-intercept,
and y-intercept;
Hence, the sum of intercept made on the axes of coordinates
is,
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Solution 5 :- (a) The total number of solutions is same as the
number of points of intersection of the curves.
It is evident the curves that these two curves intersect at
exactly one point.
Solution 6:- (a, b, c)
The correct answers are (a), (b) and (c).
Clearly at x = , f (x) has relative minimum f (x) is continuous
but not differentiable at x =
Solution 7:- (b, d)
The correct answers are (b) and (d).
Solution 8:- (c, d)
The correct answers are (c) and (d).
As x is real.
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Solution 9:- (a, b)
The correct answers are (a) and (b).
Solution 10:- (a, b, d)
The correct answers are (a), (b) and (d).
We know that sin x in an increasing function of x in
Solution 11:- (c)
The correct answer is (c).
Solution 12:- (b)
The correct answer is (b).
Solution 13:- (b)
The correct answer is (b).
Solution 14:- (b)
The correct answer is (b).
Now, consider the function y = h(x), where
On solving we get
Solution 15:- (c)
The correct answer is (c).
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Now, consider the function y = h(x), where
On solving we get
Domain of h(x) is (0, 1)
Solution 16:- (d)
The correct answer is (d).
Now, consider the function y = h(x), where
On solving we get
Solution 17:- (1)
So period of f (x) = L.C.M. (Period of cos 6x, period of tan
4x)
Solution 18:- (2)
f (x) vanishes at x = 2
Also f (x) has relative maximum/minimum at x = 1 and
From (i), (ii), (iii) and (iv), we get on solving
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a = 1, b = 1, c = 1, d = 2.
Solution 19:- (5)
Solution 20:- (4)
For (i) & (ii) f (x) = f (y)
As f (0) = 2
f (x) = x + 2
f (x) 2 + 2 = 4
