Chapter 2 Differentiation
MCQ's with answers from chapter 1 Functions and Limits Mathematics book 2 for FSC pre engineering for Board of Intermediate and Secondary education. Also For Entry Test Preparation for UET, NUST, PIEAS, GIKI, AIR, FAST, WAH University, other engineering Universities.
Chapter 2 DIFFERENTIATION
4) The
slope of the tangent to the curve y = x3 + 5 at the point (1, 2) is
A)
6
B)
2
C)
5
D)
3
Answer: D
5) If
a particle thrown vertically upward move according to the law, x = 32t – 16 t2
(x in ft, t in sec) then the height attained by the particle when the velocity
is zero is
A)
0
B)
32t
C)
16ft
D)
2ft
Answer: C
6) If
a particle moves according to the law x = 16 t – 4 then acceleration at time t
= 20 is
A)
6
B)
0
C)
116
D)
4
Answer: B
7) If
a particle moves according to the law x = et then velocity at time t
= 0 is
A)
0
B)
1
C)
e
D)
none of these
Answer: B
4. Differentiation
of Trigonometric, Logarithmic and Exponential Function
1) The derivative of sin (a + b) w.r.t x
is
A)
cos (a + b)
B)
– cos (a + b)
C)
cos (a – b)
D)
0
Answer: D
2) The
derivative of x sina w.r.t x is
A)
cos a
B)
x cos a + sin a
C)
– x cos a + sin a
D)
sin a
Answer: D
5) The
derivative of tan (ax + b) w.r.t tan (ax + b) is
A)
sec2 (ax + b)
B)
a sec2 (ax + b)
C)
b sec2 (ax + b)
D)
1
Answer: D
6) If
x = 2cos7q,
y = 4sin7q
then dy/dx is equal to
A)
4tan7q
B)
– 4tan7q
C)
4tan5q
D)
– 2tan5q
Answer: D
10) The
base of the natural logarithmic function is
A)
10
B)
2
C)
e
D)
none of these
Answer: C
11) The
natural exponential function is defined by the equation
A)
y = ax
B)
y = 2x
C)
y = ex
D)
y = 3x
Answer: C
12) The
derivative of sin (sin a) w.r.t x is
A)
cos (sina)
B)
cos (sina) cosa
C)
cos (cosa)
D)
0
Answer: D
13) If
ay = x then the value of y is
A)
ax
B)
logax
C)
x/a
D)
a/x
Answer: B
15) The derivative of exp (sinx) is
A)
exp (cosx)
B)
sinx exp(cosx)
C)
(cosx) exp (sinx)
D)
cosx exp (cosx)
Answer: C
16) The
derivative of e2 w.r.to x is
A)
2e
B)
2
C)
1
D)
0
Answer: D
17) The derivative of Xx is
A)
X x – 1
B)
X.X x – 1
C)
Xx (1+ln x)
D)
Xx ln x
Answer: C
18) If
dx
or dx is quite small then the difference between dy and dy will be
A)
very large
B)
large
C)
small
D)
negligible
Answer: D
19) If
radius of a circular disc is unity then its area will be
A)
pc2
B)
2pc
C)
p
D)
2p
Answer: C
20) the
derivative of the function f(x) = sinx + sinx + …. Up to 9 times, is
A)
cosx + cosx + cosx
B)
9 cosx
C)
9 sin x
D)
3 cos x
Answer: B
23) The
derivative of the function y = tanx is
A)
tanx sec2 45o + sec2 x
tan 45o
B)
sec2x sec245o
C)
Sec2 45o
D)
Sec2x
Answer: D
24) A
particle thrown vertically upward, moves according to the law, x = 32 – 16t2
(x in ft, t in sec) then the maximum height attained by the particle is
A)
32ft
B)
16ft
C)
48ft
D)
2ft
Answer: B
25) If
in a function y = x2 – 2x, x = 4, increment in x = 0.5 then the
value of differential of the dependent variable is
A)
4.5
B)
3.5
C)
3
D)
2.5
Answer: C
Higher order Derivatives Maxima and Minima
1) If
y = e2x the y9 is
A)
e2x
B)
29
C)
29 e2x
D)
28 e2x
2) In
the interval (- ¥,
¥)
the function defined by the equation y = x3 is
A)
increasing
B)
decreasing
C)
constant
D)
even
3) The
origin for the function y = x3 is a point of
A)
Maxima
B)
Minima
C)
Inflexion
D)
Absolute Maxima
4) If
f¢
( c ) exists then f ( c) is a maximum or minimum value of f, only if
A)
f¢( c) > 0
B)
f¢( c) < 0
C)
f¢( c) = 0
D)
f¢( c) = 1
5) If
f¢(
c) < 0 for every c Î (a, b) then in (a, b) f is
A)
increasing
B)
decreasing
C)
constant
D)
zero
6)
A function f will have a minimum value at x = a, if
f¢ (a) = 0 and f¢¢
(a) is
A)
+ ve
B)
– ve
C)
0
D)
¥
7) The
function f(x) = x2 increases in the interval
A)
[1, 5]
B)
[- 1, 5]
C)
[- 5, 1]
D)
[-5, - 1]
8) The
function f(x) = 1 – x2 increases in the interval
A)
(- 5, 1)
B)
(-5, 2)
C)
(–5, 3)
D)
(-5, -1)
9) The
function f(x) = 1 – x3 decreases in the interval
A)
(-1, 1)
B)
(-2, 2)
C)
(-3, 3)
D)
All A, B and C are true
10) In
the interval (-2, 3) the function f(x) = x2 is
A)
increasing
B)
decreasing
C)
neither increasing nor decreasing
D)
maximum
12) The
function f(x) = x3 – 1 is increasing in the interval
A)
(-5, -1)
B)
(-5, 1)
C)
(-5, 5)
D)
All A, B, C are true
13) The
function f(x) = 1 – x3 has a point of inflexion at
A)
origin
B)
x = 2
C)
x = - 1
D)
x = 1
14) The
function f(x) = x2 – 3x + 2 has a minima at
A)
x = 1
B)
x = 3/2
C)
x = 3
D)
x = 2
17) The
function f(x) = 3x2 – 4x + 5 has a minima at
A)
x = 2/3
B)
x = 2
C)
x = 3
D)
x = - 2
18) The
function f(x) = 5x2 – 6x + 2 has a minima at
A)
x = 3
B)
x = 5
C)
x = 3/5
D)
x = - 3/5
19) In
the interval (0, p)
the function sinx has a maxima at the point
A)
x = 0
B)
x = p/2
C)
x = p
D)
x = p/4
20) In
the interval (0, p)
the function f(x) = sin x has a minimum value at the point
A)
x = 0
B)
x = p/2
C)
x = p/4
D)
x = p
30) Two
positive real numbers, whose sum is 40 and whose product is a maximum are
A)
30, 10
B)
25, 15
C)
20, 20
D)
19, 21
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