StudyNp
BIT
CSIT
MOCKTEST
02:00:00
Math
Physics
Chemistry
English
Computer
1. Number of nonempty singleton subsets from the elements of the set {l,m,n,p} is
4
3
2
1
2. Let f : A→B, then f is invertible if
f is one-one
f is onto
f is both one-one and onto
f is one-one into
3. Let
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be defined by
f
(
x
)
=
3
x
−
4
f(x) = 3x - 4
f
(
x
)
=
3
x
−
4
. Then what is
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
?
(x+4)/3
x-4/3
x+4
x-4
4. What is the value of the limit?
lim
x
→
∞
(
1
+
3
x
)
x
\lim_{x \to \infty} \left(1 + \frac{3}{x}\right)^x
lim
x
→
∞
(
1
+
x
3
)
x
e
3
e^3
e
3
3
e
3e
3
e
3
e
3
3e^3
3
e
3
1
e
3
\frac{1}{e^3}
e
3
1
5. lim x→∞ sinx/x is equal to
3
2
1
0
6. Analyze the properties of the function
f
(
x
)
f(x)
f
(
x
)
defined as:
f
(
x
)
=
{
2
x
if
x
<
2
2
if
x
=
2
x
2
if
x
>
2
f(x) = \begin{cases} 2x & \text{if } x < 2 \\ 2 & \text{if } x = 2 \\ x^2 & \text{if } x > 2 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
2
x
2
x
2
if
x
<
2
if
x
=
2
if
x
>
2
Continuous at x = 2
discontinuous at x = 2
removable discontinuous at x = 2
does not exist
7. d/dx(log|x| is equal to )
1/|x|
±1
1/x
1/x^2
8. The derivative of
sin
3
(
x
)
\sin^3(x)
sin
3
(
x
)
with respect to
cos
3
(
x
)
\cos^3(x)
cos
3
(
x
)
is?
tanx
-tanx
tan^3 x
cot x
9. If
f
(
x
)
=
log
(
log
x
)
f(x) = \log(\log x)
f
(
x
)
=
lo
g
(
lo
g
x
)
, then what is
f
′
(
e
)
f'(e)
f
′
(
e
)
equal to?
e
1/e
1
-1
10. The minimum value of f(x) = sinx.cosx is
-1/2
1/2
0
1
11. ∫ logx dx is equal to
(logx-1)+C
(xlogx-1)+C
(xlogx+1)+C
x(logx-1)+C
12. What is the value of the definite integral
∫
0
3
/
2
d
x
1
−
x
2
\int_{0}^{\sqrt{3}/2} \frac{dx}{\sqrt{1-x^2}}
∫
0
3
/2
1
−
x
2
d
x
?
π/3
π/6
π/4
π/2
13. The area bounded by the parabola y2 = x, the line y = 4 and y-axis is
16/3
32/3
64/3
125/3
14. The modulus of
(
1
−
i
)
3
1
−
i
3
\frac{(1-i)^3}{1-i^3}
1
−
i
3
(
1
−
i
)
3
is equal to?
-1
i
0
2
15. The roots of the equation
2
x
2
−
3
x
+
1
=
0
2x^2-3x+1 = 0
2
x
2
−
3
x
+
1
=
0
are
real, unequal, rational
real, equal
perfect square, equal
unequal, imaginary
16. If A=(1 2; 3 4) and B=(5 6; 7 8) then (AB)` is :
(1 0;0 1)
(19 43; 22 50)
(19 22; 43 50)
(22 50; 43 19)
17. The two lines of the system 6x - 4y = 10, 3x - 2y = 5 are
parallel
intersecting
coincident
independent
18. If the A.M. and G.M. between two given numbers are 81 and 18, respectively, then H.M. is
99
49.5
4.5
4
19. The most general value of
θ
\theta
θ
satisfying the equation
3
tan
2
(
θ
)
=
1
3 \tan^2(\theta) = 1
3
tan
2
(
θ
)
=
1
is?
n
π
+
π
6
n\pi + \frac{\pi}{6}
nπ
+
6
π
n
π
±
π
6
n\pi \pm \frac{\pi}{6}
nπ
±
6
π
2
n
π
±
π
6
2n\pi \pm \frac{\pi}{6}
2
nπ
±
6
π
(
−
1
)
n
π
6
(-1)^n \frac{\pi}{6}
(
−
1
)
n
6
π
20.
tan
−
1
(
x
)
−
tan
−
1
(
1
x
)
\tan^{-1}(x) - \tan^{-1}\left(\frac{1}{x}\right)
tan
−
1
(
x
)
−
tan
−
1
(
x
1
)
is equal to
1
pi/2
pi/4
0
21. In a
△
A
B
C
\triangle ABC
△
A
BC
, the inradius
r
r
r
is equal to?
(
s
−
a
)
tan
(
B
/
2
)
(s - a)\tan(B/2)
(
s
−
a
)
tan
(
B
/2
)
(
s
−
b
)
tan
(
B
/
2
)
(s - b)\tan(B/2)
(
s
−
b
)
tan
(
B
/2
)
(
s
−
b
)
tan
(
C
/
2
)
(s - b)\tan(C/2)
(
s
−
b
)
tan
(
C
/2
)
(
s
−
a
)
tan
(
C
/
2
)
(s - a)\tan(C/2)
(
s
−
a
)
tan
(
C
/2
)
22. Find the distance between the two parallel lines
3
x
+
4
y
=
6
3x + 4y = 6
3
x
+
4
y
=
6
and
6
x
+
8
y
=
16
6x + 8y = 16
6
x
+
8
y
=
16
.
2/3 units
2/5 units
10/3 units
3/10 units
23. For what value of
λ
\lambda
λ
does the equation
12
x
2
−
10
x
y
+
2
y
2
+
11
x
−
5
y
+
λ
=
0
12x^2 - 10xy + 2y^2 + 11x - 5y + \lambda = 0
12
x
2
−
10
x
y
+
2
y
2
+
11
x
−
5
y
+
λ
=
0
represent a pair of straight lines?
1
2
3
4
24. The equation of the circle having the ends of its diameter at
(
1
,
−
1
)
(1, -1)
(
1
,
−
1
)
and
(
0
,
2
)
(0, 2)
(
0
,
2
)
is?
x
2
+
y
2
−
x
−
y
−
2
=
0
x^2 + y^2 - x - y - 2 = 0
x
2
+
y
2
−
x
−
y
−
2
=
0
x
2
+
y
2
+
x
+
y
−
2
=
0
x^2 + y^2 + x + y - 2 = 0
x
2
+
y
2
+
x
+
y
−
2
=
0
x
2
+
y
2
−
x
−
2
y
+
2
=
0
x^2 + y^2 - x - 2y + 2 = 0
x
2
+
y
2
−
x
−
2
y
+
2
=
0
x
2
+
y
2
−
x
+
2
y
−
2
=
0
x^2 + y^2 - x + 2y - 2 = 0
x
2
+
y
2
−
x
+
2
y
−
2
=
0
25. The direction cosines of a line equally inclined to the axes are
1/2,1/2,1/2
1/3,1/3,1/3
±1/√2, ±1/√2, ±1/√2
±1/√3, ±1/√3, ±1/√3
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