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VITEEE Maths Test - 4

40 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE Maths Test - 4

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This mock test of VITEEE Maths Test - 4 for JEE helps you for every JEE entrance exam. This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 4 (mcq) to study with solutions a complete question bank. The solved questions answers in this VITEEE Maths Test - 4 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this VITEEE Maths Test - 4 exercise for a better result in the exam. You can find other VITEEE Maths Test - 4 extra questions, long questions & short questions for JEE on EduRev as well by searching above.

QUESTION: 1

A condition for a function y = f(x) to have inverse is that it should be

A.
defined for all x
B.
continueous everywhere
C.
strictly monotomic and continuous in the domain
D.
an even function

Solution:

QUESTION: 2

The area bounded by the x-axis and the curve y = 4 x − x² − 3 is

A.
1/3
B.
2/3
C.
4/3
D.
8/3

Solution:

y = 0, y = 4x - x² - 3
⇒ 4x - x² - 3 = 0
⇒ x² - 4x + 3 = 0
⇒ (x - 1) (x - 3) = 0
⇒ x = 1, 3

QUESTION: 3

If

A.
z
B.
C.
iz
D.

Solution:

QUESTION: 4

If then

A.
Δ = Δ ′
B.
Δ ′ = 1/Δ
C.
Δ ′ = Δ²
D.
Δ ′ = 2 Δ

Solution:

QUESTION: 5

If the function f is defined by then at what points is f differentiable

A.
Every where
B.
At x = 1
C.
Except at x = 0
D.
Except at x = 0 or 1

Solution:

QUESTION: 6

If z² + z + 1 = 0, where z is a complex number then the value of

A.
6
B.
12
C.
18
D.
24

Solution:

QUESTION: 7

If is continuous at π/4 , then a =

A.
4
B.
2
C.
1
D.
1/4

Solution:

QUESTION: 8

A.
e/2
B.
C.
D.

Solution:

QUESTION: 9

The solution of the differential equation cos(x + y)dy = dx is

A.
y = tan⁻¹x + y
B.
C.
y = C + sin(x + y)
D.
y = C + cos(x + y)

Solution:

QUESTION: 10

The solution of differential equation (dy/dx)=[(x(2logx+1))/(siny+ycosy)] is

A.
ysiny=x²logx+(x²/2)+c
B.
ycosy=x²(logx+1)+c
C.
ycosy=x²logx+(x²/2)+c
D.
ysiny=x²logx+c

Solution:

QUESTION: 11

The roots of the equation are

A.
0, -3
B.
0, 0, - 3
C.
0, 0, 0, - 3
D.
0, 0, 3

Solution:

QUESTION: 12

The degree of the differential equation

A.
1/3
B.
4
C.
1
D.
3/4

Solution:

QUESTION: 13

The differential equation which represents the family of plane curves y=exp. (cx) is

A.
y'=cy
B.
xy'-logy=0
C.
x log y=yy'
D.
y log y=xy'

Solution:

y = e^cx
dy dx = c. e^cx
y' = cy

QUESTION: 14

If x=a[(cost)+(log tan(t/2))], y=a sint, (dy/dx)=

A.
cot t
B.
tan t
C.
sin t
D.
cos t

Solution:

QUESTION: 15

The range of the function f(x) = x² - x/x² + 2x is

A.
R - {- 1/2, 1}
B.
R
C.
R - {1}
D.
none of these

Solution:

QUESTION: 16

A.
+cotx-2x+c
B.
-2cotx+2x+c
C.
-2cotx-x+c
D.
-2cotx+x+c

Solution:

QUESTION: 17

If where n > 1 , then I_n − I_{n − 2}

Solution:

QUESTION: 18

sec²(tan^-1 2) + cosec²(cot^-1 3) =

A.
5
B.
10
C.
15
D.
20

Solution:

QUESTION: 19

Let
What is the value of

A.
0
B.
-1/9
C.
1/3
D.
1/9

Solution:

QUESTION: 20

The value of

A.
-1
B.
0
C.
11e/24
D.
− 11e/24

Solution:

QUESTION: 21

Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?

A.
Today is Sunday and Matt can play hockey.
B.
If Matt plays hockey, then today is not Sunday.
C.
Today is Sunday and Matt cannot play hockey.
D.
Today is not Sunday if and only if Matt plays hockey.

Solution:

Statements are logically equivalent to their contrapositives.

QUESTION: 22

If A is a singular matrix, then A adj (A)

A.
is an identity matrix
B.
is a zero scalar
C.
is a scalar matrix
D.
is an orthogonal matrix

Solution:

QUESTION: 23

If A and B both are of order 2 x 3 , which one of these is not defined ?

A.
AB^T
B.
A + B
C.
B^T A^T
D.
A^T B

Solution:

QUESTION: 24

Twelve students compete for a race. The number of ways in which first three prizes can be taken is

A.
(12)! - 3
B.
(12)! ÷ 3!
C.
3!
D.
12.11.10

Solution:

QUESTION: 25

An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

A.
16/81
B.
1/81
C.
80/81
D.
none of these

Solution:

QUESTION: 26

A committee of 5 is to be chosen from a group of 9 people. What is the probability that a certain married couple serve together or not at all ?

A.
1/2
B.
5/9
C.
4/9
D.
2/3

Solution:

QUESTION: 27

Two dice are thrown simultaneously. The probability of obtaining a total score of seven is

A.
1/6
B.
5/36
C.
7/36
D.
1/4

Solution:

There are six possible ways as to the number of points on the first die; and to each of these ways, there corresponding 6 possible numbers of points on second die.
Hence total number of ways S = 6 x 6 = 36
We now find out how many ways are favorable to the total of 7 points.
This may happen only in following ways:
(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3).
Hence, required Probability = 6/36 =1/6.

QUESTION: 28

In a triangle , then b =

A.
16
B.
20
C.
24
D.
28

Solution:

QUESTION: 29

If the sum of n terms of the series 2³ + 4³ + 6³ + ... ∞ is 3528, then n equals

A.
6
B.
7
C.
8
D.
9

Solution:

QUESTION: 30

The Quartile Deviation of the daily wages (in Rs) of 7 persons given below :
12, 7, 15, 10, 17, 19, 25 is

A.
14.5
B.
5
C.
9
D.
4.5

Solution:

QUESTION: 31

The S.D. of 5 scores
1 2 3 4 5 is

A.
2/5
B.
3/5
C.
√2
D.
√3

Solution:

QUESTION: 32

If x is positive, the greatest value of 5+4x-4x² is

A.
5
B.
6
C.
1
D.
2

Solution:

QUESTION: 33

The degree of the equation is ____

A.
4
B.
6
C.
8
D.
none of these

Solution:

QUESTION: 34

A st. line which makes an angle of 60⁰ with each of y and z axes, inclines with x-axis at an angle

A.
45⁰
B.
30⁰
C.
75⁰
D.
60⁰

Solution:

QUESTION: 35

The direction ratios of a normal to the plane through (1, 0, 0), (0, 1, 0), which makes an angle of π/4 with the plane x + y = 3 are

A.
< 1, √2, 1 >
B.
< 1, 1, √2 >
C.
< 1, 1, 2 >
D.
< √2, 1, 1 >

Solution:

QUESTION: 36

If sin2x+sin4x=2sin3x, then x=

A.
nπ/3
B.
nπ+(π/3)
C.
2nπ (π/3)
D.
nπ-(π/3)

Solution:

QUESTION: 37

Locus of centroid of the triangle whose vertices are (a cost, a sint), (b sint, -b cost) and (1, 0), where t is a parameter, is

A.
(3x - 1)² + (3y)² = a² + b²
B.
(3x + 1)² + (3y)² = a² + b²
C.
(3x + 1)² + (3y)² = a² - b²
D.
(3x - 1)² + (3y)² = a² - b²

Solution:

QUESTION: 38

In a ∆ABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is

A.
(1, 4)
B.
(7, -2)
C.
(4, 1)
D.
(-2, 7)

Solution:

QUESTION: 39

If θ is the angle between vectors a and b and |axb|=a.b, then θ=

A.
π
B.
π/2
C.
π/4
D.
0

Solution:

QUESTION: 40

The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k is

A.
[(√115)/(√14)(√194)]
B.
[(51)/(√14)(√144)]
C.
[(√64)/(√14)(√194)]
D.
none of these

Solution:

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VITEEE Maths Test - 4

40 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE Maths Test - 4

A condition for a function y = f(x) to have inverse is that it should be

The area bounded by the x-axis and the curve y = 4 x − x² − 3 is

If

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VITEEE Maths Test - 4

40 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE Maths Test - 4

A condition for a function y = f(x) to have inverse is that it should be

The area bounded by the x-axis and the curve y = 4 x − x2 − 3 is

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The area bounded by the x-axis and the curve y = 4 x − x² − 3 is