TIME LEFT -

Question 1
5 / -1

If A is a singular matrix, then adj A is

A
Singular

B
Non-singular

C
Symmetric

D
Not defined

Question 2
5 / -1

What is the degree of the following differential equation?
\(\rm x=\sqrt{1+\frac{d^2y}{dx^2}}\)

A
1

B
2

C
3

D
Degree is not defined

Question 3
5 / -1

The variance σ² of a random variable X is given by

A
E[X²]

B
{E[X]}²

C
E[X²] – {E[X]}²

D
E[X²] + {E[X]}²

Question 4
5 / -1

What is the interval over which the function f(x) = 6x - x², x > 0 is increasing?

A
(0, 3)

B
(3, 6)

C
(6, 9)

D
None of the above

Question 5
5 / -1

A coin is tossed 5 times. The probability of head is \(\frac{1}{2}\). The probability of exactly 2 heads is

A
\(\frac{1}{16}\)

B
\(\frac{3}{10}\)

C
\(\frac{5}{16}\)

D
\(\frac{7}{16}\)

Question 6
5 / -1

Which of the following is correct regarding the analysis of four components of time series analysis?

A
The additive model is used when all the four components of the time series analysis are independent of each other.

B
The multiplication model is used when all the four components of the time series analysis are independent of each other.

C
The multiplication model is used when all the four components of the time series analysis are dependent of each other.

D
None

Question 7
5 / -1

If \(4\hat i + \hat j - 3\hat k\) and \(p\hat i + q\hat j - 2\hat k\) are collinear vectors, then what are the possible values of p and q respectively?

A
4, 1

B
1, 4

C
\(\frac{8}{3}, \frac{2}{3}\)

D
\(\frac{2}{3}, \frac{8}{3}\)

Question 8
5 / -1

If aN = {ax : x∈N} then 2N ∩ 5N is

A
10N

B
7N

C
N

D
21N

Question 9
5 / -1

What is the general solution of (1 + e^x) ydy = e^x dx ?
where c is a constant of integration.

A
y² = ln [c² (e^x + 1)²]

B
y = ln [c(e^x + 1)]

C
y² = ln [c (e^x + 1)]

D
None of the above

Question 10
5 / -1

If I₃ is the identify matrix of order 3, then \(I_3^{ - 1}\) is

A
0

B
3I₃

C
I₃

D
Does not exist

Question 11
5 / -1

Max z = 4x₁ + 3x₂ subject to constraints
2x₁ + x₂ ≤ 1000
x₁ + x₂ ≤ 800
x₁ ≤ 400
x₂ ≤ 700
x₁, x₂ ≥ 0
To maximize the profit ‘z’, find the optimum units of x₁ & x₂ to be used.

A
x₁ = 100, x₂ = 700

B
x₁ = 400, x₂ = 200

C
x₁ = 200, x₂ = 600

D
x₁ = 300, x₂ = 500

Question 12
5 / -1

Let f(x) = x + x^-1. Then which of the following is correct?

A
f(x) has a maximum but no minimum

B
f(x) has a maximum and a minimum and max f(x) > min f(x)

C
f(x) has a maximum and a minimum and max f(x) < min f(x)

D
f(x) has a minima but no maxima

Question 13
5 / -1

Rate of growth of bacteria is proportional to the number of bacteria present at time. If x is the number of bacteria present at any instant t, then which one of the following is correct? (Let the proportional constant equal to 2)

A
\(\sqrt{x}=-~C~{{e}^{t}}\)

B
\(\sqrt{x}=2C~{{e}^{t}}\)

C
\(\sqrt{x}=C~{{e}^{t}}\)

D
None of these

Question 14
5 / -1

Find the condition on k, so that the system of equations: x + 3y = 5 and 2x + ky = 8 has a unique solution.

A
k = 6

B
k ≠ 6

C
k ≠ 4

D
k = 4

Question 15
5 / -1

If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?

A
θ = 30°

B
θ = 45°

C
2 cos θ = 1

D
3 cos θ = 1

Question 16
5 / -1

The value of
\(\rm [\vec{a} + 2\vec{b} - \vec{c}, \vec{a} - \vec{b}, \vec{a}-\vec{b}- \vec{c}]=\) is ?

A
0

B
\(\rm[\vec{a}, \vec{b}, \vec{c}]\)

C
\(\rm 2[\vec{a}, \vec{b}, \vec{c}]\)

D
\(\rm 3[\vec{a}, \vec{b}, \vec{c}]\)

Question 17
5 / -1

If f(x) = |x + 1| + |x + 10|, then find the minimum value of f(x).

A
10

B
1

C
9

D
21

Question 18
5 / -1

The length of the perpendicular drawn from the origin to the plane 2x - 3y + 6z - 42 = 0 is

A
3

B
4

C
5

D
6

Question 19
5 / -1

If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the squares of its direction cosines?

A
(a + b + c)²

B
2 (a + b + c)

C
3

D
1

Question 20
5 / -1

If x^e = e^{\(\rm {x^2+y^2}\)}, then find \(\rm dy\over dx\)

A
\(\rm -{x\over y}\)

B
\(\rm e- 2x^2\over2xy\)

C
\(\rm e- x^2\over x\)

D
\(\rm e + 2x\over xy\)

Question 21
5 / -1

Consider the Linear Programming problem:
Maximize: 7X₁ + 6X₂ + 4X₃
subject to:
X₁ + X₂+ X₃ ≤ 5;
2X₁ + X₂ + 3X₃≤ 10,
X₁, X₂, X₃ ≥ 0 (Solve by algebraic method).
The number of basic solutions is:

A
10

B
7

C
9

D
8

Question 22
5 / -1

A manufacturing firm has its variable cost given by C(x) = x(12 - x³) where 'x' is the number of quantities produced. The price per unit is p(x) = 6x - 2 where 'x' is the number of units in demand. The ratio of marginal cost and marginal revenue when 3 units were both produced and in demand -

A
34 Rs

B
28 Rs

C
36 Rs

D
None

Question 23
5 / -1

A solution of 100L contains 75 percent water and rest liquid sugar. How much liquid sugar must be added to make 50 percent sugar solution?

A
30 L

B
20 L

C
25 L

D
50 L

Question 24
5 / -1

A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either Ace or a King?

A
\(\frac{4}{13}\)

B
\(\frac{1}{13}\)

C
\(\frac{2}{13}\)

D
None of the above

Question 25
5 / -1

The mean of the probability distribution function given by the following table will be:
x 1 2 3 4 5
P(x) 0.2 0.35 0.25 0.15 0.05

A
2.5

B
3.2

C
2.7

D
None of these

Question 26
5 / -1

Maximize, z = 5x₁ + 3x₂ subjected to the following constraint
x₁ + x₂ ≥ 3
x₁ - x₂ ≤ 2
and the solution is in first quadrant. What can be said about the solution of this LPP?

A
Unbounded solution

B
Unique solution

C
No solution

D
None of these

Question 27
5 / -1

If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ϵ (0, 1)

A
2f'(c) = g'(c)

B
2f'(c) = 3g'(c)

C
f'(c) = g'(c)

D
f'(c) = 2g'(c)

Question 28
5 / -1

Given that x is a random variable in the range [0, ∞] with a probability density function \(\frac{e^-{\frac{x}{2}}} {K}\) the value of the constant K is___________.

A
2

B
-7

C
-2

D
4

Question 29
5 / -1

Find the present value of a sequence of payments of Rs 432 made at the end of each 5 months and continuing forever if money is worth 5% compounded at the end of each 5 months.

A
Rs. 43,200

B
Rs. 48,200

C
Rs. 45,000

D
None

Question 30
5 / -1

A cricket bat manufacturing firm assesses its variable cost to be ‘2x’ times ‘x - 40’, where ‘x’ is the number of bats produced, and also the cost incurred on storage is Rs. 1200. Then how many bats should be manufactured for the minimum total cost?

A
14 Bats

B
12 Bats

C
20 Bats

D
6 Bats

Question 31
5 / -1

The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has non-trivial solution is

A
k = 0 or \(\frac{9}{2}\)

B
k = 10

C
k < 9

D
k > 0

Question 32
5 / -1

Consider the data given in the table -
Item Year 1985 (Price per unit in dollars) Year 1986 (Price per unit in dollars)
A 75 90
B 85 115
C α 75
D 100 β
Taking the base year 1985, the index number calculated by the simple aggregate method comes out to be 125, then the value of (4β - 5α) will be -

A
185

B
240

C
180

D
Can not be calculated

Question 33
5 / -1

Let k be the order of a mod n then a^b ≡ 1(mod n) if and only if

A
k divides a

B
k divides b

C
k divides n

D
k divides 1

Question 34
5 / -1

Which of the following statement is true regarding sinking fund and saving account?

A
The sinking fund and saving account both are the same and are used for a particular purpose in the future.

B
The sinking fund is set up for a particular purpose and is to be used at a particular time,

C
We can use the sinking fund at any point in time.

D
None of the above

Question 35
5 / -1

If |3x - 5| ≤ 2 then

A
\(\rm -1 \le x \le \dfrac{7}{3}\)

B
\(\rm 1 \le x \le \dfrac{7}{3}\)

C
\(\rm 1 \le x \le \dfrac{9}{3}\)

D
\(\rm -1 \le x \le \dfrac{9}{3}\)

Question 36
5 / -1

A continuous random variable, X is distributed in interval 0 to 10.
The probability, P(X = 2) is ______.

A
0.7

B
1/2

C
0

D
None

Question 37
5 / -1

\(\mathop \smallint \limits_{\frac{1}{2}}^2 \frac{1}{x}sin\left( {x - \frac{1}{x}} \right)dx = \)

A
0

B
2

C
3

D
1

Question 38
5 / -1

Let, R = {(a, b): a, b ϵ N and a² = b}, then what is the relation R

A
Reflexive

B
Symmetric

C
Transitive

D
None of the above

Question 39
5 / -1

\(\rm \int \frac{1}{e^x+e^{-x}}dx=\)

A
log |cot(e^x) + tan(e^x)|

B
\(\rm sin^{-1}(e^x)+c\)

C
log |1 + e^x|

D
\(\rm tan^{-1}(e^x)+c\)

Question 40
5 / -1

Find the area under the curve y = cos x in the interval \(\rm 0

A
0.5

B
1

C
0.7

D
1.2

Question 41
5 / -1

Consider the following statements
I. The derivative, where the function attains maxima or minima be zero.
II. If a function is differentiable at a point, then it must be continuous at that point.
Which of the above statement(s) is/are correct?

A
Only I

B
Only II

C
Both I and II

D
Neither I nor II

Question 42
5 / -1

If \({a_{ij}} = \frac{1}{2}\left( {3i - 2j} \right)and\,A = {\left[ {{a_{ij}}} \right]_{2 \times 2}}\), then A is equal to

A
\(\left[ {\begin{array}{*{20}{c}} {1/2}&2\\ { - 1/2}&1 \end{array}} \right]\)

B
\(\left[ {\begin{array}{*{20}{c}} {1/2}&{ - 1/2}\\ 2&1 \end{array}} \right]\)

C
\(\left[ {\begin{array}{*{20}{c}} 2&2\\ {1/2}&{ - 1/2} \end{array}} \right]\)

D
None of these

Question 43
5 / -1

Find the area of the region (in sq. units) bounded by the curve y = x, y = x² + 2 for x ∈ (‑1, 1)

A
11/3

B
1/3

C
2/3

D
14/3

Question 44
5 / -1

Let \(A = \left[ {\begin{array}{*{20}{c}} 4&6&{ - 1}\\ 3&0&2\\ 1&{ - 2}&5 \end{array}} \right]\),\(B = \left[ {\begin{array}{*{20}{c}} 2\\ 0\\ { - 1} \end{array}\begin{array}{*{20}{c}} 4\\ 1\\ 2 \end{array}} \right]\)and C = [3 1 2]. The expression which is not defined is

A
B'B

B
CAB

C
A + B'

D
A² + A

Question 45
5 / -1

The area bounded by the curve x² = ky, k > 0, and the line y = 3 is 12 unit². Then k is?

A
3

B
3√3

C
3/4

D
none of these

Question 46
5 / -1

Find the value of f(x) when \(\rm f(x)=\int_{0}^{x} \frac{dt}{t^{2}+9}\)

A
\(\rm\frac{1}{3}tan^{-1}\frac{x}{3}\)

B
\(\rm\frac{1}{9}tan^{-1}\frac{x}{9}\)

C
\(\rm tan^{-1}\frac{x}{3}\)

D
\(\rm tan^{-1}\frac{x}{9}\)

Question 47
5 / -1

If tan^-1(2), tan-1(3) are two angles of a triangle, then what is the third angle ?

A
3π/4

B
π/4

C
π/3

D
π/6

Question 48
5 / -1

What is the domain of the function f(x) = cos sin-1 (x + 1) ?

A
[-2, 0]

B
[-1, 0)

C
(-2, 0)

D
None

Question 49
5 / -1

If the area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 square units, then what is the value of k?

A
3

B
6

C
9

D
12

Question 50
5 / -1

If y = cos (sin² x), then find the value of \(\rm\frac{dy}{dx}\) at x = \(\rm\frac{\pi}{2}\).

A
0

B
1

C
\(\rm\frac{1}{2}\)

D
\(\rm\frac{1}{3}\)

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Question Analysis

Answered - 0
Unanswered - 50

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Item	Year 1985 (Price per unit in dollars)	Year 1986 (Price per unit in dollars)
A	75	90
B	85	115
C	α	75
D	100	β

x	1	2	3	4	5
P(x)	0.2	0.35	0.25	0.15	0.05

Mathematics Moc...

Question 1

Singular

Non-singular

Symmetric

Not defined

Question 2

1

2

3

Degree is not defined

Question 3

E[X2]

{E[X]}2

E[X2] – {E[X]}2

E[X2] + {E[X]}2

Question 4

(0, 3)

(3, 6)

(6, 9)

None of the above

Question 5

\(\frac{1}{16}\)

\(\frac{3}{10}\)

\(\frac{5}{16}\)

\(\frac{7}{16}\)

Question 6

The additive model is used when all the four components of the time series analysis are independent of each other.

The multiplication model is used when all the four components of the time series analysis are independent of each other.

The multiplication model is used when all the four components of the time series analysis are dependent of each other.

None

Question 7

4, 1

1, 4

\(\frac{8}{3}, \frac{2}{3}\)

\(\frac{2}{3}, \frac{8}{3}\)

Question 8

10N

7N

N

21N

Question 9

y2 = ln [c2 (ex + 1)2]

y = ln [c(ex + 1)]

y2 = ln [c (ex + 1)]

None of the above

Question 10

0

3I3

I3

Does not exist

Question 11

x1 = 100, x2 = 700

x1 = 400, x2 = 200

x1 = 200, x2 = 600

x1 = 300, x­2 = 500

Question 12

f(x) has a maximum but no minimum

f(x) has a maximum and a minimum and max f(x) > min f(x)

f(x) has a maximum and a minimum and max f(x) < min f(x)

f(x) has a minima but no maxima

Question 13

\(\sqrt{x}=-~C~{{e}^{t}}\)

\(\sqrt{x}=2C~{{e}^{t}}\)

\(\sqrt{x}=C~{{e}^{t}}\)

None of these

Question 14

k = 6

k ≠ 6

k ≠ 4

k = 4

Question 15

θ = 30°

θ = 45°

2 cos θ = 1

3 cos θ = 1

Question 16

0

\(\rm[\vec{a}, \vec{b}, \vec{c}]\)

\(\rm 2[\vec{a}, \vec{b}, \vec{c}]\)

E[X²]

{E[X]}²

E[X²] – {E[X]}²

E[X²] + {E[X]}²

y² = ln [c² (e^x + 1)²]

y = ln [c(e^x + 1)]

y² = ln [c (e^x + 1)]

3I₃

I₃

x₁ = 100, x₂ = 700

x₁ = 400, x₂ = 200

x₁ = 200, x₂ = 600

x₁ = 300, x₂ = 500

(a + b + c)²