IPMAT Mock Test - 7 (New Pattern) - Commerce MCQ

Average =sum of all observation / Number of observation

The first three odd multiples of 9 = 9, 27 and 45

Average = (9 + 27 + 45) / 3

= 81 / 3

= 27

∴ Average of first three odd multiples of 27.

Hence, the correct option is (C).

log₂⁡(log₆⁡216)

Let log_2⁡(log₆⁡216) = y

As we can write,

As we know,

Hence, the correct option is (C).

Speed of train x = 74 km/h

Speed of train y = 52 km/h

Train x crosses train y in opposite direction in 12 seconds.

Length of train y = 2 / 3 of length of train x

1 km/h = 5 / 18 m/s

As we know,

If speed of body A is x and speed of body B is y then, Relative speed of two bodies moving in opposite direction = (x + y)

Relative speed =

⇒ Total length = 35 × 12

⇒ Total length = 420 m

Let the length of train x be 3a.

So, length of train

y = 2 / 3 × 3a = 2a

⇒ 2a + 3a = 420

⇒ 5a = 420

⇒ a = 84

Length of train y = 2a

= 2 × 84

= 168 m

∴ The length of train y is 168 m.

Hence, the correct option is (C).

Number of literates in village B = 54% of 150000 = 81000

Now,

Total number of literates in three villages = 285000

Number of literates in village C = 285000 − (60000 + 81000) = 144000

72% of total population of village C = 144000

∴ Total population of village C in

2015 = 144000 / 0.72 = 200000

Hence, the correct option is (B).

Number of literate males = 42000 + Number of literate females

Number of literate males - Number of literate females = 42000...(1)

Also,

Number of literate males + Number of literate females = Total number of literates

Number of literate males + Number of literate females = 75% of the total population of village A

But, the total population of village A is not given.

∴ The data is insufficient to solve the question.

Hence, the correct option is (D).

In the year 2016,

Literate population of village A = 64% of x = (16/25)x

Literate population of village B = 60% of y = (3/5)y

Literate population of village C = 80% of z = (4/5)z

Ratio of literate population of three villages = 2 : 3 : 5

∴ In 2016, the total populations of the three villages is in the ratio 5 : 8 : 10.

Hence, the correct option is (C).

Literate population of village B in 2016 = 60% of x = 0.6x

The population of village B increased by 20% from 2016 to 2017

Population of village B in 2017 = 120% of x = 1.2x

Literate population of village B in 2017=80% of 1.2x = 0.96x

Increase in literate population of village B from 2016 to 2017

= 0.96x − 0.6x = 0.36x

∴ Percentage increase = 0.36 / 0.6x × 100 = 60%

Hence, the correct option is (B).

Two sets A and B are disjoint sets if the intersection of two sets is a null set or an empty set.

A∩B = ϕ

Given, A, B, C and D are four sets such that A ∩ B = C ∩ D = ϕ

Statement 1:A∪C and B∪D are always disjoint,

⇒ (A ∪ C) ∩ (B ∪ D) = [(A ∪ C) ∩ B] ∪ [(A ∪ C)∩D]

= [(A ∩ B) ∪ (C ∩ B)] ∪ [(A ∩ D) ∪ (C ∩ D)]

= [ϕ ∪ (C ∩ B)] ∪ [(A ∩ D) ∪ ϕ]

= (C ∩ B)] ∪ [(A ∩ D) (∵A ∪ ϕ = A)

(A ∪ C) and (B ∪ D) is not disjoint set.

Statement 2:A ∩ C and B ∩ D are always disjoint,

⇒ (A ∩ C) ∩ (B ∩ D) = [(A ∩ C) ∩ B] ∩ [(A ∩ C) ∩ D]

= [(A ∩ B) ∩ C] ∩ [(A ∩ (C ∩ D)]

= [ϕ ∩ C] ∩ [(A ∩ ϕ](∵A ∩ ϕ = ϕ)

= (ϕ ∩ ϕ)

= ϕ

(A ∩ C) and (B ∩ D) are always disjoint.

So, statement 2 is correct.

Hence, the correct option is (B).

f(x) = x² + 4x + 4

Replace x by − x.

We know that:

If f(x) is even function then f(-x) = f(x)

If f(x) is odd function then f(-x) = -f(x)

⇒f(−x) = (−x)² + 4(−x) + 4

= x² − 4x + 4(∵(−x)² = x²)

⇒ f(−x) ≠ ±f(x)

Therefore, function is neither odd nor even.

Hence, the correct option is (C).

Where P is symmetric and Q is a skew-symmetric matrix.

As we know,

Any square matrix can be expressed as the sum of the symmetric and skew-symmetric matrix. i.e If A is a square matrix then A can be expressed as where A + A′ is symmetric and A − A′ is skew-symmetric matrix.

On comparing we get

Similarly,

So,

Hence, the correct option is (B).

I = a² + b² + c², where a and b are consecutive integers and c = ab

Let a and b be 1 and 2 respectively (a and b are consecutive numbers)

So, c = 1 × 2=2

Now

⇒ I = 1² + 2² + 2²

⇒ I = 9

Now let the values of a and b be 2 and 3 respectively

So, c = 2 × 3 = 6

Now,

⇒ I = 2² + 3² + 6²

⇒ I = 49

In both cases, it is coming out to be the square of an odd integer.

Hence, the correct option is (D).

f(x) is a rational function of the form g(x)hh(x), where g(x) = x and h(x) = x² + 3x + 2

Now h (x) ≠ 0

Therefore, the domain of the given function is R − {−1, −2}.

Hence, the correct option is (C).

SELECT = Combination =

SELECT and ARRANGE = Permutation =

Now in the remaining letters, there are two K's. So now there are 3 possibilities

1) KK - Take two K's and the third letter can be from remaining 6

alphabets (S,M,O,E,A,C). So possible combinations = ⁿC_r = 6C1 OR

2) K - Take one K and the two letters can be from remaining 6

alphabets (S,M,O,E,A,C). So possible combinations = ⁿC_r = ⁶C₂ OR

3) No K and three letters can be from remaining 6 alphabets (S, M, O, E, A, C). So possible combinations = ⁿC_r = ⁶C₃ OR

Total combinations = ⁶C₁ + ⁶C₂ + ⁶C₃ = 6 + 15 + 20 = 41 ways

Hence, the correct option is (D).

On squaring both sides, we get

Also,

Since a², p², b² are in A.P.

Putting value of a² + b² from equation (2) in equation (1), we get

a²b² = p²(a² + b²) = 2p⁴

Putting value of b2 from equation (3), we get

2p⁴ = a²(2p² − a²)

⇒ 2p⁴ = 2p²a² − a⁴

⇒ a⁴ − 2p²a² + 2p⁴=0

Hence, the correct option is (B).

Number of distinct relations from A to B = 2^{Number of elements in set A×Number of elements in set B}

Calculation:

Let A = {x, y ,z} and B = {p, q ,r, s}

Number of elements in set A = n(A) = 3

Number of elements in set B = n(B) = 4

∴ Number of distinct relations from B to A = 2ⁿ(B) × n(A) = 2^{4 × 3} = 2¹² = 4096

Hence, the correct option is (A).

Hence, the correct option is (A).

First by solving the inequation: 2(3x − 4) − 2 < 4x − 2 we get,

⇒ 6x − 10 < 4x − 2

⇒ 2x < 8

⇒ x < 4.....(1)

Similarly, by solving the inequation 4x−2≥2x−4 we get,

⇒ 2x ≥ − 2

⇒ x ≥ −1.....(2)

From equation (1) and (2) we can say that −1 ≤ x < 4

So, out of the given options the possible value which x can take is 2.

Hence, the correct option is (A).

Let a number N be equal to x³ + x² + 16.

N = x³ + x² + 16

Now divide N/x

As N is divisible by x so 16 must be divisible by x.

Values of x that can divide 16 are 1, 2, 4, 8 and 16.

So, there are total 5 values of x that can divide N without leaving the remainder.

Hence, the correct option is (C).

Transpose of matrix

Now,

Hence, the correct option is (A).

Radius of sphere = 3 cm

Height of the cone = Half of the radius of the cone

Volume of Sphere = Volume of Cone

Volume of Sphere

= 4/3 × πR³

Volume of Cone

=1/3 × πr²h

Suppose the height and radius of the cone are ' h ' and ' r ' respectively.

∴ h = r/2

Applying the formula:

43 × π × 3 × 3 × 3 = 1/3 × π × r × r × h

Put

h = r/2

⇒ 4/3 × 3 × 3 × 3 = 1 / 3 × r × r × r/2

⇒ r³ = 216

⇒ r = 6

∴ Radius of the cone =6 cm.

Hence, the correct option is (D).

[x]² − 5[x] + 6 = 0, where [ . ] denotes the greatest integer function.

[x]² − 5[x] + 6 = 0

[x]² − 2[x] −3[x] + 6 = 0

[x]([x − 2) − 3([x] −2) = 0

([x] − 2)([x] − 3) = 0

When [x] = 2, 2 ≤ x < 3

When [x] = 3, 3 ≤ x < 4

When [x] = 3, 3 ≤ x < 4

From the above, x ∈ [2, 4).

Hence, the correct option is (D).

Increase in length

57.13% = 4/7

Decrease in breadth

41.66% = 5/12

Decrease in height

46.66% = 7/15

Let initial length, breadth and height as 7x, 12y, 15z respectively.

Increase in length

= 7x × 4/7 = 4x

Decrease in breadth

= 12y × 5/12 = 5y

Decrease in height

= 15z × 7/15 = 7z

Final length = 7x + 4x = 11x

Final breadth = 12y − 5y = 7y

Final breadth = 15z − 7z = 8z

Initial volume = 7x × 12y × 15z = 1260xyz

Final volume = 11x × 7y × 8z = 616xyz

Percentage change =

∴ Percentage change in the volume of a cuboid is −51.11%.

Hence, the correct option is (D).

= 1² = 1

Hence, the correct option is (D).

P = S.P. – C.P.

L = C.P. – S.P.

L% = (L / C.P.) × 100

Where, P= profit, S..P.= Selling price, C.P.= cost price, L= loss.

Let the C.P. be x.

According to question,

So, loss = 600 – 500 = 100

∴ The required loss% is 50/3%

Hence, the correct option is (A).

So, the odd positive integers less than 10 are 1, 3, 5, 7, 9.

Now, the set O that represents the set of odd positive integers less than 10 is given as follows:

Set O = {1, 3, 5, 7, 9}

Hence, the correct option is (B).

∴ A(3,0) does not lie on the diagonal x = 2y.

Let m be the slope of a side passing through A(3, 0).

Equation of the side is: y − 0 = m(x − 3)

⇒ y = m(x − 3)...(i)

Slope of the diagonal x = 2y is 1/2.

Formula to find the angle between two lines:

Where θ is the angle between the two lines and m1 and m2 are the slope of the two lines.

Substituting m = 3, −1/3 in equation (i), we get

Hence, the correct option is (A).

Number of people = 30

A handshake needs 2 people. So total ways of two people shaking hands with each other = ³⁰C?

We know that,

where n = 30 and r = 2

Therefore,

= 435

Hence, the correct option is (B).

First speed = 8 km/hrs and second speed = 12 km/hrs.

Starting time will be same in both conditions.

Distance travelled by first speed in 2 hours,

We know that,

Distance = Speed × Time

⇒ Distance = 8 × 2 km

⇒ Distance = 16 km

Now,

Time taken by second speed to travel distance 16 km.

Time = 4 hours

So, total time is taken by second speed =4 hrs.

Therefore, total distance = 4 × 12 = 48 km.

Starting time to travel at second speed:

= 9 am −4 hrs = 5 am

According to question,

At 10 am required time to reach the office:

= 10 am −5 am = 5 hrs

So,

Required Speed = Total Distance / Time

⇒ Required Speed = 48/5

⇒ Required Speed = 9.6 km/hr.

Hence, the correct option is (A).

As we know,

Any real square matrix A = (a_ij) is said to be a symmetric matrix if a_ij = a_ji or in other words if A is a real square matrix such that A = At then A is said to be a symmetric matrix.

On comparing, we get

3 + x = 1 − x

⇒ x + x = 1 − 3

⇒ 2x = −2

⇒ x = −1

And, y + 1 = 5 − y

⇒ y + y = 5 − 1

⇒ 2y = 4

⇒ y = 2

Now,

3x + y = 3 × (−1) + 2

⇒ 3x + y = −3 + 2

⇒ 3x + y = −1

Hence, the correct option is (A).

The simple interest in two years is Rs. 1000

The compound interest in two years is Rs. 1040

Simple interest remains same for every year:

⇒ SI for 1 year = Rs. 1000/2

⇒ SI for 1 year = Rs. 500

Difference between the Compound interest and Simple interest is

CI − SI = Rs. 1040 - Rs. 1000

CI − SI = Rs. 40

Rate percent is:

Rate = 8%

∴ The rate percent per annum is 8%.

Hence, the correct option is (B).