IPMAT Mock Test - 2 (New Pattern) - Commerce MCQ

Given: There are 5 subjects and for a student to pass in an examination the students has to pass in each of the 5 subjects.

Here, we have to find in how many ways a student can fail in the examination.

In order to fail in the examination the student can fail in 1 or 2 or 3 or 4 or 5 subjects out of the 5 subjects in each case.

Case 1: Student fails in any 1 subject out of the 5 subjects.

No. of ways in which student can fail in any 1 subject out of the 5 subjects = ⁵C₁

Case 2: Student fails in any 2 subjects out of the 5 subjects.

No. of ways in which student can fail in any 2 subjects out of the 5 subjects = ⁵C₂

Case 3 : Student fails in any 3 subjects out of the 5 subjects.

No. of ways in which student can fail in any 3 subjects out of the 5 subjects = ⁵C₃

Case 4: Student fails in any 4 subjects out of the 5 subjects.

No. of ways in which student can fail in any 4 subjects out of the 5 subjects = ⁵C₄

Case 5: Student fails in all 5 subjects.

No. of ways in which student can fail all 5 subjects. = ⁵C₅

∴ Total number of ways in which a student can fail in an examination

= ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅ = 31

Hence, the correct option is (A).

A certain sum is given on Compound Interest at some rate. The sum amounts to Rs. 7350 and Rs. 8575 at the end of 2 years and 3 years respectively.

Interest for 1 year is the same whether it's Simple Interest or the compound Interest.

Now, interest of third year

= 8575 − 7350 = 1225

Principal for this interest is 7350 if Compound Interest is taken.

If 7350 is the principal then interest = 1225

if 100 is the principal interest

For two successive times the overall increase on initial amount

Overall interest for two years

Amount after 2 years

If 1225/9 is the amount principal =100

If 7350 is the amount principal

= 5400

∴ Required sum = Rs. 5400.

Hence, the correct option is (B).

So, the number is 10x+y

Then, according to the question,

⇒ xy = 12⋯ (1)

Also, the number after interchanging the digits = 10y + x

⇒10x + y + 36 =10y + x

⇒ 9x − 9y = −36

⇒ x − y = −4

⇒ x = (y − 4) ⋯(2)

On substituting the value of x in equation (1), we get,

y⋅(y − 4) = 12

⇒ y² − 4y − 12 = 0

⇒ y² − 6y + 2y − 12 = 0

⇒ y(y − 6) + 2(y − 6) = 0

⇒ (y − 6)(y + 2) = 0

⇒ y = 6 or −2

But the unit digit of the two-digit number can't be negative.

⇒ y = 6

On substituting this value in equation (2), we get,

x = 6 − 4

⇒ x = 2

⇒ 10x + y = 10 × 2 + 6 = 26

∴ The number is 26.

Hence, the correct option is (C).

Given

The average of seven consecutive odd numbers (in increasing order) is k.

Let seven consecutive odd numbers be a, a + 2, a + 4, a + 6, a + 8, a + 10 and a + 12

Accordingly,

a + a + 2 + a + 4 + a + 6 + a + 8 + a + 10 + a + 12 = k × 7

⇒ 7a + 42 = 7k

⇒ a + 6 = k

⇒ a = k − 6

∴ New average = k - 6 + 10 = k + 4

Hence, the correct option is (C).

Time taken by first man to cover journey = 2 PM − 6 AM = 8 hours.

Time taken by another man to cover journey = 3 PM − 8 AM = 7 hours.

Let total distance from P to Q be 56x km (LCM of 8 & 7)

⇒ Speed of first man = 7x km/hr.

⇒ Speed of second man = 8x km/hr.

⇒ Distance covered by first man in 2 hours = 14x km

⇒ Remaining distance = 56x − 14x = 42x km.

⇒ Time taken to meet each other

= 2 hrs 48 min.

⇒ Time of meeting = 8:00 + 2:48 = 10:48 AM.

Hence, the correct option is (C).

Principal, P = 10000

Number of years, N = 3

Amount, A = 11664

We know that:-

∴ Rate of interest =8%

Hence, the correct option is (D).

(a+b)² = a² + b² + 2ab

(a−b)² = a² + b² − 2ab

Given,

Hence, the correct option is (C).

It can be written as , which is comparable with the first standard form

Here, a² = 5 and b² = 4.

The given line is 3x + 2y - 5 = 0, its slope = -(3/2)

Since the tangents are perpendicular to the given line, the slope of the required tangents is ⅔ (from m₁ m₂ = -1)

Thus equation of the required tangents are,

Hence, the correct option is (A).

Let the direction cosines be l, m, n.

Let P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) be two point which joins the line.

∴ x₁ = 1, y₁ = 2, z₁ = −3

and x₂ = −2, y₂ = 3, z₂ = 1

Now, we know that,

Putting the values according to the question, in equation (1), we get,

Putting the values according to the question, in equation (2), we get,

= 1

Probability of getting a queen of clubs = (1 / 52).

Probability of getting a king of hearts = (1 / 52).

The probability of getting either a queen of clubs or a king of hearts

= (1 / 52) + (1 / 52) = (2 / 52) = (1 / 26).

The distance remaining is 1080 km.

This distance travelled before meeting is directly proportional to their speed.

They meet 360 km from B.

So, train Y must've travelled 360 km.

X has travelled 720 km and Y has travelled only 360 km at the same time.

This means that the speed of X is twice of Y.

Since speed of X is 60 kmph therefore speed of Y is 30 kmph.

Hence, the correct option is (D).

A + B + C = π

⇒ A + B = π - C

Now,

sin (A + B) + sin C = sin (π – C) + sin C

= sin C + sin C (∵ sin (π – θ) = sin θ)

= 2 sin C

Hence, the correct option is (B).

[log₁₀ (5 log₁₀ 100)]² = [log₁₀ (5 log₁₀ 10²)]²

= [log₁₀ (10 log₁₀ 10)]²

= [log₁₀ 10)]² (∵ log₁₀ 10 = 1)

= 1² = 1

Hence, the correct option is (D).

Selling price = Rs. 17000

Loss % = 15%

Hence, the correct option is (C).

Sale of A in 2016 = 160

Sale of A in 2017 = 210

Sale of C in 2016 = 190

Sale of C in 2017 = 220

Sale of E in 2016 = 150

Sale of E in 2017 = 190

∴ Total Sale of branches A, C and E together for both the years = 160 + 210 + 190 + 220 + 150 + 190

= 1120

Hence, the correct option is (C).

Sale of branch B in 2017 = 130

Total sale of branch B in both the years = (150 + 130) = 280

Sale of branch D in 2016 = 170

Sale of branch D in 2017 = 190

Total sale of branch D in both the years = (170 + 190) = 360

∴ Required Ratio = 360/280

= 9 : 7

Hence, the correct option is (D).

Given,

x + 2y ≤ 3

x > 0 and y > 0

We need to satisfy the equation x + 2y ≤ 3 from the options

Option (A): x = −1 and y = 2

This will be incorrect as we have x and y>0

In option (A) x is less than 0, so we can't take this

Option (B): x = 2, y = 1

2 + 2 ≤ 3, which is incorrect.

Option (C): x = 1, y = 1

1 + 2 ≤ 3

3 ≤ 3, which is correct.

∴ The correct answer is x = 1, y = 1

Hence, the correct option is (C).

A = {1, 2, 3, 4, 6} and R is a relation on A such that:

R = {(a, b) : a, b ∈ A and b is exactly divisible by a}

The given R can be re-written in roaster form as:

R = {(1, 1),(1, 2),(1, 3),(1, 4),(1, 6),(2, 2),(2, 4),(2, 6),(3, 3),(3, 6),(4, 4),(6, 6)}

As we know that,

Range (R) = {b : (a, b) ∈ R}

⇒ Range (R) = {1, 2, 3, 4, 6} = A

⇒ n(A) = 5

Hence, the correct option is (D).

A and B are the domain and range respectively for the relation R such that

R = {(1, 3), (2, 4),(3, 5),(5, 7)}

As we know that,

Domain of (R) = {a : (a, b) ∈ R}.

⇒ A = {1, 2, 3, 5}

We also know that,

Range of (R) = {b : (a, b) ∈ R}.

⇒ B = {3, 4, 5, 7}

Hence, the correct option is (A).

Observing the pattern here

Aⁿ = 2ⁿ⁻¹⋅A

⇒ A¹⁰⁰ = 2⁹⁹A

Hence, the correct option is (B).

A = {1, 2, 3,…, 14} and R is a relation defined on A such that:

R = {(x, y) : 3x − y = 0 where x, y ∈ A}

When x = 1∈, then:

y = 3x

= 3 × 1

= 3 ∈ A

⇒ (1,3) ∈ R

When x = 2 ∈ A, then:

y = 3x

= 3 × 2

= 6 ∈ A

⇒ (2, 6) ∈ R

When x = 3 ∈ A, then:

y = 3x

= 3 × 3

= 9 ∈ A

⇒ (3, 9) ∈ R

When x = 4 ∈ A, then:

y = 3x

= 3 × 4

= 12 ∈ A

⇒ (4, 12) ∈ R

So,

R = {(1,3),(2,6),(3,9),(4,12)}

As, we know that,

Range (R) = {b:(a, b) ∈ R}

⇒ Range (R) = {3,6,9,12}

Hence, the correct option is (A).

Cost price of 24 kg sugar = Rs. 1056

Let selling price of sugar per kg be Rs. a.

Profit = selling price - cost price

⇒ 4a = 24a − 1056

⇒ a = 52.80

∴ The selling price of a sugar per kg is Rs. 52.80.

Hence, the correct option is (D).

Hence, the correct option is (A).

The system of equations

2x + y - 3z = 5

3x - 2y + 2z = 5 and

5x - 3y - z = 16

So,

det (A) = |A| = 2 × {( - 2 × - 1) - ( - 3 × 2)} - 1 × {(3 × - 1) - (2 × 5)} + ( - 3) × {(3 × - 3) - (5 × - 2)}

⇒ |A| = 2 × (2 + 6) - 1 × ( - 3 - 10) - 3 × ( - 9 + 10)

⇒ |A| = 16 + 13 - 3 = 26

∴ |A| ≠ 0

So, system is consistent having unique solution.

Hence, the correct option is (B).

Set A = {1, 2, 7, 9, 12}

x² −10x + 16 = 0

x² − 2x − 8x + 16 = 0

(x − 2)(x − 8) = 0

x = 2,8

Set B = {2, 8}

∴ Set (A ∪ B) = {1, 2, 7, 9, 12}

Hence, the correct option is (C).

⇒ P − Q = {1, 2}

⇒ Q − P = {5, 6}

⇒ P ∪ Q = {1, 2, 3, 4, 5, 6}

⇒ P ∩ Q = {3, 4}

⇒ (P − Q) ∪ (Q − P) ∪ (P ∩ Q) = {1, 2} ∪ {5, 6} ∪ {3, 4} = {1, 2, 3, 4, 5, 6} = P ∪ Q

Hence, the correct option is (A).

i.e. for matrix A to be singular, |A| = 0.

The determinant of a square matrix of order two:

If is a square matrix of order 2 then the determinant is given by:

det(A) = |A|

Given: is a singular matrix

Therefore, |B| = 0

⇒ (k - 8) = 0

∴ k = 8

Hence, the correct option is (D).

Given,

Length of the train = 480 m

Length of the second train coming from opposite direction = 480 m

Time is taken to cross the second train = 8 second

Hence, the correct option is (A).

Here we can see, for x = 5, there are two corresponding y values −6 and 3. So, this relation is not a function.

Also, there are four elements in the domain and five elements in the range. This implies two values in the range is associated with one value in the domain.

So, the given domain and range will not form a function.

Hence, the correct option is (D).

⇒ (4 + a + 8) − (2 + 4 + b) = 0 or multiple of 11

⇒ (12 + a) − (6 + b) = 0 or multiple of 11

⇒ 6 + a − b = 0 or multiple of 11

⇒ (a − b) = 11 − 6

⇒ (a − b) = 5

Hence, the correct option is (B).