IPMAT Mock Test - 3 (New Pattern) - Commerce MCQ

Multiplying by 2 in the equation (1), we get

Subtracting equation (3) from equation (2), we get

Therefore,

Hence, the correct option is (C).

A 250 meters long train crosses a bridge 750 meters long in 20 seconds

And crosses a platform in 15 seconds.

Distance = Speed × Time

Let the speed of the train be S

And let the length of the platform be x

According to the question,

250 + 750 = S × 20

⇒ S = 1000 / 20

⇒ 50 m/sec

Now, Again according to the question

The train crosses the platform in 15 seconds

250 + x = 50 × 15

⇒ x = 750 - 250

⇒ x = 500 m

∴ The length of the platform is 500 m.

Hence, the correct option is (C).

Given-

(√3 + 1)(10 + √12)(√12 − 2)(5 − √3)

= (√3 + 1)(10 + 2√3)(2√3 − 2)(5 −√ 3)

= (√3 + 1) × (5 + √3) × 2(√3 − 1)(5 −√3)

= 4(√3 + 1)(√3 − 1)(5 − √3)(5 + √3)

According the formula-

[(a + b)(a − b) = a² − b²]

= 4(3 − 1)(25 − 3)

= 4 × 2 × 22

= 176

Hence, the correct option is (C).

Given,

From equation (1) and (2), we get

= tan30^o

= 1/√3

⇒ −2 + 1 < 2x < 2 + 1

⇒ −1 < 2x < 3

⇒ −12 < x < 3/2

⇒ x ∈ (−12, 3/2)

Hence, the correct option is (B).

⇒ 2x > 3 – 1

⇒ 2x > 2

⇒ x > 1

⇒ x ∈ (1, ∞)

Hence, the correct option is (B).

In CBE -

BC = 24cm and BE = 30 cm

∴ CE = √30² − 242 = √324 = 18 cm

Side of square = 24 cm

Thus, PX = 12 cm

As QY is the incentre of △BCE

QY = CB + CE − BE / 2 = 24 + 18 − 30 / 2 = 6 cm

Distance between centre XY = 12 + 6 = 18 cm

Hence, the correct option is (C).

Cost Price of 12 articles = Rs.12

Selling Price of 12 articles = Cost Price of 18 articles = Rs.18

We know that,

Profit = Selling price- Cost price

Profit = 18-12 = Rs. 6

Profit percentage = Profit × 100 / Cost price

Profit percentage = 6 × 100 / 12 = 50%

Hence, the correct option is (B).

= x⁰

= 1

Hence, the correct option is (A).

Hence, the number of diamonds before he gave some diamonds to the third watchman,

x − 42 = 1

or x = 6

Hence, he had 6 diamonds before he gave 5 to the third watchman.

Similarly number of diamonds before giving to second watchman,

or, x = 16

And number of diamonds before giving to the first watchman,

x − 42 = 16

or, x = 36

∴ The thief has stolen 36 diamonds originally

Hence, the correct option is (A).

% contribution of the power sector to total CO₂ emissions in the year

2008 = 700 / 1700 × 100 = 41.18%

Hence, the correct option is (B).

Percentage Growth

=

Power: % = (800 - 500) / 500 × 100 = 60%

Industry: % = (450 - 200) / 200 × 100 = 125%

Commercial: % = (320-150) / 150 × 100 = 113%

Agriculture: % = (200 - 80) / 80 × 100 = 150%

Domestic: % = (180 - 100) / 100 × 100 = 80%

So, the maximum growth in CO₂ is Agriculture.

Hence, the correct option is (D).

Percentage growth

=

Percentage growth = (800 - 500) / 500 × 100%

= 300 / 500 × 100 = 60%

Hence, the correct option is (A).

Total emissions of CO₂ in 2009 = 800 + 450 + 320 + 200 + 180 = 1950

Percentage growth

=

% increased = (1950 - 1030) / 1030 × 100 = 89.32%

Hence, the correct option is (A).

In 2005 to 2006: 100 / 500 × 100 = 20%

In 2006 to 2007: 5 / 600 × 100 = 8.33%

In 2007 to 2008: 50 / 650 × 100 = 7.69%

In 2008 to 2009: 100 / 700 × 100 = 14.28%

Average Annual growth rate

= 50.30 / 4 =12.57%

Hence, the correct option is (A).

There are 20 cricket players, out of which 5 players can bowl.

We have to make a team of 11 players so to include 4 bowlers.

So, we select 4 bowlers out of 5 players and the remaining 7 players must be selected from 15 players, i.e.,

Total ways = ⁵C₄ × ¹⁵C₇

Hence, the correct option is (A).

Length of the plot = 122 m

The breadth of the plot = 88 m

Width of the path = 2 m

Cost of the construction of the path = Rs 2 per sq m

Area of the rectangle = Length × breadth

Area of the path = Area of the plot including path – Area of the plot

Area of the path= (122 + 4) × (88 + 4) – 122 × 88

Area of the path = 856 m²

∴ Cost of constructing = 856 × 2 is Rs 1712

Hence, the correct option is (B).

Since diagonal of a parallelogram bisect each other,

∴ BO = OD = 18/2 = 9 cm

P = centroid of △ADC

OP = 1/3OD = 1/3 × 9 = 3 cm

Q centroid of △ABC

OQ = 1/3OB = 1/3 × 9 =3 cm

∴ PQ = OP + OQ = 3 + 3 = 6 cm

Hence, the correct option is (D).

Adding equation (1) and (2), we get

Now, subtracting equation (2) from (1), we get

So, the value of

Hence, the correct option is (B).

Transpose of B is B′ will have order q × p.

For matrix, is defined.

.∴ q = 3

Given,

AB^T is a square matrix.

∴ p = 2

So, the order of B = p × q = 2 × 3

Hence, the correct option is (B).

Let the principal amount = 8x

And simple interest = 7x

We know,

⇒ SI = (p × r × t)/100

⇒ 7x = (8x × r × 5)/100

⇒ r = 17.5%

Hence, the correct option is (B).

Now, we will check for each property one by one.

The relation is obviously reflexive as a has the same father as a.

Therefore, aRa .... (1)

If a has the same father as b, then that means both a and b have the same father.

Therefore, b also has the same father as a. Thus, the relation is symmetric.

Therefore, aRb implies bRa .... (2)

Now, assume that aRb and bRc.

That means a has the same father as b and b has the same father as c. This implies that a, b and c have the same father.

Therefore, a has the same father as c. Thus, the relation is transitive.

Therefore, aRb, bRc implies aRc .... (3)

Thus, from (1), (2) and (3), we conclude that the given relation is an equivalence relation.

Hence, the correct option is (D).

log₁₀(2x + 3) − 1 = log₁₀x

⇒ log₁₀(2x + 3) − log₁₀10 = log₁₀x

⇒ 2x + 3 = 10x

⇒ 8x = 3

⇒ x = 3 / 8

Hence, the correct option is (A).

It is given that in a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks.

Therefore,

n (C) = 37, n (T) = 52 and n (C υ T) = 70.

We know that n(C υ T) is given by,

n (C υ T) = n (C) + n (T) - n (C ∩ T)

From this,

n (C ∩ T) = n (C) + n (T ) - n (C υ T)

= 37 + 52 - 70

= 89 - 70

= 19

Therefore, 19 people like both coffee and tea.

Hence, the correct option is (A).

Suppose a set of n objects has n₁ of one kind of object, n₂ of a second kind, n₃ of a third kind, and,

So, on with n = n₁ + n₂ + n₃ +…+ n_k then the number of distinguishable permutations of the n objects is:

=

Given: Three a’s and two b’s

Total number = 3 + 2=5

In the set of 5 words has 3 words of one kind and 2 words of the second kind.

Therefore, number of different messages that can be represented by three a's and two b's,

= 5! / 3!2! = 10

Hence, the correct option is (D).

Reflexive: Every line is parallel to itself. It means that lRl for all l∈L. Therefore, R is reflexive.

Symmetric: If a line l is parallel to m, then m is parallel to l, i.e., if lRm ⇒ mRl, ∀ l ,m∈L. Therefore, R is symmetric.

Transitive: If a line l is parallel to m and m is parallel to k, then l is also parallel to k, i.e., if lRm and mRk ⇒ lRk,∀ l, m, k ∈ L. Therefore, R is transitive.

Since, the relation R is reflexive, symmetric and transitive as well, it is an equivalence relation.

Hence, the correct option is (D).

Discount = MRP- Selling Price

According to the question,

Discount =80,000 − 60,000

= Rs. 20,000

Therefore, the rate of discount will be,

Discount % = Discount / MRP × 100

= 20,000 / 80,000 × 100

= 25%

Hence, the correct option is (D).

Average =sum of number / total numbers

⇒14 = sum of 12 numbers / 12

⇒ sum of 12 numbers = 14 × 12 = 168

Let the numbers be a₁, a₂, a₃……a₁₂

⇒ a₁ + a₂ + a₃ +……+ a₁₂ = 168

If each number is doubled,

Numbers will be, 2a₁, 2a₂, 2a₃……2a₁₂

⇒ 2a₁ + 2a₂ + 2a₃ +…. + 2a₁₂

⇒ 2(a₁ + a₂ + a₃ +…+ a₁₂)

⇒ 2 × 168 = 336

New average = sum of numbers / total numbers = 336 / 12 = 28

Hence, the correct option is (A).

As we know,

Speed = Distance / Times

The speed of the car = x / 8

7 hours 30 minutes = 7 + 1 / 2 hours

= 15 / 2 hours

If the speed was increased by 4 km/h, then the speed of the car = x / 15 / 2

According to the question,

x /15 / 2 − x / 8 = 4

⇒16x − 15 x /120 = 4

⇒ x = 480 km

Hence, the correct option is (B).

(x² − y²) = 45

Or, (x − y)(x + y) = 45

Thus, the factors of 45 possibles are 15, 3, 9, 5, 1 and 45 Hence, numbers are 9 and 6 or 7 and 2 or 23 and 22 So, number of such pairs = 3

Hence, the correct option is (C).