Maths-

General

Easy

### Question

#### The maximum value of P such that 3^{P} divides 99 × 97 × 95 × .... × 51 is-

- 11
- 14
- 13
- 12

#### The correct answer is: 14

#### 99 × 97 × 95 ×....× 51

maximum power of 3 in 100 !

= 33 + 11 + 3 + 1 = 48.

maximum power of 3 in 50! =

= 16 + 5 + 1 = 22

maximum power of 3 in 25! =

= 8 + 2 = 10

exponent of 3 = 48 + 10 –

(22 × 2) = 14

## Book A Free Demo

+91

Grade*

Select Grade

### Related Questions to study

maths-

#### If for , then

#### If for , then

maths-General

maths-

#### The largest value of r satisfying inequality ^{20}C_{r }^{20}C_{r}_{ – 1 }is -

#### The largest value of r satisfying inequality ^{20}C_{r }^{20}C_{r}_{ – 1 }is -

maths-General

maths-

#### A double decker bus can accommodate (u + ) passengers, u in the upper deck and in the lower deck. The number of ways in which the (u + ) passengers can be distributed in the two decks, if r () particular passengers refuse to go in the upper deck and S(u) refuse to sit in the lower deck, is -

#### A double decker bus can accommodate (u + ) passengers, u in the upper deck and in the lower deck. The number of ways in which the (u + ) passengers can be distributed in the two decks, if r () particular passengers refuse to go in the upper deck and S(u) refuse to sit in the lower deck, is -

maths-General

maths-

#### Domain of f(x) = log_{10}(log_{10}(1 + x^{3})) is -

log

(1 + x

1+ x

x (0, ) or x R

_{10}(1 + x

^{3}) > 0 Take antilog1+ x

^{3}> 1 x^{3}> 0 x > 0x (0, ) or x R

^{+}#### Domain of f(x) = log_{10}(log_{10}(1 + x^{3})) is -

maths-General

log

(1 + x

1+ x

x (0, ) or x R

_{10}(1 + x

^{3}) > 0 Take antilog1+ x

^{3}> 1 x^{3}> 0 x > 0x (0, ) or x R

^{+}chemistry-

#### The correct orders about compounds I and II are:

i)

ii)

#### The correct orders about compounds I and II are:

i)

ii)

chemistry-General

chemistry-

#### Which of the following is correct method for separating a mixture of following compounds?

#### Which of the following is correct method for separating a mixture of following compounds?

chemistry-General

chemistry-

#### The order in which the reagent must be used to separate the compound I - IV is:

#### The order in which the reagent must be used to separate the compound I - IV is:

chemistry-General

chemistry-

#### Decreasing order of solubility of following compounds is:

i)

ii)

iii)

iv)

#### Decreasing order of solubility of following compounds is:

i)

ii)

iii)

iv)

chemistry-General

chemistry-

#### Which of the following statement is correct about tropolone?

#### Which of the following statement is correct about tropolone?

chemistry-General

chemistry-

#### In which case first has higher solubility than second?

I) Phenol, Benzene

II) Nitrobenzene, Phenol

III) o–Hydroxybenzaldehyde, p–Hydroxy benzaldehyde

IV) CH_{3}CHO, CH_{3}–O–CH_{3}

V) o–Nitrophenol, p–Nitrophenol

VI)

#### In which case first has higher solubility than second?

I) Phenol, Benzene

II) Nitrobenzene, Phenol

III) o–Hydroxybenzaldehyde, p–Hydroxy benzaldehyde

IV) CH_{3}CHO, CH_{3}–O–CH_{3}

V) o–Nitrophenol, p–Nitrophenol

VI)

chemistry-General

chemistry-

#### Arrange the following in decreasing order of their solubility in water

#### Arrange the following in decreasing order of their solubility in water

chemistry-General

maths-

#### 18 points are indicated on the perimeter of a triangle ABC (see figure). How many triangle are there with vertices at these points ?

#### 18 points are indicated on the perimeter of a triangle ABC (see figure). How many triangle are there with vertices at these points ?

maths-General

Maths-

#### If A and B are two events such that and then A and B are

#### If A and B are two events such that and then A and B are

Maths-General

maths-

#### Number of rectangles in the grid shown which are not squares is:

^{7}C

_{2}.

^{5}C

_{2}–

(6.4 + 5 × 3 + 4 × 2 + 3 × 1) = 160

#### Number of rectangles in the grid shown which are not squares is:

maths-General

^{7}C

_{2}.

^{5}C

_{2}–

(6.4 + 5 × 3 + 4 × 2 + 3 × 1) = 160

maths-

#### If and then

#### If and then

maths-General