Mix Test 8...

The HCF of two numbers is 27 and their LCM is 162. If one of the number is 81. Then, the other number is

Total number of terms in the AP 7, 11, 15, …, 139 is

We have two system of linear equation, given as:

\(\mathrm{\frac{3}{x+y}+\frac{2}{x-y}}=2\) and \(\mathrm{\frac{9}{x+y}-\frac{4}{x-y}=1}\)

When \(u = \frac{1}{\mathrm x+y}\) and \(v = \frac{1}{\mathrm x-y}\), the system of equation becomes:

We have two system of linear equation, given as:

\(\mathrm{\frac{3}{x+y}+\frac{2}{x-y}=2}\) and \(\frac{9}{\mathrm x+y}-\frac{4}{\mathrm x-y}=1\)

Let u = \(\frac{1}{\mathrm x+y}\) and v = \(\frac{1}{\mathrm x-y}\). Then given system of equations has solution (in terms of u and v) as:

We have two system of linear equation, given as:

\(\frac{3}{\mathrm x+y}+\frac{2}{\mathrm x-y}=2\) and \(\frac{9}{\mathrm x+y}-\frac{4}{\mathrm x-y}=1\)

Let u = \(\frac{1}{\mathrm x+y}\) and v = \(\frac{1}{\mathrm x-y}\) and solve the given system of equations and get solution in terms of u and v. After substituting the value of u and v, the original system of equation becomes :

We have two system of linear equation, given as:

\(\mathrm{\frac{3}{x+y}+\frac{2}{x-y}=2}\) and \(\mathrm{\frac{9}{x+y}-\frac{4}{x-y}=1}\)

Solution of given system of equations (in terms of x and y), is :

We have two system of linear equation, given as:

\(\frac{3}{\mathrm x+y}+\frac{2}{\mathrm x-y}=2\) and \(\frac{9}{\mathrm x+y}-\frac{4}{\mathrm x-y}=1\)

Let u = \(\frac{1}{\mathrm x+y}\) and v = \(\frac{1}{\mathrm x-y}\) and solve the given system of equations and get solution in terms of u and v. After substituting the value of u and v we get a modified system of equations (in terms of x and y). Type of straight line represented by the modified system of equations is :

The length of the longest pole that can be kept in a room of dimension \(12m \times 9m\times 8m\) is

In a ΔABC, ∠C = 3∠B = 2(∠A+∠B). Then ∠A – ∠B + ∠C is

\(\frac{1}{\sec\theta - \tan\theta} - \frac{1}{\cos\theta}\) = ?

The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. Median of the data is 63.

The value of ‘x’ is :

The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. Median of the data is 63.

Find the value of x. After putting the value of ‘x’, observations when arranged in ascending order looks like:

The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. Median of the data is 63.

The mean of given data is:

The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. Median of the data is 63.

The mode of given data is:

The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. Median of the data is 63.

If class-width of 6 is allowed to be taken to construct grouped distribution, how many class-intervals are possible?

[Take 29–35, 35–41, ……, 89–95, 95–101]

If the radius of a circle is decreased by 30%. Then percent change in the area of the circle is

Fill in the blank:

\(\pi\) is an __________ number.

One card is drawn from a well-shuffled deck of 52 cards.

The probability of getting a king of red suit is :

One card is drawn from a well-shuffled deck of 52 cards.

The probability of not getting a king of red suit is :

One card is drawn from a well-shuffled deck of 52 cards.

The probability of getting a face card is :

One card is drawn from a well-shuffled deck of 52 cards.

The probability of getting a red face card is :

One card is drawn from a well-shuffled deck of 52 cards.

The probability of getting a spade is :

Three coins are tossed simultaneously. The probability of getting exactly two heads is