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Solve for x:
(x+5)/6−(x+1)/9=(x+3)/4

(a) −2/7

(b) −1/7

(c) −5/7

(d) 7

Two dice are rolled, the probability that the sum on their faces is equal to 1 is

An article is bought from Jaipur for Rs.4,800 and is sold in Delhi for Rs.5,820. If Rs.1,200 is spent on its transportations, etc.; find the loss or the gain as percent.

Construct:

(i) 2 binomials with 3 variables.

(ii) 3 polynomials with 3 terms and 2 variables.

(iii) 2 trinomials with x as the only variable.

(iv) 3 binomials with x and y as variable.

Consider set of linear equations :$Qx+18y=27$ and $9y=12x+72$, Where $Q$ is a constant and no ordered pair satisfies both the equation simultaneously. Then, What will be the value of $Q$?

Question 45

5% sales tax is charged on an article marked Rs 200 after allowing a discount of 5%, then the amount payable is ___.

A man plants 5625 trees in his orchard in such a way that there are as many rows as there are trees in each row. How many rows are there?

Question 1

In the following question, out of the four options, only one is correct. Write the correct answer:

In $2^n,$ n is known as :

(a)Base

(b)Constant

(c)Exponent

(d)Variable

Find the area of the rectangle given that:

(i) Perimeter = 72 cm

(ii) Length = 12 cm

The square of which among the following numbers is a palindrome?

If you fold a square in half and then fold it in half again, how many equal parts are made by the fold lines?

Express 16,200 as a product of powers of prime numbers in the exponential form.

Use a suitable identity to get each of the following products:
$(\frac{x}{2}+\frac{3y}{4})(\frac{x}{2}+\frac{3y}{4})$

Question 1(iii)
Carry out the following divisions.
$66p{q}^2{r}^3÷11q{r}^2$

Direction(1-4): Read the following information carefully and answer the following questions that follow:

Mr. Sharma, a truck driver drives his truck every day. He travels a different distance by his truck on each day.

The pie chart given below shows the percentage of distance travelled on a particular day (one out of Monday to Friday) out of the total distance that he travelled in the five days (Monday-Friday) of a particular week.

Total distance travelled by the truck = 2000 Km

The table given below shows the average speed (in km/hr) of Mr. Sharma's truck on the five weekdays. Some of the data is missing.

The truck started with its usual speed on Tuesday but when half of the distance was covered, there was a breakdown due to which the truck travelled at $\frac{5}{13}ths$ of its usual speed. Find the additional time taken (in hours) to cover the same distance.

What property of a rectangle do we use if we need to construct a rectangle whose adjacent sides are given?

If the word "MATH" is randomly rearranged, what is the probability that the new word starts with M? Give the answer up to 2 decimal places

__

Three infinitely long wires are arranged at the virtices of an equilateral triangle of side a. Find $B_0$

Find the value of x.

$3x+\frac{9}{3}=5x+\frac{5}{9}$

A metal cylinder has height of 7 cm. The inner radius of cylinder is 1 cm and outer radius is 1.5 cm. Calculate outer surface area and total surface area.

Question 23

Write the correct answer from the given four options.

The value of $\sqrt{248+\sqrt{52+\sqrt{144}}}$ is

a) 14
b) 12
c) 16
d) 13

What is the minimum number that should be multiplied by 360 in order to make it a perfect cube?

If $\frac{dy}{dx}=\frac{2^{x+y}-2^x}{2^y},y\left(0\right)=1,$ then which of the following is/are true

$△$ ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?

i) $△ABC\sim △$ ADE

ii) $\frac{AD}{BD}=\frac{AE}{EC}$

iii) $DE=\frac{BC}{2}$

Find the area of the given triangle $△XYZ$ in arbitrary units whose one of the sides passes through the center of the circle.

Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part 146. Find each part.

In the figure of a cube,

i) Which edge is the intersection of faces EFGH and EFBA?

ii) Which faces intersect at edge FB?

iii) Which three faces from the vertex A?

iv) Which vertex is formed by the faces ABCD, ADHE and CDHG?

v) Give all the edges that are parallel to edge AB

vi) Give the edges that are neither parallel nor perpendicular to edge BC.

vii) Give all the edges that are perpendicular to edge AB.

viii) Give four vertices that do not all lie in one plane.

A well is dug 20 m deep and it has a diameter 7 m. The earth which is so dug out is spread on a rectangular plot 22 m long and 14 m broad. What is the height of platform formed?