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Akash draws a straight line on a sheet of paper. Then he draws another line such that the distance between the two is same throughout. Similarly, he draws one more line in the same manner. He names these line as l, m and n. Which of the following is correct? ( Select all that apply)

Arrange the numbers in ascending order (Starting from the top)

The length of the parallel sides of a trapezium are in the ratio 3: 2 and the distance between them is 10 cm. If the area of the trapezium is 325 cm², find the length of the parallel sides.

Find the height of the cylinder whose capacity is 1540 L and diameter of the base is 140 cm?

Let ABCD be a square and let points P on AB and Q on DC be such that DP = AQ. Prove that BP = CQ.

Question 1(ii)
Identify the terms, their coefficients for the following expression:
$1+x+x^2$

Word probems in it

Dice are cubes where the numbers on the opposite faces must total 7. Which of the following are dice?

Q. एक बेलनाकार ओवरहैड टंकी को, जिसकी त्रिज्या 2 मीटर और ऊँचाई 7 मीटर है, 5.5 मीटर × 4 मीटर × 6 मीटर माप वाली किसी भूमिगत टंकी के जल से भरा जाना हैं। ओवरहैड टंकी को पूरा भर देने के बाद, भूमिगत टंकी का कितना भाग पानी से भरा हैं?

A bag contains 5 red marbles, 8 white marbles, 4 green marbles. What is the probability that if one marble is taken out of the bag at random, it will be

(i) red (ii) white (iii) not green

Students in Mrs. Smeera's class were surveyed about snacks and asked to choose the one snack food they liked most from a list. The bar graph below summarizes the data collected from this survey.

Assuming that one student likes only one of the given snacks ___ percentage of students liked mixture.

Solve, $\frac{x-4}{2}+\frac{2x-3}{3}=\frac{5x-32}{2}-\frac{x+9}{3}$.

Using Eulier's formula, find the values of x, y and z.

$\begin{array}{cccc}& \text{Faces}& \text{Vertices}& \text{Edges}\\ \left(i\right)& x& 15& 20\\ \left(ii\right)& 6& y& 8\\ \left(iii\right)& 14& 26& z\end{array}$

Question 1

Show that the cube of a positive integer of the form 6q + r, where q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r.

The slope intercept form of equation of a line with slope as $m$ and $y$-intercept as $b$ is:

Which of the following is/are the irreducible factor(s) of $3m^2+9m+6?$

The dimension of a cuboids are x units, y units and z units where x<y<z. If a cube of side length x units is cut from this cuboids, find the volume of remaining portion.

Question 3 (i)

The squares of which of the following would be odd number:

431

If an angle of a parallelogram is two-third of its adjacent angle , the smallest angle of the parallelogram is

(a) ${54}^{\circ }$ (b) ${72}^{\circ }$

(c)${81}^{\circ }$ (d) ${108}^{\circ }$

Find the greatest common factor of the terms in each of the following expressions:

$5a^4+10a^3-15a^2$

Question 73

State whether the following statement is true or false:

Square root of a number x is denoted by $\sqrt{x}$.

Question 5(d)

Substract: $3a(a+b+c)-2b(a-b+c)from4c(-a+b+c).$

If the price of a petrol is increased by $40\%,$ then by what fraction must its consumption be reduced to keep the same expenditure on its consumption?

If the sum of two numbers is 50 and their ratio is 2:3, then the first number is:

1. 6

Question 9 (ii)

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:



$\begin{array}{cc}\text{Number of letters}& \text{Number of surnames}\\ 1-4& 6\\ 4-6& 30\\ 6-8& 44\\ 8-12& 16\\ 12-20& 4\end{array}$

(ii) Write the class interval in which the maximum number of surname lie.

Study the following information carefully and answer the questions given below:

A, B, C, D, E, F, G and H are sitting around a circle facing at the centre. B is second to the right of H and third to the left of A. D is not an immediate neighbor of either B or H and is second to the right of F. C is fourth to the right of G.

If E and F interchange their places, who will be second to the right of B?

Which of the following is an oblique sketch of a cube of edge 4 cm?