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The amount of extension In an elastic string varies directly as the weight hung on it. If a weight of 150 gm produces an extension of 2.9 cm, then what weight would produce an extension of 17.4 cm ?

Fill in the blank in the given table

$$\begin{array}{ccccccccc}X& 100& 250& 200& 50& 125& 1000& 4& 40\\ Y& 20& 8& 10& 40& & 2& 500& 50\end{array}$$

___

Two adjacent sides of a parallelogram are $15cm$ and $12cm$. If the distance between $15cm$ sides is $8cm$, then the distance between the $12cm$ sides is _____ $cm$.

Which among the figures is not a convex polyhedron?

The figure given above contains the following 2-Dimensional shapes.

Question 92 (xxx)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$x^2-\frac{y^2}{100}$

On a certain sum of money, lent out at C.I., interests for first, second and third years are Rs. 1,500; Rs.1,725 and Rs. 2,070 respectively.

Find the rate of interest for the

(i) second year

(ii) third year.

Question 8

Which quantities in the previous question vary inversely with each other?

(a) x and y

(b) p and q

(c) r and s

(d) u and v

The teacher divided the students of grade $7$ into $4$ groups and conducted a test. The number of students in the $4$ groups formed were $12,16,13$, and $15$ and the corresponding average score of these groups were $23,25,19$, and $27$.



What will be the weighted average score of the students of grade $7$?

Which of the following are true?

i) All squares are rhombuses.

ii) All parallelograms are rectangles.

iii) All rhombuses are kites.

iv) All squares are rectangles.

Factorise:

$a^3+2a^2-a-2$

The Marked Price of 1 kg tomatoes was ₹ 20. The shopkeeper started selling the tomatoes ₹ 13 per kg. The Discount percentage given by the shopkeeper is ___ %.

For the two waves $y_1\text{and}{y}_2$ whose equation is given by



$y_1=\left(10\text{cm}\right)\sin (5x-2t)$



$y_2=\left(10\text{cm}\right)\sin (10x-t)$



Ratio of their wavelengths, $({\lambda }_1:{\lambda }_2)$ is,

Question 83 (vii)

Multiply the following:

7pqr, (p - q + r)

Find the area of quadrilateral ABCD in sq.units. Given AE = 5 units, BD =8 units and CF = 4 units

Simplify :

$(ab-c{)}^2+2abc$

Evaluate ${\left(99\right)}^3$ using suitable identities

Which of the following equations represents a line parallel to x – axis?

If P = {4, 5, 6, 7, 8, 9}, Q = {2, 3, 4}, R = {4, 5, 8} then .

For two simultaeous linear equations with two variables, say $x$ and $y,$ arrange the given steps in proper order to find solution of the equations using substitution.

Step a: Solve the $2^{nd}$ equation to find $y.$

Step b: Substitute the value of $y$ in one of the given equations to obtain the value of $x.$

Step c: Inject/ substitute $x$ in the $2^{nd}$ equation to make it a linear equation in one variable.

Step d: In $1^{st}$ equation, solve for $x$ in terms of $y.$

The value of $(x+y{)}^2$ , $x\ne 0$ and $y\ne 0$ would be $0$ when

Question 30

Upper limit of class interval 75 - 85 is

(a) 10

(b) -10

(c) 75

(d) 85

Factorise the following expressions :
$a^2+8a+16$

Draw a rhombus $ABCD$ if $AB=6$ cm and $AC=5$ cm

A shopkeeper bought rice worth Rs. 4,500. He sold one-third of it at 10% profit. If he desires a profit of 12% on the whole; find : (i) the selling price of the rest of the rice. (ii) the percentage profit on the rest of the rice.

Find the number of coins , 1.5cm in diameter and 2mm thick, to be melted to form a right circular cylinder of radius 2.25cm and height 10cm.

$8(3x-2y{)}^2-6x+4y-1$

By selling a book for $Rs.258,$ a book seller gains $20\%$. For how much should he sell it to gain $30\%$?

The screw of a screw gauge moves $4.5mm$ linearly for every $3$ complete rotations of the ratchet. If the circular scale of the gauge has $95$ divisions, the least count of the screw gauge is:

1. 33.4

You have seen earlier that the set of all natural numbers is closed under addition (closure property). Is this an axiom or something you can prove?

Verify whether -2, $\frac{1}{2}$ are zeroes of $2x^3-3x^2-11x+6$. [2 MARKS]

You have an eight-faced die. In this die, one of the faces contains 1, two faces contain 2, three faces contain 3 and other faces contain a 4 and a 5 respectively. What is the probability of getting a 3 when the die is rolled? (All outcomes are equally likely).