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Question 58

In the class intervals 10-20 and 20-30 respectively, 20 lies in the class___.

Choose the correct answer:

4a + 12b is equal to

A. 4a

B. 12b

C. 4(a + 3b)

D. 3a

Identify the terms, their coefficients for each of the following expressions.

(i) $5xy{z}^2-3zy$

(ii) $1+x+x^2$

(iii) $4x^2{y}^2-4x^2{y}^2{z}^2+z^2$

(iv) $3-pq+qr-rp$

(v) $\frac{x}{2}+\frac{y}{2}-xy$

(vi) $0.3a-0.6ab+0.5b$

We cut a corner of a cube as shown in the figure. The cut out piece is _________.

Question 1 (ix)

What will be the unit digit of the squares of the following number:

12796

Find each of the following products:

$(x^3-5x^2+3x+1)\times (x^2-3)$

25698 x 12506 x 0 x 125 = ___

Question 5 (i)

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

525

Question 15

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

The sum of three consecutive multilpes of 7 is 357. Find the smallest multiple.

(a) 112

(b) 126

(c) 119

(d) 116

Question 06.

A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?

Construct a rectangle ABCD whose one side BC = 4.5 cm and diagonal AC = 6 cm [3 MARKS]

Determine the total surface area of a cone of diameter 6 cm and depth of 5 cm.

Question 112(ii)

Sonia picks up a card from the given cards



Find the probability of getting a Y card ?

Based on the sides, classify the following triangles (figures not drawn to the scales):

Select the statements that are true.

A polygon having eight sides is called:

Substituting $x=-3$ in $\left(x^2\right)-5x$ gives

Question 115(viii)

Express the following in standard form:
$Express5hectaresinc{m}^2.(1hec=10000m^2)$

If $x+y+z=0$
then $x^3+y^3+z^3$ =___?

Calculate the sum of all the interior angles of a polygon having $8$ sides.

If $a+b=1$ and $a^2+b^2=2$, then find the value of $a^8+b^8$.

The equations of the tangents to the circle $x^2+y^2-6x+4y=12$ which are parallel to the straight line $4x+3y+5=0$, are

What are the possible expressions for the dimensions of cuboid , whose volume is : 12ky^2 +8ky- 20 k?

Let ABCD be a quadrilateral with diagonals AC and BD. Prove the following statements (Compare these with the previous problem);

(a) AB + BC + CD > AD;

(b) AB + BC + CD + DA > 2AC;

(c) AB + BC + CD + DA > 2BD;

(d) AB + BC + CD + DA > AC + BD.

A milkman has 80% milk in his stock of 800 L of adulterated milk. How much 100% pure milk should be added to it, so that purity is between 90% and 95% ?

If measure of sides of a quadrilateral are given as AB = 4cm, CD = 5cm, and angles are given as ∠ ABC = ${75}^{\circ }$, ∠ BCD = ${35}^{\circ }$ and ∠ CDA = ${135}^{\circ }$, can you construct a quadrilateral ABCD?

In the above figure, X and Y are the two axes and O is the origin. The two axes X and Y divide the plane into 4 parts. Which of the 4 parts is the III quadrant?

find the following product 43x45?

A shopkeeper buys a DVD player at a discount of 20% on the Marked price. He spends ₹20 on transportation. If he sells it for ₹ 660 inclusive of sales tax 10%, then his profit % is _____.

Which among the following is not a polynomial?

A box contains $50$ packets of biscuits each weighing $180$ g. How many such boxes can be loaded in a van which cannot carry beyond $450$ kg?

Let ∪ = {x: x is a natural number and x $\le$ 10}

A = {a: a is an even number and a $<$ 10}

B = {b: b is a prime number and b $\le$ 9}

Then A^I $\cap$ B^I is