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In the given figure, a || b and c || d. If $\angle 1={75}^{\circ }$, what is the measure of $\angle 3$?

Classify the following into monomial, binomial and trinomial expression.

(a) 5abc

(b) x − y + z

(c) ab + bc

(d) ab × d

(e) 5x + 1

(f) 6m + 7n − 10

Which number must be subtracted from 1786 to make it a perfect square?

If you roll 2 dice together then the sum of outcomes will be:

$0$ was very happy to finally get to meet other numbers after a long long time. Also, every number was very angry at $-1$. Everybody told Ted to be the judge of what should be done to $-1$. $-1$ realized its mistake and asked for forgiveness. Ted forgave $-1$ and finally, a world of integers was formed where no number was largest or smallest.

Then out of curiosity, Ted asked $0$, “How many integers actually are there in this world?” $0$ replied – “There are __ integers.”

Two quantities are in the ratio 1 : 4. On increasing the smaller one by 6 and decreasing the larger one by 6, The quantities are now in the ratio 7 : 13.

What were the original quantities ?

Actual length of a rope is 22.5 m but it is wrongly meassured as 21.6 m. Find the percentage error

$(9.5+0.5-7.5)+\frac{5}{2}÷5=$

Find the area of the following circles given that : (i) Diameter $49$ m

Look at the image below. What fraction of the icreams are blue in color.

The Students' Council of Greenland School, New Delhi has organized an excursion to Kulu, Manali and Rohtang Pass for students of Classes XI and XII during the Easter break. As the Head girl/ Head boy of the school draft a notice for the notice board of your school to this effect inviting students who wish to join the excursion to give in their names for the same. Add relevant details like duration and cost of excursion and last date for submission of authority letter signed by parents and making the payment.

Do not exceed 50 words. Put the notice in a box.

Solve the following: $7^2\times 7^3=?$

A die is thrown at random. What is the probability of getting an even number?

A consumer spends Rs. 1000 on a good priced at Rs. 10 per unit. When its price falls by 20 per cent, the consumer spends Rs. 800 on the good. Calculate the price elasticity of demand by the percentage method.

A's weight is 50 kg more than that of B. What is the ratio of A's weight to B's weight? (Let's take B's weight as $x$)

An auditor estimates that $100$ calculators of the 450 calculators manufactured on a particular day by a company are defective. $50$ calculators are tested, out of which $8$ turn out to be defective. Is the auditor's claim accurate?

Find the value of $n$ such that

If the angles in a triangle are in the ratio 1 : 3 : 5, then the smallest and largest angles are

In Ted’s class, he counted 24 students. Now, there were 15 boys in his class, and the remaining were girls. After the attendance, Ted’s teacher asked him to identify the correct way of comparing the number of boys and girls. What could be the answer?

Subtract by using number line:

(1) 6 from 8

(2) 9 from 6

(3) +5 from −7

(4) −4 from +5

(5) −2 from −5

If 'a' and 'b' are any two integers and a × (b + c) = (a × b) + (a × c). The property used here is __.

What rate
gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?

Like fractions for the given pair of fractions $\frac{1}{2}$ and $\frac{3}{4}$ are.

Find the missing model in the given pattern:

Pair the polynomials with their respective zeroes.

Subtract:

(1) 5a from 3a

(2) −3b from 2b

(3) 3x² from (−8x²)

(4) −11xyz from −7xyz

(5) 7xy from 14xy

(6) What should be added to 8ab to get 15ab?

Question 51

In questions 24 to 59, fill in the blanks to make the statements true.
If A is increased by 20 %, it equals B. If B is decreased by 50%, it equals C. Then, ___ % of A is equal to C.

'Add thrice a number to four times the same number' is algebraically written as

If we are at -7 on the number line and move 9 units to the right, we would reach ___.