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If a 25 cm long candle burns for 45 minutes how long will another candle of the same material and same thickness 15 CM longer than the previous ?

In a right-angled triangle, which of the following is true? (h=hypotenuse, a and b are the perpendicular sides)

Choose the option that contains like terms from the following terms.

$12x,12a,25p,25q,xand12y.$

If $3^x=81$, which of the following is NOT true?

A bulb is kept burning
just right above the following solids. Name the shape of the shadows
obtained in each case. Attempt to give a rough sketch of the shadow.
(You may try to experiment first and then answer these questions).

Choose the wrong number in the series given below :

$2,6,22,30,62,126.$

Three similar coins were tossed simultaneously for 100 times and the data recorded is as given below :

$$\begin{array}{ccccc}\text{No of heads}& 0& 1& 2& 3\\ \text{No of tosses = Frequency}& 10& 35& 40& 15\end{array}$$

(i) What is the probability of getting more tails than heads?
(ii) What is the probability of getting more heads than tails?
(iii) Are (i) and (ii) complementary? Will they be complementary if we had 4 coins? [4 MARKS]

Among the following pairs, in which pairs, the first number is to the right of the second number on the number line?
i. 3, 7
ii. 0, -4
iii. 2, 5
iv. -4, -8
v. 1, -10
vi. -1, 3

Alex and shalini went to the amusement park and took two rides. How much did they pay and how much time did they get for both the rides?

Tina noticed juicy oranges in a shop and asked the shopkeeper for the price. He said each costs Rs x. She bought 3 of them. What is the coefficient of x after calculating the total amount spent by Tina and her friend Rina, if Rina had already spent Rs (6x + 4y)?
___

Two complementary angle are (x+4)°and(2x-7)°.find the value of x.

Express the exponential form with prime number as base.

(1) 4

(2) 8

(3) 16

(4) 49

(5) 81

In the figure, D and E trisect BC, Prove that $8{AE}^2=3{AC}^2+5{AD}^2$ [4 MARKS]

Question 30

Fill in the blanks to make the statement true.

On adding a monomial ___ to $-2x+4y^2+z,$ the resulting expression becomes a binomial.

a-[b-{a-(b-1)+3a }]

Two lines are drawn parallel to the diagonal of a square as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square of the area $61c{m}^2$ as shown in the second figure, then the area of the original square is

$-16÷4$ is not same as

Question 31

In the given figure, POQ is a line, then a is equal to

(a) ${35}^{\circ }$
(b) ${100}^{\circ }$
(c) ${80}^{\circ }$
(d) ${135}^{\circ }$

What is the number of matchsticks needed to make n C patterns?

Express the given statement, "the product of 6 and 2 is subtracted from the product of 5 and 3", as a mathematical expression.

The average spacing between vehicles in a traffic stream is $50m$ then the density in (veh/km) of the stream is

1. 20

A student while going to school on a school bus, observes the average speed of the bus to be 20 km/h. On his return trip along the same way, average speed is 30 km/h. What is the average speed of the bus during the entire journey?

In integers, 0 is the identity for-

In a class of 30 students if there are 24 boys, then the ratio of girls to the boys is:

If (a + 3b)(3a + b) = $4h^2$, then the angle between the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is

The point of intersection of axes is __.

Question 2(ii)

State True or False.

A perfect cube does not end with two zeroes.

Question 84 (ix)

Simplify

$(a-b)(a^2+b^2+ab)-(a+b)(a^2+b^2-ab)$

Question 81

State whether the statement is True or False.

It is possible to have a triangle in which each angle is less than ${60}^{\circ }$

The number of $3$ digit numbers having exactly one of their digits as $5$, repetition is not allowed is

$\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}$=___

A bus travels 500 km with 70 litres of petrol. The distance covered by the bus in 7 litres of petrol is ___.

Choose the options which is equivalent to the following expression:

$\left[\right(4.2\times {10}^3)+(7.8\times {10}^4)-(12\times {10}^2\left)\right]\times 120,000$

ABCD is a quadrilateral , Is AB +BC+CD+DA < 2(AC+BD)