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Express 32000 as a product of powers of prime factors

1. 16

If the supplement of an angle is three times its complement, then angle is:

In the previous question, if b is nonzero, what can be said about $(4–3^b)$?

Bill understood the meaning of the engravings. He had a better idea of the nature of the occupants of “The House of Rational Numbers, Q”. He saw another stone which had the following message engraved:

"This hall would always be associative for any occupants of the "House of Rational Numbers, Q""

This stone could correspond to which of the four halls?

A bicycle dealer buys 30 Razorback cycles for ₹48000. Of these, 10 are with gears and the rest are without gears.(Assume that the cost price of geared and non-geared cycle is same). At what price must he sell each geared cycle so that if he sells the non - geared ones at $\frac{3}{4}$ of their cost price, he makes a profit of 40% on his total outlay.

If A and B are two disjoint sets, then $n(A\cup B)$ is equal to

By what numbers should $\frac{-15}{28}$ be multiplied, so that the product may be $\frac{-5}{7}$?

Question 157 (i)

The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground

Find the length of the ladder.

Represent the given data using a suitable bar graph. [4 MARKS]

$\begin{array}{cccccc}Fruits& Mango& Apple& Orange& Papaya& Banana\\ \text{Sales on Monday}& 17.5& 7.5& 27.5& 22.5& 32.5\\ \text{Sales on Tuesday}& 22.5& 10& 35& 22.5& 27.5\end{array}$

In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then angle BAC is ________

Question 7 (v)

Simplify these expressions and find their values if x = 3, a = -1, b = -2:
2a - 2b - 4 - 5 + a

Question 139

Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.

Question 30

In the given figure, lines PQ and ST intersect at O. If $\angle POR={90}^{\circ }$and
x:y = 3:2, then z is equal to

(a) ${126}^{\circ }$
(b) ${144}^{\circ }$
(c) ${136}^{\circ }$
(d) ${154}^{\circ }$

Question 3(b)
Fill in the blanks:
(- 75) $÷$ ___ = - 1

A slice of pizza is a ___.

Question 134

In each of the given pairs of triangles in given figures, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

Question 72(i)

State whether the statement is True or False.

Write down each pair of adjacent angles shown in the following figure.

Question 85 (v)

Expand the following, using suitable identities.

${(\frac{4}{5}p+\frac{5}{3}q)}^2$

How to found average of the 8.2,22.0,1128.7

The temperature at 12 noon 10°C above zero.if it decreases at the rate of 2°C per hour until mid night ,at what time would the temperature is 8°C below zero?what would the temperature at midnight?

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

$△$ABC is constructed such that AB = 5 cm, AC = 5 cm and $\angle$B = 50${}^{\circ }$.

Statement A: $\angle$C = $\angle$A

Statement B: $\angle$C + $\angle$B = 100${}^{\circ }$

In the evening, Ted went to a stationery shop and asked for a pen. The shopkeeper gave the pen and he took out ₹ 10 as he remembered paying the same amount the last time.

Shopkeeper: Hey, there’s 20% increase on the price of this pen.

How much should Ted pay now?

Question 53

Fill in the blanks to make the statement true.

Median is also called ___ in an equilateral triangle.

$5a{b}^3+22abc+10bc$ is a ____________.

What is the number of matchsticks you need to make '$n$' number of $2$s if 5 matchsticks are used to make one 2?

A boy contains 1Rs coins and 2 Rs coins whose total value is 70 R's. If the number of 1Rs coins is five times that of 2 Rs coins ,find the number of coins of each type.

If P(A) and P(not A) are complementary events and P(A) = 0.15, then P(not A) = ?

Question 98(ii)

Simplify:
${\left({\left(\frac{-2}{3}\right)}^{-2}\right)}^3\times {\left(\frac{1}{3}\right)}^{-4}\times 3^{-1}\times \frac{1}{6}$

Find the area of the square of side 15 cm.

If $\frac{x}{y}$ and $\frac{y}{x}$ are rational numbers, then which of the following options is correct?

Match the following figures according to the number of matchsticks required to make them.

Question 2 (iii)
Find the values of unknowns x and y in the following diagram:

Consider the following table and answer the following question:

_______ student/s has/have same marks in all three terms.

What is the significant figure of ?:

1. 100

2. 20

3. 0.100

4. 0.200

Dipanshu purchased a computer for 32,000 and sold it for25,000 after 6 months. Find its loss percent.

$\begin{array}{cccccccccccccccc}\text{Bus}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12& 13& 14& 15\\ \text{Arrival time(hr:min)}& 8:15& 8:18& 8:23& 8:29& 8:32& 8:40& 8:45& 8:52& 8:54& 9:00& 9:07& 9:13& 9:20& 9:25& 9:32\end{array}$

In the above observation, how many buses have arrived within 5 minutes of the bus just before them?

Find the greatest number that will divide 28, 143, 303 leaving the same remainder of 3 in each case.

1. 6.6

How many ST girls leave school when they reach the secondary section?

Two adjacent angle are in the ratio 5:3 and they together from an angel of 128°.find these angles