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In the figure, PQ || RS, TR|| QU and $\angle PTR={42}^{\circ }$. Then $\angle QUR$ is equal to:

Which of the following pair of angles formed are not equal when a transversal intersects two parallel lines?

$(2a^3{)}^4÷(4a^2{)}^2=$

Write the following fractions in descending order by

(a) equalising the numerators

(1)

(2)

(3)

(4)

Solve:
(i) $-96÷16$
(ii) $98÷-28$
(iii) $-51÷68$
(iv) $38÷-57$
(v) $-85÷20$
(vi) $-150÷-25$
(vii) $100÷60$
(viii) $9÷-54$
(ix) $78÷65$
(x) $-5÷-315$

Find the result obained by the addition of

$\frac{2}{3}\text{to the reciprocal of}\frac{-2}{3}.$

If the perimeter of a square is 16 cm, then its area is:

A pair of shoes marked at Rs 115 is being offered at Rs 95. Find the discount percent being offered

Simplify:

(a) 6,048 + 36 + 8 + 769

(b) 4,670 − 3,294

(c) 6,847 + 3,521 − 4,053 − 3,082

(d) 5,609 × 84

(e) 4,536 ÷ 42

In the given figure, $\angle x={20}^{\circ },\angle y={160}^{\circ },\angle w={105}^{\circ },\angle z={75}^{\circ }$



Which of the following is correct?

Which one of the following represents $x=3$ ?

$△$DEF is drawn with the length of side EF being 7.5 cm. If $\angle$E is 75${}^{\circ }$ and $\angle$F is 55${}^{\circ }$, then the measure of $\angle$D is

What do we get when 8abc is divided by 4ab?

Once a person joins the gym his weight starts to decrease. As he left the gym it started to increase again.

Which of the following graphs best reflects the situation in this state?

State the lines of symmetry for the rectangle PQRS.

What is the value of -7 + 2?

An open cuboidal box has dimensions $20cm\times 10cm\times 5cm$. Find the cost of painting the box from outside if the painting cost is ₹ $2/c{m}^2$.

$A=\{0^2,1^2,2^2,3^2,4^2\}andB=\{16,9,4,1,0\}$ then the Set A and Set B are ___sets.

Two manufacturers Ram and Shyam manufacture only three wooden items; bed, table and sofa. The sales (in rupees) of these three items by both of manufacturers in month of June and July are given by the following matrices $A$ and $B$ respectively.



Sale in June

$\begin{array}{ccccccc}& & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}A=\left[\begin{array}{ccc}5000& 10000& 15000\\ 25000& 15000& 5000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$



Sale in July

$\begin{array}{ccccccc}& & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}B=\left[\begin{array}{ccc}2500& 5000& 3000\\ 10000& 5000& 5000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$



If both manufacturers receive $1\%$ profit on gross sale, then profit of both manufacturers for each item in June is given by



[1 mark]

The length of a rectangular playground is $40m$ and breadth is $15m$. Find the cost of fencing it at the rate of ₹ $5$ per metre.

By what rational number should we divide $\frac{22}{7}$ so as to get the number $\frac{-11}{14}$?

Find the solution set of the inequality
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$\frac{2}{4x-12}$ <
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$\frac{-3}{3-5x}$, if the replacement set is a set of real numbers.

The weight of 80 identical books is 320 kg. What could be the ratio of weight of one such book?

Question 179(i)

Express each of the following in exponential form.

$\frac{-1296}{14641}$

Mt.Everest is at a height of 8850 m. Its base is at an elevation of 5400m. The temperature here drops at the rate of 1 degree per 100

metres.If the temperature at the base is -5 degree c, what is the

temperature at the top?

Find the circumference of circles whose diameters are

(1) 7 cm

(2) 14 cm

(3) 3.5 cm

(4) 5.6 cm

Triangle ABC is constructed with BC = 5.5 cm, AB = 5.5 cm and AC = 5 cm. Two angular bisectors are drawn of angle A and C intersected at point O. Drop a perpendicular OD on any of the sides of the triangle. The length of OD is ____.

Which is the best bargain?