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What is the value of $\text{n.P(n-1, r-1)}$?

In figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the midpoint of line segment AB as well as PQ.

Question 68

Mukesh walks around a circular track of radius 14 m with a speed of 4 km/h. If he takes 20 rounds of the track, for how long does he walk?

Rational numbers are not closed under which operation?

Cost of one pen is Rs. $10\frac{1}{4}$. What is the cost of 20 such pens?

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

$\begin{array}{cc}Assertion\left(A\right)& Reason\left(R\right)\\ \text{The area of a trapezium whose}& \text{The area of an equailateral traingle}\\ \text{parallel sides measure 25 cm and}& \text{of side 8 cm is}16\sqrt{3}c{m}^2.\\ \text{15 cm respectively and the distance}& \\ \text{between them is 6 cm,is}120c{m}^2.& \end{array}$

The correct answer is :(a)/(b)/(c)/(d).

Twenty years from now, Arjun will become three times as old as he is now. His present age is

A triangle can be classified on the basis of

In a two-digit number, the digit at the units place is double the digit in the tens place. The number exceeds the sum of its digits by 18. Find the number.

Prime factorization of 18 would be

How many
diagonals does each of the following have?

(a) A
convex quadrilateral

(b) A
regular hexagon

(c) A
triangle

Which of the following is the formula for calculating profit $\%$ ?

Question 177(iii)

Find x.
$2^x+2^x+2^x=192$

Given below is the concentration of SO₂ in air(in ppm = parts per million) in 30 localities:
$\begin{array}{cc}S{O}_2\text{concentration (in ppm)}& \text{Number of localities}\\ 0.00-0.04& 4\\ 0.04-0.08& 9\\ 0.08-0.12& 9\\ 0.12-0.16& 2\\ 0.16-0.20& 4\\ 0.20-0.24& 2\end{array}$
Find the mean of $S{O}_2$ concentration using assumed - mean method.

Given below ar the angles x and y.

Without measuring these angles, construct :

$\left(i\right)\angle ABC=x+y\left(ii\right)\angle ABC=2x+y\left(iii\right)\angle ABC=x+2y$

The expansion of $(2x+y-5{)}^2$ is :

Consider a market with two firms. In the following table, columns labelled as $S{S}_1$ and $S{S}_2$ give the supply schedules of firm 1 and firm 2 respectively. Compute the market supply schedule.

$\begin{array}{cccccccccc}\text{Price(Rs.)}& 0& 1& 2& 3& 4& 5& 6& 7& 8\\ S{S}_1\text{(kg)}& 0& 0& 0& 1& 2& 3& 4& 5& 6\\ S{S}_2\text{(kg)}& 0& 0& 0& 0& 0.5& 1& 1.5& 2& 2.5\end{array}$

If the ratio of sides (taken in order) of a quadrilateral is a:b:a:b, then it is a

In the figure, if $OC\perp AB,$ then $AC:CB=$

Divide 2.64 by 8.

In the given frequency distribution, marks are ordered. Which 2 observations (students) are the median observations?

$$\begin{array}{cc}Marksobtained& Numberofstudents\left(Frequency\right)\\ 20& 6\\ 25& 20\\ 28& 24\\ 29& 28\\ 33& 15\\ 38& 4\\ 42& 2\\ 43& 1\end{array}$$

Question 84(iii)

Given below is a pie chart showing the time spend by a group of 350 children in different games. Observe it and answer the questions that follow.



How many children spend 3 or lesser hours in playing games?

If R1 and R2 are two congruent circles with BD and CE as diameters , then find which angle is equal to 30°.

Find the compound interest at the rate of $8\%$ per annum for 3 years on that principal which in 3 years at the rate of $5\%$ per annum gives Rs. 1200 as simple interest.

What quadrant is (3, -6) in?

Ravi deposited 50,000 rupees in a bank, which gives 6% interest, compounded quarterly. How much would he get back after 9 months?

Question 92 (xxii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$16x^4-81$

Which of the following is true in case of direct proportions?

Question 10 (i)

In the following figure, find the area of the shaded portion:

Match the following with their square roots.

$\begin{array}{cc}Numbers& Squareroots\\ 1.289& a.22\\ 2.1225& b.17\\ 3.196& c.35\\ 4.484& d.14\end{array}$

Which of the following represents the correct value equals to $1089$?