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If AD and PM are medians of triangles ABC and PQR, respectively where

Out of 100 students sitting in an examination, 40 students got more than 60 marks out of 100. So, percent of students got more than 60 marks.

In figure, ABCD is a trapezium in which AB || DC and AB = 3DC. Determine the ratio of the areas of $△$ AOB and $△$COD.

In Fig. the line segment joining the mid-points M and N of opposite sides AB and DC of quadrilateral ABCD is perpendicular to both these sides. Prove that the other sides of the quadrilateral are equal. [4 MARKS]

Find the reminder when 19^{92 is divided by 92}

Question 160(i)

For each hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.

The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.

The following is the record of goals scored by team A in a football session:

$\begin{array}{cccccc}No.ofgoalsscored& 0& 1& 2& 3& 4\\ No.ofmatches& 1& 9& 7& 5& 3\end{array}$

For the team B, mean number of goals scored per match was 2 with standard deviation 1.25 goals. Find which team may be considered more consistent?

A, B and C are the points on a coordinate plane. The $\Delta ABC$ is a right-angled triangle (right-angled at C ). If $AC$ is parallel to the X-axis and the angle between $AB$ and $AC$ is ${45}^o$. The slope of $AB$ is___ .

$\text{What are the conditions under which the}$
$\text{logarithm}$ $lo{g}_{2x}(x-1)$ is defined ?

Question 86

Solve the following:

The sum three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.

Which of the following expression gives the 36th triangular number?

The difference between the sides at right angles in a right-angled triangle is 7 cm, The area of the triangle is 60 $c{m}^2$. Find its perimeter.

Find the square root of the following expressions.

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at a number less than 9?

Question 5 (i)
Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and

deg p(x) = deg q(x)

Two dice, one blue and one grey, are thrown at the same time.

(i) Write down all the possible outcomes and complete the
following table:

Event: Sum of two dice	2	3	4	5	6	7	8	9	10	11	12
Probability

(ii) A student argues that ‘there are 11 possible outcomes
2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a
probability.
Do you agree with this argument?

Using quadratic formula solve the following quadratic equation: [3 MARKS]

$p^2{x}^2+(p^2-q^2)x-q^2=0,p\ne 0$

Find the condition to be satisfied by the coefficient of factor equal to x^3-px^2+qx-r when sum of its zeroes is zero

Can the sum of the first few consecutive terms of the arithmetic sequence 5, 7, 9, ….be 140? What about 240?

The set of values of m for which the roots of the equation $x^2-(m+1)x+m+4=0$ are real and negative consists of all m such that

Which of the following options gives all the real roots of the equation $x^4-11x^2+28=0$?

In the given figure, areas have been drawn of radius 21 cm each with vertices A,B,C, and D of quadrilateral ABCD as centres. Find the area in ${cm}^2$of the shaded region. [1 MARK]

The roots of the equation $a(x^2+1)-(a^2+1)x$ = 0 are

Determine, by drawing graphs, whether the following system of linear equations has a unique solution or not:

(i) 2x - 3y = 6, x + y = 1

(ii) 2y = 4x - 6, 2x = y + 3

In the figure BC || DE, area of ΔABC = 25 sq. cm, area of trapezium BCED = 24 sq. cm and DE = 14 cm. Calculate the length of BC.