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$\begin{array}{cc}\text{Assertion (A)}& \text{Reason (R)}\\ \text{ABCD is a quadrilateral in which}& \text{The line segment joining the}\\ \text{P, Q, R and S are the midpoints of}& \text{midpoints of any two sides of a}\\ \text{AB, BC, CD and DA respectively.}& \text{triangle is parallel to the third side}\\ \text{Then, PQRS is a parallelogram.}& \text{and equal to half of it.}\end{array}$

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

Question 14(iii)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{array}{cccccc}Distance\left(inm\right)& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 6& 11& 17& 12& 4\end{array}$


Calculate the median distance by using the formula for the median.

The polynomial a$x^3$ + b$x^2$ + x – 6 has (x + 2) as a factor and leaves a remainder 4 when divided by (x – 2). Find a and b.

³√3 or ⁴√4 which is greater?

A number is said to be an irrational number if its decimal form is ___________.

In a right -angled triangle, one of the acute angles measures ${53}^{\circ }$ .Find the measure of each angle of the triangle.

$In\Delta ABCand\Delta DEF,\text{it is given that}\angle B=\angle Eand\angle C=\angle F.\text{In order that}\Delta ABC\cong \Delta DEF,\text{we must have}\left(a\right)AB=DF\left(b\right)AC=DE\left(c\right)BC=EF\left(d\right)\angle A=\angle D$

Let $f\left(x\right)=(x+1{)}^2-1,(x\ge -1)$. Then the set $S=\{x:f(x)=f^{-1}(x\left)\right\}$. is

Shreya, when measured the angles in a triangle, they came out to be 60°, 50°, and 70° respectively. Now she wants to know what type of triangle it is.
Can you tell what type of triangle it is?

Question 6(ii)

Evaluate:

${\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-4}$

For the system shown in the figure, the cylinder on left has a mass (M) of 25 kg and cross-sectional area 20cm² and is connected to a spring of spring constant 1400 N/m. The piston on the right has mass m =5kg and cross-sectional area 4 cm² . The minimum mass m^, to be kept on m so that water spills out from the left is(initially water level in both limbs is same) [The height of cylinder in left limb is 5 cm]$(g=10m/s^2)$

$△$ ABC, right angled at B, $\angle$ACB = ${60}^{\circ }$, expressions for sec 60 and cosec 60 is

In countries like USA
and Canada, temperature is measured in Fahrenheit, whereas in
countries like India, it is measured in Celsius. Here is a linear
equation that converts Fahrenheit to Celsius:

(i) Draw the graph of the linear equation above using Celsius for
x-axis and Fahrenheit for y-axis.

(ii) If the temperature
is 30°C, what is the
temperature in Fahrenheit?

(iii) If the
temperature is 95°F, what is
the temperature in Celsius?

(iv) If the temperature is 0°C,
what is the temperature in Fahrenheit and if the temperature is 0°F,
what is the temperature in Celsius?

(v) Is there a temperature which is numerically the same in both
Fahrenheit and Celsius? If yes, find it.

Which of the following is a binomial?

Three angles of a quadrilateral are equal. If the fourth angle is twice the value of the equal angles, then find the measure of the fourth angle.

If $\Delta ABC$ is isosceles with AB = AC and C(O,r) is the incircle of the $\Delta ABC$ touching BC at L, prove that L bisects BC.

In the given figure, O is equidistant from the vertices C and B. Then, the value of x - 3 is ___.

Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)

Question 1 (i)

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$x^2-2x-8$

The polynomial $a{x}^3+b{x}^2+x–6$ has $(x+2)$ as a factor and leaves a remainder $4$

when divided by $(x–2)$. Find $a$ and $b$.

The length of a room is 20m and its breadth is 5m. The sum of the areas of floor and the ceiling is equal to the area of the four walls. Find the height of the room.

In the figure, which of the following is the diameter of the circle ?

Which of the following expressions are polynomials? In case of a polynomial, write its degree.



(i) $\frac{x^2}{2}-\frac{2}{x^2}$

(ii) $\sqrt[2]{22}{x}^2-8$

(iii) $\frac{1}{2x^2}$

In the given figure AB||CD.

If $\angle CDE={85}^{\circ }$,then find the value of x and y respectively.

(ii) $36x^2-12x+1-25y^2$

(iii) $x^4+x^2+1$

$\text{In the given figure, ABCD is a}\text{parallelogram. From the given options,}\text{select the values of x and y.}$