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One card is drawn at random from a pack of $52$ cards. What is the probability that the card drawn is a face card?

If a diagonal of the given polygon is selected at random, what is the probability that it divides the polygon into two equal halves?

If 3x + 2y = 12 and xy = 6, find the value of 9x2+ 4y2

Which of the following polynomials is a trinomial of degree 3?

If the fourth term in the expansion of ${(x+x^{{\log }_{2}x})}^7$ is $4480,$ then the value of $x$ where $x\in N$ is equal to:

If $x=1-\sqrt{2}$, find the value of ${(x-\frac{1}{x})}^3$

Match the two column;

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) In the given figure,}& \text{(p)}{60}^{\circ }\\ \text{ABCD is a cyclic Quadrilateral.}& \\ \text{O is the centre of the circle.}& \\ \text{If}\angle \text{BOD}={160}^{\circ }\text{find the Measure of}\angle \text{BPD.}& \end{array}$





$\begin{array}{cc}\text{(B) In given figure, ABCD is a cyclic}& \text{(q)}{65}^{\circ }\\ \text{quadrilateral whose side AB is a diameter}& \\ \text{of the circle through A, B, C, D.}& \\ \text{If}\angle {\text{ADC = 130}}^{\circ }\text{, find}\angle \text{BAC.}& \end{array}$





$\begin{array}{cc}\text{(C) In the given figure BD = DC and}& {\text{(r) 40}}^{\circ }\\ \angle {\text{CBD = 30}}^{\circ }\text{Find m}\left(\angle \text{BAC}\right)& \end{array}$





$\begin{array}{cc}\text{(D) In the given figure, O is the centre of the}& {\text{(s) 100}}^{\circ }\\ {\text{arc ABC subtends an angle of 130}}^{\circ }\text{at the centre.}& \\ \text{If AB is extended to Pm find}\angle \text{PBC.}& \end{array}$





Choose the correct option:

The co-ordinates of the vertices of Triangle ABC are $A(4,1),B(–3,2)$ and $C(0,k)$. Given that the area of $△ABC$ is 12 sq. units. Find the value(s) of $k$.

The population of a town is 50,000. It decreases by 50 per thousand per year. Find out the population after 2 years.

Draw a line segment of length 8.6 cm. Bisect it and measure the length of each part.

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the length(in cm) of the smallest part.

1. 2.9

A point C is called the midpoint of a line segment $\overline{AB}$ if

(a) C is an interior of AB

(b) AC=CB

(c) C is an interior point of AB such that $\overline{AC}=\overline{CB}$

(d) AC+CB=AB

In the given figure, ABCD is parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 6 cm, AE = 8cm and CF = 12 cm, find AD.

[2 MARKS]

Simplify: $(a+b+c)(a+b-c)$

Triangle $ABC$ has $AB=5,$ $BC=12$ and $AC=13.$ The perpendicular bisector of $AC$ intersects the extension of $AB$ at $O.$ Then $OC$ is

Question 11(i)

Zero has ________ reciprocal.

Using ruler and compasses only, construt a $△ABC,$ given base BC = 7 cm, $△ABC={60}^{\circ }$ and AB + AC = 12 cm.

If the radii of two cylinders are in the ratio 2:3 and their heights are in the ratio of 5:3, then find the ratio of their volumes?

Given that ACBD is a kite. By which congruency property are the triangles ACB and ADB congruent?

Factorise:
$3x^2-14x+8$

Find the Perimeter of the Square ADEC given in the figure.