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In each of the figures given below, ABCD is a rectangle. Find the values of x and y in each case.

In the given figure, O is a point on side CD of a parallelogram ABCD such that the ratio of areas of $\Delta$OAD and $\Delta$ OBC is 1:2. If area of parallelogram is $60c{m}^2$, then the area of $\Delta$OBC will be

In triangles ABC and CDE, if AC = CE, BC = CD, $\angle A={60}^{\circ },\angle C={30}^{\circ }and\angle D={90}^{\circ }$

Are two triangles congruent?

If the point P(a,1) lies on the line 2x-3y-5=0, then find the value of a.

The value of x - y${}^{x-y}$ when x = 2 and y = -2 is

Find an irrational number between 2.5 and 2.3

Given a base angle B and the difference of the sides AC and AB (not necessarily in this order), what is the difference in the steps of constructions when

i) AC $>$ AB

ii) AC $<$ AB

If the difference of mode and median of a data is 24, then find the difference of median and mean.

The graph of a linear equation is

If (1,3k) lies on $kx+4y=26,$ the value of $k$ is

$ABC$ is a triangle right angled at $C$. A line through the mid-point $M$ of hypotenuse $AB$ and parallel to $BC$ intersects AC at D. Show that

$CM=MA=\frac{1}{2}AB$

The volume of a triangular base prism as shown with given dimensions is cu ft.

In ∆ABC, E is the mid-point of median AD. Area(∆BED)=

A coin is tossed 10 times with the following frequencies:
Head : 6 , Tail : 4
What is the probability for a tail coming up?

A certain sum of money is invested at a certain fixed rate compounded yearly. If the interest accured in two years is 44% of the sum borrowed, find the rate of compound interest.

What is the period of f(x) = Sinx. Cos3x ?

Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the surface area of the new cube.

The points (-2,0), (3,0) and (-6,0) lie ______.

Assertion: The expression $3x^4-4x^{\frac{3}{2}}+x^2$ is not a polynomial because the term $-4x^{\frac{3}{2}}$ contains a rational power of x.



Reason: The highest exponent(of the variable) in various terms of a polynomial in one variable is called its degree.



Which of the following is true?

Question 3(a)

See the figure and find the ratio of:

The number of triangles to the number of circles inside the rectangle.

For constructing an angle of ${75}^{\circ }$.

Steps of construction:

Step 1: Draw ray AB

Step 2: Construct $\angle BAC={60}^{\circ }$

Step 3: Construct

Question 6: Consider the following figure of line $\overleftrightarrow{MN}$. Say whether the following statement is true or false in the context of the given figure:



(a) O is not an initial point of $\overrightarrow{OP}$.

In the figure below, AB = 6 cm and AC = 8 cm. If D and E are the midpoints of AB and AC respectively, find the area of $\Delta ADE\left(inc{m}^2\right)$.

Construct a triangle ABC in which BC = 4 cm, $\angle ACB={45}^{\circ }$ and perpendicular from A to BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and find its radius.

In the following figure, ABCD is parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, show that

ar (BPC) = ar (DPQ).

[Hint: Join AC.]

1. 15120

Question 13

In the given figure, l||m and line segments AB, CD and EF are concurrent at point P. Prove that

$\frac{AE}{BF}=\frac{AC}{BD}=\frac{CE}{FD}$.