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Find the perimeter of the given right-angled triangle.

In the given figure, if $\angle$ACB = ${30}^{\circ }$, what is the value of $\angle$ACD in degrees?

ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O,
show that area($△$ABC) = area($△$ABD). [2 MARKS]

The percentage of marks obtained by a student in monthly unit tests are given below:

$\begin{array}{cccccc}\text{unit test}& I& II& III& IV& V\\ \text{Percentage of marks obtained}& 69& 71& 73& 68& 76\end{array}$

Find the probability that the student gets:

(i) more than 70% marks (ii) less than 70% marks (iii) a distinction.

Question 20

In the following question, out of the four options, only one is correct. Write the correct answer:

$(-9{)}^3÷(-9{)}^8$ is equal to:
(a) $(9{)}^5$
(b) $(9{)}^{-5}$
(c) $(-9{)}^5$
(d) $(-9{)}^{-5}$

In a quadrilateral PQRS, the diagonals PR and QS bisect each other. If $\angle Q={56}^{\circ }$, determine $\angle R$.

In the figure, chords AD and BC intersect each other at right angles at a point P. If $\angle DAB={35}^o,then\angle ADC=$

If the supplement of an angle is three times its complement, find the angle.

Monica has a piece of canvas whose area is 551 $m^2$.She uses it to have a conical tent made,with a base radius of 7 m.Assuming that all the stitching margins and wastage incurred while cutting,amounts to approximately 1 $m^2$.Find the volume of the tent that can be made with it.

In a quadrilateral ABCD, the bisectors of $\angle A$ and $\angle B$ meet at E. If $\angle C={75}^{\circ }$ and $\angle D={125}^{\circ }$, then find the measure of $\angle AEB$.

Find the median of
(i) 2, 10, 9, 9, 5, 2, 3, 7,11
(ii) 15, 6, 16, 8, 22, 21, 9, 18, 25
(iii) 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22
(iv) 7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2

Visualize the representation of 3.765 on the number line using successive magnification.

$\text{The dimensions of a room are}(9m\times 8m\times 6.5m).\text{It has one door of dimensions}(2m\times 1.5m)\text{and two windows, each of dimensions}(1.5m\times 1m).\text{Find the cost of whitewashing the walls at Rs25 per square metre.}$

The points (other than the origin) for which the abscissa is equal to the ordinate lie in which quadrants? [2 MARKS]

$\Delta ABC$ is right angled at B, given $5\times sinA=3$.
Find cosC+tanA + cosecC.

A triangle ABC is drawn to circumscribe a circle such that the segments BS and SC are of lengths 6 cm and 8 cm respectively. If the length of the segment AT is x cm , then find the perimeter of the triangle.

If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are
[RPET 1999]

Assertion: Area of a triangle
$=\sqrt{s(s-a)(s-b)(s-c)}$ where a, b and c are the sides of the triangle and $s=\frac{a+b+c}{2}$

Reason: Area of a triangle $=\frac{1}{2}\times base\times height$
Which of the following is correct?

Question 1

In the following question, out of the four options, only one is correct. Write the correct answer:

In $2^n,$ n is known as :
(a)Base
(b)Constant
(c)Exponent
(d)Variable

Find the complement of each of the following angles:

(i) ${55}^{\circ }$

(ii) ${16}^{\circ }$

(iii) ${90}^{\circ }$

(iv) $\frac{2}{3}$ of a right angle

The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result.

If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.

There are two cones.The curved surface area of one is twice that of the other.The slant height of the later is twice that of the former. Find the ratio of their radii.

In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is

A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is

(a) 27 kg (b) 48 kg (c) 36 kg (d) 56 kg

A measuring jar of internal diameter 10 cm is partially filled with water. Four equal spherical balls of diameter 2 cm each are dropped in it and they sink down in water completely. What will be the change in the level of water in the jar?

Write the truth value (T/F) of the following with suitable reasons :

(i) A circle is a plane figure.

(ii) Line segment joining the centre to any point on the circle is a radius of the circle.

(iii) If a circle is divided into three equal ares each is a major are.

(iv) A circle has only finite number of equal chords.

(v) A chord of a cirlce, which is twice as long is its radius is a diameter of the circle.

(vi) Sector is the region between the chord and its corresponding are.

(vii) The degree measure of an are is the complement of the central angelcontaining the are.

(viii) The degree measure of a semi-circle is ${180}^o$.

Diagonals of a quadrilateral ABCD bisect each other. If $\angle A={45}^{\circ }$, then $\angle B=$

Question 72

What is the cost of 27.5 m of cloth at Rs. 53.50 per metre?

PQ and RS are two equal and parallel line segments.
Any point M not lying on PQ or RS is joined to Q and S and lines through P parallel to QM and through R parallel to SM meet at N . Prove that line segments MN and PQ are equal and parallel to each other.

If $8^{x+1}$ = 64, what is the value of $3^{2x+1}$ ?

Question 2
Write whether the following statements are true or false. Justify your answer.

i. A Binomial can have atmost two terms.

ii. Every polynomial is a Binomial.

iii. A binomial may have degree 5.

iv. Zero of a polynomial is always 0.

v. A polynomial cannot have more than one zero.

vi. The degree of the sum of two polynomials each of degree 5 is always 5.

If x is parallel to y and z where $x=2\hat{i}+\hat{j}+\alpha k,y=\alpha \hat{i}+\hat{k}$ and $z=5\hat{i}-\hat{j},$ then $\alpha$ is equal to

In the given circle with centre ‘O’, the mid – points of two equal chords $AB$ & $CD$ are $K$ & $L$ respectively.



If $\angle OLK={25}^{\circ }$,then $\angle LKB=$?

The angles of a quadrilateral are 2a, 4a, 7a and 5a. The measure of angles of quadrilateral are:

The measure of each exterior angle of a regular octagon is

The number of lines passing through (3, 5) are:

For $3\times 3$ matrices M and N, which of the following sttements (s) is/are not correct?

If y = $\frac{1}{2}$ (3x+7) is written in the form ax + by + c = 0, then the values of b is -

$O$ is the circumcentre of $△ABC$. If $\angle BOC={120}^{\circ }$, then $\angle BAC=$

If you throw three coins simultaneously, the probability of getting all heads is

Find the values of a and bin which x² -1 is a factor of x⁴+ax³-3x²+2x+b

The dimensions of the room are 7 m × 6m × 5 m. The cost of white washing the walls of the room and the ceiling at the rate of Rs 10.50 per m² is

Question 6 (b)

Express the following as the sum of two odd primes:
36

1,2,3,4,5......
The above set of numbers are known as _______.

In a quadrilateral ABCD, if AB = 5 m, BC = 5 m, CD = 6 m, AD = 6 m and diagonal AC = 6 m, what is its area?

In $△ABC$, $\angle ABC={30}^{\circ }$ and $\angle ACB={45}^{\circ }$. Which is the longest side in this triangle?

In the given figure, ABCD is a parallelogram and PD is parallel to QC.

S1 : $△$APD $\cong$ $△$BQC

S2 : ar($△$APD) + ar(PBCD) = ar($△$BQC) + ar(CDPB)