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A cylinder whose height is two thirds of its diameter has the same volume as a sphere of radius 4 cm. The radius of the base of the cylinder will be

AE is a median to side BC of triangle ABC. If area(∆ABC) = 24 cm, then area(∆ABE) =

Question 02.

In a Television game show, the prize money of Rs1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners:

$\begin{array}{cccccccc}No.ofwinners& 1& 2& 4& 5& 8& 10& 20\\ Prizeforeachwinner(inRs.)& 1,00,000& 50,000& \dots & \dots & \dots & \dots & \dots \end{array}$

In the given image, the same ||gm has been represented by diff. colors. Which of the triangles are congruent?

In PQR, right-angled at Q, PR + QR = 25 and PQ = 5. The value of sinR is:



[1 mark]

If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are_______.

The distance between the top of two trees 20 m and 28 m high is 17 m. Find the horizontal distance between the trees.

______ is a unit of speed:

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Hannah takes a paper and cuts out a circle from it. Now, she folds the circle from the center and then folds it upside down. Later, she draws and cut out a pattern as shown below.



Find the figure that resembles the unfolded form of figure Z the most.

The mean of 5 observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is:

Find the quantity of concrete required to make 70 cylindrical pillars of radius $5cm$ and height $10m$.

Question 3

The number of line segments in the given figure is

a) 5

b) 15

c) 10

d) 20

What is the maximum number of obtuse angles in a triangle?

Find the value of j from the following ,given that mode = 7

Observation :- 1,4,4,7,6,8,7,j

In the adjoining figure, AOB is a straight line. Find the value of x.

Find median

Class interval 0-2. 2-4 4-6 6-8 8-10 10-12 12-14

Plants. 1. 2. 1. 5. 6. 2. 3

The PDF of a Gaussian Random Variable is given as :



$f_x\left(x\right)=\frac{1}{\sqrt{32\pi }}{c}^{-\frac{(x-5{)}^2}{32}}$



Which of the following options is/are correct?

The statements given below are the steps that need to be followed in the method of substitution in random order. Arrange them in correct order to solve two equations.

1) Find the value of one variable, say y in terms of the x if x and y are the two variables.

2) Substitute the x we got from step 2 in either of the equation to get y.

3) Substitute this y in the second equation and it will be reduced to an equation in x, find x.

Multiply 9x²+25y²+15xy+12x-20y+16 by 3x-5y-4 using suitable identity

‘I
wind about, and in and out.' What kind of a picture does this line
create in your mind?

Question 166

Find a repeater machine that will do the same work as a $(\times \frac{1}{8})$ machine.

Which of the following options is not a closed shape?

A coin was flipped 100 times. What is the maximum probability of occurrence of tail?

In the given figure, the value of x will be

A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability of not getting a black ball?

In triangle ABC, side AB is produced to D so that BD = BC. If angle B = 60^o and angle A = 70^o, then

A square PQRS and an equilateral triangle XYZ are rearranged to form a figure as shown.

What is the perimeter of the ABDF ? (Take $\sqrt{2}$ = 1.4 and $\sqrt{3}$ = 1.7)

If pentagon 1 is folded along the dotted line over pentagon 2, which of the options represents the folded form?

Question 10

The area of an equilateral triangle ABC is $17320.5c{m}^2$. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region. $(Use\pi =3.14and\sqrt{3}=1.73205)$

Question 20

Radhika bought a car for Rs. 250000. Next year, its price decreased by 10% and further next year, it decreased by 12%. In the two years, overall decrease per cent in the price of the car is
(a) 3.2%
(b) 22%
(c) 20.8%
(d) 8%

Total surface area of a cylinder of radius r and height h is

Construct a triangle with sides 5 cm , 5.5 cm and 6.5 cm. Construct another triangle whose sides are $\frac{3}{5}$ times the corresponding sides of the first triangle.

[3 MARKS]

Construct the following angles at the initial point of a given ray and justify the construction:

(i) ${45}^{\circ }$

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