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A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{array}{cccccccc}2.6& 3.0& 3.7& 3.2& 2.2& 4.1& 3.5& 4.5\\ 3.5& 2.3& 3.2& 3.4& 3.8& 3.2& 4.6& 3.7\\ 2.5& 4.4& 3.4& 3.3& 2.9& 3.0& 4.3& 2.8\\ 3.5& 3.2& 3.9& 3.2& 3.2& 3.1& 3.7& 3.4\\ 4.6& 3.8& 3.2& 2.6& 3.5& 4.2& 2.9& 3.6\end{array}$

The number of batteries having a life of 3.5-4.0 years is:
(Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5)

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

The nth term of the sequence 1, 3, 7, 15 can be written as

Given:
$sin(B+C)=\frac{\sqrt{3}}{2}$
$sin(A+C)=sinB\text{and}$
$sinA=\frac{1}{2}.$

$\text{Find the value of}sin(A+B-C)?$

Match the following for a square pyramid with base edge length 24 cm, and height 16 cm.

If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$, then $A^2-4A$ is:

1. 5

Question 21

Fill in the blanks to make the statements true.

In the given figure, points A, B, C, D and E are collinear, such that AB = BC = CD = DE. Then,

a) AD = AB + _________

b) AD = AC + _________

c) Mid-point of AE is ______

d) Mid-point of CE is ______

e) AE = ______ AB.

Solve the equations $3x–y=5,x+3y=5$

The diameter of a metallic sphere is equal to 9 cm. It is melted and drawn into a long wire of diameter 2 mm having uniform cross-section. Find the length of the wire.

Which of the following should be the SECOND sentence after rearrangement?

What is the curved surface area of a cone of base radius 12 centimetres and slant height 25 centimetres?

The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is , then the coordinates of the point are

If $y=f\left(x\right),$ where $f:A\to B$ is a function in $x,$ then which of the following statements is true?



(i) Every element of $A$ needs to have an image.



(ii) $x\in A$ must be related to one and only one value of $y$ of $B.$

$\frac{\text{cos}\theta }{\text{cosec}\theta +1}+\frac{\text{cos}\theta }{\text{cosec}\theta -1}=$ ___

If the points A (-1, -4), B (b,c) and C (5, -1) are collinear and 2b + c =4, find the values of b and c.

Consider the 4 to 1 multiplexer with two select line $S_1$ and $S_0$ given below.





The minimal sum of products form of the Boolean expression for the output F of the multiplexer is

If 512 is as much as 16 times 32, then it can be represented using the equation

The product of 2 consecutive natural numbers is 56. Solve this problem using completing the square method of a quadratic equation. Write the equation obtained after completing the square and also write the smaller of the 2 consecutive positive integers.

Write the component statement of the following compound statement and check whether the compound statement is true or false.

$\sqrt{2}$ is a rational number or an irrational number'.

Which of the following is an irrational number?

Due to some technical problems, an aeroplane started late by one hour from its starting point.The pilot decided to increase the speed of the aeroplane by 100km/hr from its usual speed , to cover a journey of 1200km in time .Find the usual speed of the aeroplane.

The ${17}^{th}$ term of $AP$ is $5$ more than twice it's $8^{th}$ term. If the ${11}^{th}$ term of the AP is $43$, find its $n^{th}$ term

The sum S of first n even natural numbers in given by the relation S = n(n + 1). Find n, if the sum is 420.

Solve the following:
(a) If ax + by + c = 0 does not touch the Y axis anywhere, then which of these constants will be zero?
(b) Find the Y coordinates for the points which lie on y = 2x + 1, whose X coordinates are 3, 4 and 6. [4 MARKS]

In triangle $ABC,AD$ and $BE$ are the medians drawn through the angular points $A$ and $B$ respectively. If $\angle DAB=2\angle ABE={36}^0$ and $AD=6$ units, then circumradius of the triangle is equal to

(where $A,B,C$ are angles opposite to the sides $BC,CA,AB$ respectively)

Find the sum of 20 terms of the A.P. 1, 4, 7, 10, ......

Question 3

State whether the following is true or false.

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

[Thinking process

Let r = radius of circle and d = distance of a point from the centre.

1. If r = d, then point lie on the circle i.e only one tangent is possible

2. If r < d, then point lie outside the circle. i.e a pair of tangent is possible.

3. If r>d, then point lie inside the circle i.e no tangent is possible.

]

If $A$ is a $3\times 3$ matrix such that $|A|=2,$ then $|\text{adj(adj(adj}A\left)\right)|$ is

Find the mode of the following data:
(i) 3, 5, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
(ii) 3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
(iii) 15, 8, 26, 25, 24, 15, 18, 20, 24, 15, 19, 15

In real life what type of interest is most commonly applied?