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Question 7

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

If a and b are positive integers, then the solution of the equation ax=b has to be always:

(a) positive

(b) negative

(c) one

(d) zero

The following table gives the marks scored by students in an exam.

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{Above}0& 80\\ \text{Above}10& 77\\ \text{Above}20& 72\\ \text{Above}30& 65\\ \text{Above}40& 55\\ \text{Above}50& 43\\ \text{Above}60& 23\\ \text{Above}70& 16\\ \text{Above}80& 10\\ \text{Above}90& 8\\ \text{Above}100& 0\end{array}$

Find the mean for the following data using assumed mean method. [4 MARKS]

The length of minute hand of the clock is 14 cm. Find the area swept by minute hand from 9:00 to 9:30.

In what ratio does the x-axis divide the line segment joining the points (2, –3) and (5, 6)? Also, find the coordinates of the point of intersection.
[3 MARKS]

Use graph paper for this question. Take 1 cm = 1 unit on both axes.

i) Plot the points A (–2, 0), B (4, 0) and C (1, 4) on the graph.

ii) Plot D (–2, 4) and E (4, 4). Assign special name to quadrilateral ABED.

iii) Draw lines of symmetry of quadrilateral ABED, and DABC.

iv) Write the equation of lines of symmetry.

Find sub - triplicate ratio of :

(i) 64 : 27 (ii) $x^3:125y^3$

Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations:

$2x+3y=7,(a+b)x+(2a-b)y=21.$

If sec 4A = cosec $(A-{20}^o)$,where 4A is an acute angle, find the value of A.

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80cm/ sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour ?

Find the lengths of the medians of a $△$ABC having vertices at A (0, -1), B (2, 1) and C (0, 3).

If $(sin\theta +cos\theta )=\sqrt{2}cos\theta ,$ show that $cot\theta =(\sqrt{2}+1)$.

Aspherical cannonball 28 cm in diameter is melted and cast into a right circular cone mould, whose base in 35 cm in diameter. Find the height of the cone.

1. 24

Question 4

Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its

If $sec\theta +tan\theta =x,thensec\theta =$

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

Write the value of $cose{c}^2({90}^o-\theta )$-$ta{n}^2\theta$

Assertion-and-Reason Type

Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

$\begin{array}{cc}Assertion\left(A\right)& Reason\left(R\right)\\ Ifthemedianandmodeofa& Mean,medianandmodeofa\\ frequencydistributionare150and& frequencydistributionarerelatedas:\\ 154respectively,thenitsmeanis148.& mode=3median-2mean.\end{array}$

The correct answer is :(a)/(b)/(c)/(d).

The 5th term of an AP is -3 and its common difference is -4. The sum of its first 10 terms is
(a) 50 (b) -50 (c) 30 (d) -30

In an annual examination, marks(out of 90) obtained by students of Class X in mathematics are given below:
$\begin{array}{ccccccc}\text{Marks}& & & & & & \\ \text{obtained}& 0-15& 15-30& 30-45& 45-60& 60-75& 75-90\\ \text{Number of}& & & & & & \\ \text{students}& 2& 4& 5& 20& 9& 10\end{array}$ Find the mean marks.

The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students
Age (in years): 15 16 17 18 19 20
No. of students: 3 8 10 10 5 4

In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options.

At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all. Which of the following words will be most appropriate for blank (4)?

Two coins are tossed simultaneously. The probability of getting at least one head is __
(Give the answer up to 2 decimal places)

In a class of $40$ students, $\frac{1}{5}$ of the total number of students like to eat rice only, $\frac{2}{5}$ of the total number of students like to eat chapati only and the remaining students like to eat both. What fraction of the total number of students like to eat both?

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If the thickness of iron is $1cm$, find the volume of air inside the sphere. Take $\pi =3.14$

Express as product of its prime factors : 156

Question 6

A wire in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also, find which shape encloses more area?

In $△$ ABC, $\angle Aand\angle C$ are given, the number of triangles that can be constructed with this data is -

The probability of getting 'atmost two heads' on tossing three coins simultaneously is.

zeroes of $x^2+kx+k$

In the given figure O is the center of the circle and $\angle$BAC = ${25}^{\circ }$ , then the value of $\angle$ADB is :

Solve for y if the pair of linear equations are

$\frac{5}{(x-2)}=\frac{4}{(1-y)}and$

$26x+3y+4=0$

1. 3

(x+y)/x=2 , (x-y)/x=6 find x and y

Sum of the sides of a polygon is called __ of the polygon.

If the lines $2y-a^{2}x=3$ and $2y-(4ax+1)=0$ are parallel, find the value of a.

Indians , Egyptians , Europeans and Australians are residing in a village of area 200 $k{m}^2$. If the area is equally divided between the four countries, what is the probability that a particular person who lands in the village, finds himself in the area occupied by either Indians or Europeans?

Which of the following is not an example of polynomial function ?

$△$ABC is a right- angled triangle with AB = 12 cm and AC = 13 cm. A circle with center O has been inscribed inside the triangle. Calculate the radius of the inscribed circle.

In the figure shown below, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ. Then $\Delta$PQR is an__ triangle.