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Question 3

In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:





Find the probability that a student of the class was born in August.

The points P(0, 6), Q(-5, 3) and R(3, 1) are the vertices of a triangle, which is

(a) equilateral (b) isosceles (c) scalene (d) right angeled

A juice seller fills glasses from a big cylindrical container of height $35.2cm$ and radius $10cm.$ He charges $\text{Rs.}10$ for each glass of height $10cm$ and $4cm$ radius. The amount of money he earns by selling juice is $(\text{Take}\pi =\frac{22}{7})$

Which of the following is not correct about VAT.

What is the distance between the points (0,6) and (0,-2)?

In the adjoining figure, if AD, AE, and BC are tangents to the circle at D, E, and F respectively, which of the following is true?

If f = {(1, 2), (2, b), (3, c)} is a constant function, find the values of b and c.

In the given figure if 'O' is the centre of the circle then $\angle AOB$ =___

The equation of the straight line that has y - intercept of 5 units and is parallel to the straight line x - 3y = 3 is .

The frequency polygon of a frequency distribution is shown below.

Answer the following about the distribution from the histogram.

(i) What is the frequency of the class interval whose class mark is 15?

(ii) What is the class interval whose class mark is 45?

(iii) Construct a frequency table for the distribution.

Solve the given equation by undoing the operations:

$\frac{x}{5}=4$

Rationalising factor of $\frac{1}{\sqrt{3}+\sqrt{5}}$ is

Two dice are thrown together. The probability that sum of the two numbers will be 2 is:

Find the solution of the given system of equations.

$\frac{x+y-8}{2}=\frac{x+2y-14}{8}=\frac{3x+y-12}{11}$

The number of goals scored by Messi in champion's league for past 10 years is a follows: {1, 1, 6, 9, 8, 12, 14, 8, 8, 10}. Find the mean deviation about the median.

The sum of the first $n$ terms of an AP is given by $S_n=(3n^2–4n).$ Find its (i) $n^{th}$ term, (ii) first term, and (iii) common difference.

1. 24960

Let $\alpha ,\beta$ be the roots of $x^2-x+p=0and\gamma ,\delta$ be the roots of $x^2-4x+q=0.$ If $\alpha ,\beta ,\gamma ,\delta ,$ are in G.P., then the integral values of p and q respectively, are

Question 9

Which of the following equation has two distinct real roots?

(a) $2x^2-3\sqrt{2}x+\frac{9}{4}=0$

(b) $x^2+x-5=0$

(c) $x^2+3x+2\sqrt{2}=0$​​​​​​​

(d) $5x^2-3x+1=0$​​​​​​​

Why the degree of zero polynomial is undefined?

XY is drawn parallel to BC, the base of ΔABC. If ΔAXY : Trapezium XBCY = 4:5. Show that, AX : XB = 2 : 1.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

Given AB = 3 cm, AC = 5 cm and $\angle B={30}^{\circ }$, $\Delta$ABC cannot be uniquely constructed, with AC as base, why?

In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis ? Also, find the co-ordinates of the point of intersection.

1. 77

A river of 5 $\text{m}$ width and 2 $\text{m}$ depth flows at a speed of 20 $\text{km/hr}$. Water from this river is used to irrigate a field of area $x{\text{m}}^2$. The field is filled with water to a height of 0.5 $\text{m}$. If it takes 30 minutes to irrigate the field, then find $x$.

If $sinA=\frac{3}{4}$, then cos A = x and tan A = y.
Choose the correct options.

A, B, C, D are 4 non-collinear points in a plane such that $\angle$ ACB=$\angle$ ADB, then how many circle(s) can be drawn passing through all 4 points.

Question 6

The table below shows the daily expenditure on food of 25 households in a locality.

$\begin{array}{cccccc}\text{Daily expenditure (in Rs)}& 100-150& 150-200& 200-250& 250-300& 300-350\\ \text{Number of households}& 4& 5& 12& 2& 2\end{array}$

Find the mean daily expenditure on food by a suitable method.