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Three unbiased dice are rolled such that we get outcomes in the form (a, b, c). If a, b, and c are distinct, then the probability of a, b and c forming an AP is

A mathematician trying to cross a street happened to witness a bank robbery. When the police questioned him, he stated that the number plate of the van in which the thieves escaped had its last four digits as follows:
The first digit is 5. The last digit is the square of the second digit. The third digit is twice the second digit. Also he noticed the sum of digits to be “9”. What is the quadratic equation that the police need to frame to find the $2^{nd}$ digit, given that ‘b’ is the second digit?

Question 5
Classify the following as constant, linear, quadratic and cubic polynomials.

(i) $2–x^2+x^3$

(ii) $3x^3$

(iii) $5t-\sqrt{7}$

(iv) $4–5y^2$

(v) $3$

(vi) $2+x$

(vii) $y^3-y$

(viii) $1+x+x^2$

(ix) $t^2$

(x) $\sqrt{2}x-1$

Given below is a combination figure of square ABCD of side 26cm and four circles. Find the area of the shaded region.

Question 6 (i)

A teacher wanted to analyze the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above.So she decided to group them into intervals of varying sizes as follows : 0−20,20−30…60−70,70 − 100. Then she formed the following table:

$\begin{array}{cc}\text{Marks}& \text{Number of student}\\ 0-20& 7\\ 20-30& 10\\ 30-40& 10\\ 40-50& 20\\ 50-60& 20\\ 60-70& 15\\ 70-above& 8\\ \text{Total}& 90\end{array}$

(i) Find the probability that a student obtained less than 20% in the mathematics

test.

If the area of the yellow sector is $12\pi c{m}^2$, what is the measure (in cm) of the diagonal of the square?

Ogives can be helpful in locating graphically the

(i) mode

(ii) mean

(iii) median

(iv) none of the above

Prove cos^2 θ+tan^2 θ−1sin^2 θ=tan^2 θ

Solve each of the following systems of equations by using the method of cross multiplication:

$\frac{x}{6}+\frac{y}{15}=4,\frac{x}{3}-\frac{y}{12}=\frac{19}{4}.$

Find the co-ordinates of the point P if P is the midpoint of a line segment AB with A(4,1) and B(-3,5).

Solve the following by substitution method

6x+5y=11

9x+10y=21

Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.

In $\Delta ABC$, $\angle C={30}^{\circ },\angle B={80}^{\circ },\angle A={70}^{\circ },AB=12cm$ as shown in the figure. The length of the side AC is equal to ___

$\left[\begin{array}{c}sin{30}^{\circ }=0.5\\ sin{70}^{\circ }=0.93\\ sin{80}^{\circ }=0.98\end{array}\right]$

1. 266

Solve equation, given below, using factorisation method:

$2x^2-9x+10=0,when\left(i\right)xϵN\left(ii\right)xϵQ.$

The curved surface area of a shpere is 5544 $c{m}^3$. Find its volume.

What is the probability of getting a sum of 13 when rolling a pair of dice?

Given that the roots of the equation $a{x}^2+bx+c=0$ are the consecutive terms of an A.P.What is the common difference of the A.P. in terms of a, b and c?

1. 5

The base and hypotenuse of a right triangle are respectively 5cm and 13cm long. Its area is

The speed of an express train is km/hr & the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes 1 hour longer than express train to cover a distance of 240 km, find the speed of the express train.

1. 10

Question 10

Obtain the mean of the following distribution.



$\begin{array}{cc}\text{Frequency}\left(f_i\right)& \text{Variable}\left(x_i\right)\\ 4& 4\\ 8& 6\\ 14& 8\\ 11& 10\\ 3& 12\end{array}$

The point of intersection of the three medians of a triangle is called its _______

What will be the centroid of a triangle whose vertices are (2, 4), (6, 4) and (2, 0)?

Tbe base QR of an equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.