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In the adjoining figure, $AB=10cm,BC=15cm$ and $AD:DC=2:3,$ then $\angle ABC$ is equal to

Prove that the line segment joining the point of contact of two parallel tangents to a circle is a diameter of the circle.

Question 78

A car can travel 240km in 15 litres of petrol. How much distance will it travel in 25 litres of petrol?

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

The radius and height of a right circular cone are in the ratio $1:2$. If its volume is $144\pi {cm}^3$, find its slant height.

Find the equation of a line that has $y$-intercept as $4$ and is perpendicular to line joining $(2,-3)$ and $(4,2)$.

Show that the equation x²+x+2=0 equation has real roots, and solve by using quadratic formula.

Question 1 (a)
Convert the following temperatures to the Celsius scale.
(a) 293 K

The following table shows the runs scored by different batsmen in a tournament :

$\begin{array}{cc}\text{Player}& \text{Runs scored}\\ Kohli& 455\\ MSD& 243\\ Rohit& 346\\ Shikhar& 308\\ Karthik& 176\end{array}$

What is the average number of runs scored?

Question 164(ii)

If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use
$(\times 1)$ machines.

Question 150

For the following repeater machines, how many times the base machine is applied and how much the total stretch is ?

A milk carrying container has the shape of a cylinder mounted on a frustum. The radius of the cylinder is 14 cm and height is 20 cm. The other diameter of the frustum is 7 cm and its height is 5 cm. What is the curved surface area of the container?

The sides of a right triangle are in an AP. The area and the perimeter of the triangle are numerically equal. Find its perimeter.

A stone is dropped at random on a chessboard and it lands on a square. What is the probability that the square is a white square?

If point Q(x,y) divides the line segment AB with A(3,4) and B(5,7) in the ratio 3 : 5, find the co-ordinates of Q.

Find the surface area of a flute made up of African Blackwood of diameter 1.4 cm and length 25 cm having 5 holes of 1.4 cm diameter.

The ratio of sides of 2 similar triangles is 3:4. Find the ratio of their areas.

The largest sphere is curved out of a cube of a side 7 cm. Find the volume of the sphere.

Triangle ABC is similar to triangle DEF and their areas are

64 cm²and 121 cm² respectively. If EF= 15.4 cm, then BC = ?

If O is the center of the circle, then the value of $\theta$ in the adjoining figure is

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. The number of spheres formed will be

Check the values of $x$ from the given options for which the polynomial $x^3-7x^2+14x-8$ vanishes

A Group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above values you prefer more?

Prove that sin^{​​​​6}​​​A+cos^{​​​​6}​​​A=1-3sin²A .cos ²A

A girl has the following superhero toys. They are

$\begin{array}{cc}\text{Superhero}& \text{Number of toys}\\ \text{Ironman}& 3\\ \text{Batman}& 2\\ \text{Thor}& 5\end{array}$

The girl picks one of the toys at random. The probability that she gets Ironman is_____.

Question 6 (ii)
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out a lemon flavoured candy?

In the factory the ratio of salary of skilled and unskilled workers is 5:3. Total salary of one day of both of them is Rs 720. Find daily wages of skilled and unskilled workers.

$\text{If AB is the tangent to the circle with}\text{center O then, find the measure of}\angle OCP.$
$\text{Given that OP = PC.}$

The radii of the bases of two solid right circular cones of same height are $r_1$ and $r_2$ respectively. The cones are melted and recast into a solid sphere of radius R. Find the height of each cone in terms of $r_1,r_2$ and R.

Find the integral roots of the polynomial $x^3+6x^2+11x+6$

IF "N" is a positive integer, then how many values of N will give an integral value of

(16N²+7N+6)/N

Find the circumference of the circle from the figure.
(Take $\pi$ as $\frac{22}{7}$)

The point P (5, 3) was reflected in the origin to get the image P'.

(a) Write down the co-ordinates of P'.

(b) If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.

(c) If N is the foot of the perpendicular from P' to the x-axis, find the co-ordinates of N.

(d) Name the figure PMP'N.

(e) Find the area of the figure PMP'N.

If set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. Find the number of elements in P $\times$ Q.

A train covers a distance of 600km at km/hr. Had the speed been ( + 20) km/hr, the time taken to cover the distance would have been reduced by 5 hrs. Write down an equation in and solve it to evaluate .

A 13 m ladder is leaned against a wall as shown in figure. Find the distance of foot of ladder from the wall.

Question 4 (x)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(x) a, 2a, 3a, 4a …