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48 ice-creams are placed on a table. Some are chocolate flavored and others are vanilla flavored. If a person takes an ice-cream at random from the table, the probability that it is chocolate flavored is $\frac{2}{3}$. Find the number of vanilla flavored ice-creams on the table.

The equation of tangent to the curve $y=\ln (3x^2+x+8)-x\cdot {\tan }^{-1}\left(\frac{x}{3}\right)$ at $x=3$ is

The surface area of a sphere is 154 sq. cm. Find the diameter of the sphere.

If$A=\left[\begin{array}{cc}1& 2\\ -2& 9\end{array}\right]$, then -2A=_______________

Euclid’s division lemma states “Given positive integers a and b, there exist unique integers q and r satisfying $a=bq+r$".
Which of the following is true for r?

The sum of a two-digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3. Find the number.

Find the sum of the following finite series.

(a) 1 + 2 + 4 + ………+ 256

(b)

(c) 1 + 0.1 + 0.01 + ……. +(0.1)⁹

The following table shows marks secured by 140 students in an examination:
$\begin{array}{cc}Marks& Numberofstudents\\ 0-10& 20\\ 10-20& 24\\ 20-30& 40\\ 30-40& 36\\ 40-50& 20\end{array}$
Calculate mean marks by the step deviation method.

In what ratio does the point $(-4,6)$ divide the line segment joining the points $A(-6,10)$ and $B(3,-8)$?

If $a{x}^2+bx+c=0$ is a quadratic equation, then “a” cannot be:

Which of the following can not be found graphically?

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The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum.

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform cross-section . If the length of the wire is 36m, find its radius.

In the given figure chords AB and CD intersect at P. If PA = x, PB =9cm, PC =5 cm and PD = 8.1cm, find the value of ‘x’.

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Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

A train travels 360 km at a uniform speed if the speed had been 5 km more it would have taken 1 hour less from the same journey find the speed of the train​​

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

If A$(4,9)$, B$(2,3)$, and C$(6,5)$ are the vertices of ∆ABC, then the length of the median through C is
(a) $5$ units

(b) $\sqrt{10}$ units

(c) $\sqrt{25}$ units

(d) $10$ units

50 bells $B_1,B_2,B_3,.......B_{50}$ start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Answer the following questions.

1. Bells $B_1,B_2.....B_7$ ring together after how many seconds ?

Represent the given set in Roster form.

A = {x: x is an integer, $\frac{-3}{2}$ $<$ x $<$ $\frac{11}{2}$}