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If two dice are rolled simultaneously, then what is the probability of getting the LCM of numbers as 6?

$x+\frac{x}{2}+\frac{x}{3}<11$

In the figure, the mid-points of the sides of the large quadrilateral are joined to draw the small quadrilateral inside. Then the coordinates of points $P$ and $Q$ respectively are

If $sec\left(4A\right)=cosec(A-20°)$, where $4A$ is an acute angle, then what is the value of $A$?

sin A-cosA+1/sinA+cosA-1=1/secA-tanA

Determine the value of k so that the two roots of the equation x² − kx + 36 = 0 are equal.

How many cubic metres of earth must be dug out to make a well 28 m deep and 2.8 m in diameter ? Also, find the cost of plastering its inner surface at Rs. 4.50 per sq.metre.

The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.

If $\omega$ is an imaginary cube root of unity and $\alpha$, $\beta$, $\gamma$ are the roots of real p, then for any x, y and z, the

values of $\frac{x\alpha +y\beta +z\gamma }{x\beta +y\gamma +z\alpha }$ are:

Given $\left[\begin{array}{cc}x& y+2\\ 3& z-1\end{array}\right]=\left[\begin{array}{cc}3& 1\\ 3& 2\end{array}\right]$
; find x, y and z.

Construct rhombus ABCD with sides of length 5 cm and diagonal AC of length 7 cm. Find the point R on BC such that RA = RD. Then the length of CR is

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball

A circle touches all the four sides of a quadrilateral ABCD. Which one of the following is always correct?

If $\frac{n}{2}$ =any of the given $Cf$ then what is the median class

In the adjoining figure, ∆ ABC is right angled at ∠A, CD = 8cm & DB = 18cm. Find AD and the ratio of areas of ∆ ADB : ∆ CDA.

In $△ABC$, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then which of the following is true?

If the value of $tan\alpha =\frac{5}{2}$ and $\alpha +\theta ={90}^{\circ }$ then the value of $cot\theta$ =

Two or more triangles whose corresponding angles are equal and their corresponding sides are in proportion are ________.

Question 2
If the median of the distribution given below is 28.5, find the values of x and y.

$\begin{array}{cc}Classinterval& Frequency\\ 0-10& 5\\ 10-20& x\\ 20-30& 20\\ 30-40& 15\\ 40-50& y\\ 50-60& 5\\ Total& 60\end{array}$

______ satisfies the equation $3x+4y=2$.

The Age groups of workers are given in the table :

$\begin{array}{cc}\text{Age}& \text{No. of workers}\\ 25-30& 30\\ 30-35& 28\\ 35-40& 22\\ 40-45& 30\\ 45-50& 35\\ 50-55& 24\end{array}$

Find the Median from the given data.

In a $\Delta ABC$, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC:
(i) AB = 12cm, AD = 8 cm, AE = 12 cm and AC= 18cm.
(ii)AB = 5.6cm, AD= 1.4cm, AC = 7.2 cm and AE= 1.8 cm.
(iii) AB= 10.8 cm, BD= 4.5cm, AC = 4.8cm and AE =2.8 cm.
(iv)AD = 5.7cm, BD = 9.5cm, AE = 3.3cm and EC = 5.5 cm.

Pavan filled water in a cylindrical vessel of radius 7cm and height 14cm. Then he dropped a spherical ball of radius 0.7cm. Height should be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give answer in micrometre and correct up to 2 decimal places.

AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm and divides the circle into two segments. Find the area of the minor segment.

The area of a rectangle gets reduced by 8 $m^2$,when its length is reduced by 5m and its breadth is increased by 3 m.If we increase the length by 3m and breadth by 2m,the area is increased by 74$m^2$.Find the length and breadth of the rectangle.

If the height of a vertical pole is $\sqrt{3}$ times the length of its shadow on the ground then the angle of elevation of the sun at that time is

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${75}^{\circ }$

Consider the frequency distribution of the heights of 60 students of a class:

$\begin{array}{ccc}Height\left(incm\right)& No.of.Students& CumulativeFrequency\\ 150-155& 16& 16\\ 155-160& 12& 28\\ 160-165& 9& 37\\ 165-170& 7& 44\\ 170-175& 10& 54\\ 175-180& 6& 60\end{array}$

The sum of the lower limit of the modal class and the upper limit of the median class is :

(a) 310 (b) 315 (c) 320 (d) 330

Show graphically that each of the following given systems of equations has infinitely many solutions:

$x-2y=5,3x-6y=15.$

If $△$ABC is similar to $△$DEF such that BC = 3 cm, EF = 4 cm and area of $△$ABC = 54 ${cm}^2$. Determine the area of $△$DEF.

A man rowing a boat away from a lighthouse which is 100 m high takes 2 min to change the angle of elevation of the light house from ${45}^{\circ }$ to ${30}^{\circ }$. The speed of the boat is $[Tan{45}^{\circ }=1,Tan{30}^{\circ }=0.57]$

If $A=\left[\begin{array}{cc}1& 3\\ 2& 4\\ 0& 6\end{array}\right]$, then find the transpose of A.

Jyotsana bought a product for Rs. 3155 including 4.5 % sales tax. Find the price before tax was added.

A path 2 m wide surrounds a circular pond of diameter 40 m. How many cubic metres of gravel are required to grave the path to a depth of 20 cm ?

Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.
(i) 9,15,21,27,.....
(ii) 11,6,1,-4,....
(iii) $-1,\frac{-5}{6},\frac{-2}{3},\frac{-1}{2},$...
(iv) $\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32}$,...
(v) $\sqrt{20},\sqrt{45},\sqrt{80},\sqrt{125}$,....

The shadow of a 5-m-long stick is 2 m long. At the same time, the length of the shadow of a 12.5-m-high tree is

(a) 3 m

(b) 3.5 m

(c) 4.5 m

(d) 5 m

If the roots of the equation $(c^2-ab)x^2-2(a^2-bc)x+b^2-ac=0$ are equal, prove that either a $=0or{a}^3+b^3+c^3=3abc$

Is -150 a term of the AP 11, 8, 5, 2,... ?

How many three digit natural numbers are divisible by 7 ?

If PA and PB are two tangents to a circle with centre O such that $\angle$ APB = ${80}^o$. Then, $\angle$ AOP = ?

(a) ${40}^o$ (b) ${50}^o$ (c) ${60}^o$ (d) ${70}^o$

The sum of the numbers $436.32,227.2$ and $0.301$ in appropriate significant figures is

Find the total surface area of a pyramid given the base edge is 14 cm and the lateral edge is 9 cm.

If $cotA=\frac{12}{5}$, then the value of
$(sinA+cosA)\times cosecA$ is:

Factorize $\sqrt{3}{x}^2+5x+2\sqrt{3}=0$ by splitting the middle term and find the value of $x.$

The lateral surface area of a right circular cone of height 28 cm and base radius 21 cm is:

What is the probability of guessing a three digit number correctly in one guess?