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$\begin{array}{cc}\text{Class Marks}& \text{Frequency}\\ 30& 2\\ 40& 5\\ 50& 14\\ 60& 21\\ 70& 23\\ 80& 8\\ 90& 7\\ 100& 1\end{array}$

Cumulative frequency for the class interval 85-95 is ?

What is the LCM of $(2a+3b{)}^2$ and $(4a^2–9b^2)$

The sum of the first 10 whole numbers and ten highest negative integers be x. Find the value of x

Prove that $n^2-n$ is divisible by 2 for any positive integer n

It is being given that 1 is zeros of polynomial 7x-x³-6.find the other zeros of polynomial

In the given figure, LMN is tangent to the circle with centre O. If $\angle$ PMN = ${60}^{\circ }$, find $\angle$ MOP.

When the sun is at an elevation of ${40}^{\circ },$ the shadow of a flag post in 15 m. The length of the shadow when sun is at an elevation of ${45}^{\circ }$ will be $[Tan{40}^{\circ }=0.84,Tan{45}^{\circ }=1]$

Which of the following denotes the market supply curve?

PQR is a right angled triangle with PQ = 3 cm, QR = 4cm. A circle which touches all the sides of the triangle is inscribed in the triangle. Calculate the radius of the circle.

The first term and ${15}^{th}$ term of an AP are 7 and 35 respectively. Find the common difference.

If $\cos A=\frac{7}{25}$, find $\tan A+\cot A$

If sec 5A = cosec(A - ${30}^{\circ }$) and 5A is acute angle then find the value of A in degrees.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2-6x+4=0$

Jamila sold a table and a chair for Rs.1050,thereby making a profit of 10% on a table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got Rs.1065. Find the cost price of each.

The area of trapezium ABCD in the given figure is

(a) $62c{m}^2$

(b) $93c{m}^2$

(c) $124c{m}^2$

(d) $155c{m}^2$

If $x=asec\theta +btan\theta$ and $y=atan\theta +bsec\theta$, prove that

$(x^2-y^2)=(a^2-b^2)$.

The adjacent sides of a parallelogram are 32 cm and 24 cm. If the distance between the longer sides is 17.4 cm, find the distance between the shorter sides.

Fiind the sum of last ten terms of the A.P.: 8,10,12,14,..,126.

The area of an equilateral triangle whose height is 3 m is

Prove the following trigonometric identities:

$\frac{1+sec\theta }{sec\theta }=\frac{si{n}^2\theta }{1-cos\theta }$

If $S_1,S_2,S_3$ be respectively the sums of n, 2n, 3n terms of a G.p., then prove $S_1^2+S_2^2=S_1(S_2+S_3)$.

The largest possible sphere is carved out of a wooden solid cube of side $7cm.$ find the volume of the wood left.$(Use\pi =\frac{22}{7})$

Find the next three terms of the sequence :

$\sqrt{5},5,5\sqrt{5},.................$

To have a steep slide at a height of 6 m, and inclined at an angle of ${60}^{\circ }$ to the ground. What should be the length of the slide (in m)?

If a pair of dice are thrown, find the probability of getting a prime sum.

In figure, if $\angle A=\angle C={90}^{\circ }$, then prove that $△AOB\sim △COD$

Rohan attends a test with multiple choice questions with no negative marking. There were fifty questions and each question had four marks for answering right. What is the sample space of marks that Rohan could score?

Find the area of the triangle with coordinates A(-2,1), B(1,-2) and C(3,3) in square units.

Find the value of k if -1 is a zero of kx^2-4x+k

A man invests ₹ 20020 in buying share of N.V ₹ 26 at 10% premium. The dividend on the share is 15% per annum, then find

i) the annual income

ii) the rate of return

A card is drawn at random from a well shuffled of 52 cards. Find the probability of getting neither a red card nor a queen

For any positive integer n prove that n³ -n is divisible by 6

Construct the frequency table for each of the following.

$4,3,6,5,2,4,3,3,6,4,2,3,2,2,3,3,4,5,6,4,2,3,4$

The probability of getting a black face card from a well-shuffled 52 pack card is___

48 ice-creams are placed on a table. Some are chocolate flavoured and others are vanilla flavoured. If I take an ice-cream at random from the table, the probability that it is chocolate flavoured is 2/3. Find the number of vanilla flavoured ice-creams on the table.

$Inthefigure,AB\parallel DC,Area(△AOD)=8c{m}^{2}andArea(△BCD)=14c{m}^2.Calculate:\left(i\right)BO:OD$

In the formulae am+bn = HCF(a,b); how to find the values of m and n?

If -5 is a root of quadratic equation 2x^2+px-15=0 and the quadratic equation p(x^2+x)+k=0 has equal roots find the value of k

In an A.P., the first term is 22 and the nth term is -11. If the sum to first n terms is 66, then what is the value of n?

The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : $q^2=pr.$

If $A=\left[\begin{array}{ccc}a& 0& 0\\ 0& b& 0\\ 0& 0& c\end{array}\right]$, then $A^n=$

A tax whose rate remains the same irrespective of the increase in income level.

The monthly pocket money of Ravi & Sanjeev is in the ratio 5: 7. Their expenditures are in the ratio 3: 5. If each saves Rs.80 every month, find their monthly pocket money.

The dimensions of a room are $9m\times 8m\times 6.5m.$ It has one door of dimensions $2m\times 1.5m$ and two windows each of dimensions $1.5m\times 1m.$ Find the cost of whitewashing the walls at $Rs.6.40$ per $m^2$.