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The following data shows monthly savings of 100 families . Calculate the mode of the given frequency distribution.

$$\begin{array}{cc}Monthlysavings\left(Rs\right)& Numberoffamilies\\ 1000-2000& 14\\ 2000-3000& 15\\ 3000-4000& 21\\ 4000-5000& 27\\ 5000-6000& 25\end{array}$$

Find the number of prime factors of 5005.

If the given figure is folded a form a box, which among the boxes below will be formed?

A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?

Decide whether the real number 0.120 1200 12000 120000.... is rational or not. If rational, and of the form $\frac{p}{q}$, what can you say about the prime factors of q?

A circle touches all the sides of quadrilateral ABCD . If AB=8, BC=10 & CD=7, then find AD.

Find the points of trisection of the line segment joining the points :

(i) (5, -6) and (-7, 5), (ii) (3, -2) and (-3, -4), (iii) (2, -2) and (-7, 4).

The number of points at which the function $f\left(x\right)=max\{a-x,a+x,b\}$, $-\infty <x<\infty ,0<a<b$ cannot be differentiable

The interior of a building is in the form of a right circular cylinder of diameter 4.2 m and height 4 m surmounted by a cone of same diameter. The height of the cone is 2.8 m. Find the outer surface area of the building.

Find the arithmetic progression whose third tem is 16 and seventh term exceeds its fifth term by 12.

At what time (approx) between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together?

Give an example of two irrationals whose sum is rational.

If $f\left(x\right)=x^2+2bx+2c^2$ and $g\left(x\right)=-x^2-2cx+b^2$ such that in $f\left(x\right)>maxg\left(x\right)$, then the relation between $b$ and $c$, is

Factorise:

$25a^2-9b^2$

A cylindrical pipe has an inner diameter of 7 cm and water flows through it at 192.5 litres per minute. Find the rate of flow.

Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use $\pi$ = 3.14)

A shopkeeper buys a table listed at ₹2,500 and gets successive discounts of $20\%$ and $10\%$. He spends ₹60 on transportation and sells it at a profit of $20\%$. Find selling price of the table.

Question 4

Kirti Bookstore sold books worth ₹ 2,85,891 in the first week of June and books worth ₹ 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

In triangle PQR ,PS id the busectorbof angleQPR.show that

QS/SR = PQ/PR.

Simple interest on a sum of money is $\frac{1}{25}$ of the principal and the number of years is equal to the rate percent per annum. The rate percent is:

Separate the variables of the equation 7x - 2y = 5xy

After separating the variables, equation is of the form

$\frac{7}{\square }$ - $\frac{2}{\square }$ = 5 × $\square$ × $\square$

For four numbers a, b, c, d if a : b = c : d, then b : a = d : c. Which property of proportion is this?

A)What least number should be added to 1056 so that the sum is completely divisible by 23?

B)how can you add it is to get the number 1000 question mark brackets brackets? Use only addition

What is meant by a doublet in probability. With examples.

Let the degree be 45° and 105°. find radian?

Find the number of pairs of consecutive even positive integers, both of which are greater than 5 such that their sum is less than 23.

Find a,b and c such that the five numbers a+6, b+22 , c are in A.P.

What is the ratio between the circumference to the diameter of a circle?

AB & CD are two equal chords of a circle with Centre O which intersect each other at the right angle at point P. If the perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

15^th term of the A.P. x - 7, x - 2, x + 3 ... is:

In the given figure, the respective values of y and x are

Ali standing on the ground finds a bird flying at a distance of 100m from him at an elevation of 30°. Ankita standing on the roof of 20 m high building finds the angle of elevation of the same bird to be 45°. Ali and Ankita are on the opposite sides of the bird. Find the distance of the bird from Ankita.

A game consists of tossing a ₹5 coin twice and noting down its outcomes. Jesika wins if she gets exactly one head. What is the probability that she will lose the game?

Find the indicated terms in each of the sequences in where $n^{th}$ terms are :

$a_n=\frac{n(n-2)}{n+3};a_{20}$

Select the group of numbers that form an AP.

Find the common difference of an AP whose first term is 5 and the sum of first 4 terms is half of the sum of the next 4 terms.

The list price of an article is ₹ 20,000 offered at a discount of 15 % . If the sales tax is chargeable at the rate of 8 % , find the amount buyer pays for the article

Good evening,

My doubt is

The square of a positive integer CANNOT be of the form (k is an integer):

(a) 3k + 1 (b) 4k + 2 (c) 5k + 1 (d) 5k + 4

Maximum number of tangents parallel to a given secant of a circle is/ are

The length of a string between a kite and a point on the ground is 60 m. If the string makes an angle of ${30}^{\circ }$ with the ground, how high is the kite (in metre)? ___

Find the solution of the inequation:
$2\le y+5\le 9,$
when y is a whole number.

$2^{(2x+2)}-14\times 2^{(x+1)}+4=0$, then which of the following is true?

Product of two consecutive integer is divisible by 2 is the statement true or false justify

If both the zeroes of a quadratic polynomial ax²+bx+c are equal and opposite in sign, find b.