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Pawan is a cashier in a bank. He has currency notes of denominations 1000, 500 and 100 respectively. The ratio of the number of these notes is 2:3:5. If the total cash with Pawan is ₹5,00,000, then how many notes of ₹1000 denomination does he have?

A cube is painted red along all its faces and then divided into 27 smaller identical pieces. How many of the resultant pieces will have no face painted?

The area (in sq. units) of the region $\{(x,y):0\le y\le x^2+1,0\le y\le x+1,\frac{1}{2}\le x\le 2\}$ is

Question 72

In questions 60 to 79, state whether the statements are True or False.
By selling a book for ₹ 50, a shopkeeper suffers a loss of 10 %. The cost price of the book is ₹ 60.

Solve the following.

The population of Mallapur village is 4,500, of which 1,350 are literates. Find

(i) the ratio of total population to the number of illiterates in the simplest form.

(ii) the ratio of total population to the number of literates in the simplest form.

(iii) the ratio of literates to the illiterates in its simplest form.

In the given figure, AD divides $\angle BAC$ in the ratio 1:3. Find the value of X and $\angle ADC$ (in degrees).

Find the value of x in the following figure:

1. 17

Which of the following is a recurring decimal?

a) 4.171717.....

b) 5.131131131......

c) 6.989989989989......

Coefficient of $x{y}^2$ in the term -$\frac{4x{y}^2}{9}$ is:

A bicycle is purchased for Rs. 1800 and is sold at a profit of 12 %. Its selling price is

(a) Rs. 1584
(b) Rs. 2016
(c) Rs. 1788
(d) Rs. 1812

In the given figure if $\angle$ BAC = ${60}^{\circ }$, AB = AC = 6 cm then find the length of BC.

Subtract 8 from 6.

Find the result obained by the addition of

$\frac{2}{3}\text{to the reciprocal of}\frac{-2}{3}.$

Hari bought two fans for Rs 2,400 each. He sold one at a loss of 10% and the other at a profit of 15%. Find the selling price of each fan and find also the total profit or loss.

Convert 0.625 into a fraction in its simplest form

The number π + 7 is

In an equilateral triangle $ABC$ , if $AD$ is perpendicular to $BC$ , then

A man bought a shirt for Rs 500 and sold it at a loss of 20 %. Find its SP?

There is a data set with 1000 observations. Out of these observations, the observation that occurs most frequently is 9, which occurs 13 times. After taking 20 more observations, it was observed that 13, which was not there in the observations before, occurred 19 out of 20 times and 9 occurred only 1 out of 20 times. What is the mode in these 1020 observations?

If angles of a triangle are in the ratio 2:3:5, then find the smallest angle.

1. 352

Four arrows are pointing in four different directions from a point 'O' as shown. Find angle 'x'.

The infinite series $1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}+...$ corresponding to

Observe the nature of the number patterns given below.

1 + 2 + 3 = 6

5 + 10 + 15 = 30

10 + 20 + 30 = 60

What is the relation between the sum and the middle number ?

Select the correct option(s).

Question 52

In the following question, fill in the blanks to make the statements true.

$3^5÷3^{-6}$ can be simplified as ___ .

Fill in the blanks with suitable answers.

(i) A triangle has ………. Vertices.

(ii) Triangles are grouped into ………. types according to their sides.

(iii) Triangles are grouped into ………. types according to their angles.

(iv) In a scalene triangle three sides are not ……….

(v) If one angle of a triangle is 90°, the triangle is said to be ………..

The area of a rectangle whose length is 11 cm and width equal to half its length will be

1. 78

$15-[15-\{15-(15-15)\left\}\right]$ =