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Question 86 (xvi)

Using suitable identities, evaluate the following:

$(35.4{)}^2-(14.6{)}^2$

Construct a quadrilateral ABCD given AB = 5.6 cm, BC = 4.1, CD = 4.4 cm, AD = 3.3 cm and $\angle A={75}^{\circ }$ [3 MARKS]

By using the formula, find the amount and compound interest on:

The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is Rs 93. Find the sum.

The measures of angles of the rhombus given in the diagram are

If each side of a square, of side a, is doubled, find the new area.

By using the formula, find the amount and compound interest on:

Anand obtained a loan of Rs. 125000 from the Allahabad Bank for buying computors. The bank charges compound interest at $8\%$ per annum compounded annually. What amount will he have to pay after 3 years to clear the debt ?

Question 89

In the following question, state whether the given statements are true (T) or false (F).

Large numbers can be expressed in the standard form by using positive exponents.

Data arranged in an unorganised manner is called

Solve the following equation :

$\frac{4(y+2)}{5}=7+\frac{5y}{13}$

Choose the greatest number of the lot.

1. 70

The sides of a triangle are 5cm, 12cm and 13cm, then its area is:

Which among the following is not a factor of $4y(y+3)$?

The volume of a room is $378m^3$ and the area of its floor is $84m^2$. Find the height of the room.

By what number $\frac{-3}{8}$ be multiplied so that the product is $\frac{33}{32}$ ?

The value of [(10)¹⁵⁰ ÷ (10)¹⁴⁶] is:

A fruit-seller sells 4 oranges for Rs.3, gaining 50%. Find : (i) C.P. of 4 oranges. (ii) C.P. of one orange. (iii) S.P. of one orange (iv) profit made by selling one orange (v) number of oranges need to be bought and sold in order to gain Rs.24.

Assertion: The sides of a triangle are 3cm, 4cm and 5cm. Its area is $6c{m}^2$

Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area

$=\sqrt{(s-a)(s-b)(s-c)}$

Which of the following is correct?

Question 41

If 45 persons can complete a work in 20 days, then the time taken by 75 persons will be___hours.

Coefficient of 'b' in the expression $4b^2$ is ___.

Pie charts can be replaced by___

Which of the following numbers are perfect cubes? In case of perfect cube, find the number whose cube is the given number.
(i) 125 (ii) 243 (iii) 343 (iv) 256 (v) 8000 (vi) 9261 (vii) 5324 (viii) 3375

A submarine after travelling 100km from the shore,descended 11/10 km below the sea level. Then it ascended about 3/5 km. The next day it again descended by 9/10 km. What is it current position with respevt to the sea level?. Whar i sthe horizontal distance of the submarine from the sea shore

Shani has to cut out circle of diameter 1 1/4 cm from an aluminium strip of dimensions 8 3/4 cm by 1 1/4 cm how many full circles can Shalini cut also calculate the wastage of the aluminium strips

Solve 1/4x+1/6x=x-7

Need solution

Sum of $3x^2-2x+6$ and $6x+2x^2+4$ is .

The quotient obtained when $x^3-3x^2+x+2$ is divided by $x-2$ is .

Using the pattern:

52 = 25

502 = 2500

5002 = 250000

We get the value of 50002 as

The ratio of areas of a circular and rectangular field is 1:2. Find the area of the rectangular field if the area of a circular field is 50 m².

Find the L.C.M. and H.C.F. of $2x^2-6x,x^2+9-6xand{x}^2-x-6$

Question 98

A wooden box (including the lid) has external dimensions $40cm\times 34cm\times 30cm$. If the wood is 1 cm thick, how many $c{m}^3$ of wood is used in it?

A submarine after travelling 100 km from the sea shore, descended 1 1/10 km below the below the sea level. Then it ascended about 3/5 km. The next day, it again descended by 9/10 km. What is its current position with the respect to the sea level? Whatnis the horizontal distance of the submarine from the sea shore?

In the answer section the answer to this question is given ' 7/5 km '

$1003\times 999=$ ___

In triangle ABC, the construction required to find point P equidistant from AB and AC and also, equidistant from B and C is/are

205² can be found by visual method taking a and b as _______ and _______.

Find the reciprocal (or multiplicative inverse) of -2 + 5i

A sum of money lent out at 10 percent for 4 years produces twice as much as interest as ₹ 6000 in $3\frac{1}{2}$ at 5 percent . Find the sum

The numbers which are used for counting objects are called

Factorise : $3a^{2}b-12a^2-9b+36$

How to find the square of 45 containing 5 in the unit's place ?

A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.

1. 1.75

In what period of time will Rs. 12,000 yield Rs. 3,972 as compound interest at 10% per annum, if compounded on a yearly basis?

Factorise
$25a^2-4b^2+28bc-49c^2$

1 m³ = ______ litres.