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Question 92 (vii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$25a{x}^2-25a$

Base 3 with exponent 5 can be expressed as

Question 2

Construct the Quadrilateral GOLD where

OL=7.5 cm, GL=6cm, LD=5cm, OD=10 cm

When Rashi ordered pizza and coke, the bill had the digits A and B not visible clearly.

$$\begin{array}{ccc}PizzaA& 1& 2\\ Coke+3& 1& B\\ 5& 2& 5\end{array}$$

Using the information visible on her bill, find the digits A and B respectively.

Find the compound interest on Rs 12600 for 2 years at $10\%$ per annum compounded annually. [2 MARKS]

Suppose ABC is an equiangular triangle. Prove that it is equilateral. (You have seen earlier that an equilateral triangle is equiangular. Thus for triangles equiangularity is equivalent to equilaterality.)

Evaluate :
$\sqrt[3]{3\frac{-64}{343}}$

Get the
algebraicexpressions in the following cases using variables,
constants and arithmetic operations.

(i) Subtraction
of z from y.

(ii) One-half
of the sum of numbers x and y.

(iii) The
number z multiplied by itself.

(iv) One-fourth
of the product of numbers p and q.

(v) Numbers
x and y both squared and added.

(vi) Number
5 added to three times the product of number m and n.

(vii) Product
of numbers y and z subtracted from 10.

(viii)Sum
of numbers a and b subtracted from their product.

1. 15

Find the product :
$(5-2x)(3+x)$

Find the value of

$-13+(-69)+57-(-89)-(53+(-49\left)\right)$

Square root of 256 is __.

The side of a rhombus is 8 m, then it perimeter =

If X = $\sqrt[3]{3\frac{1728}{125}}$, then the value of (X - 0.4) is ___.

If a$\times$(b+c) = (a$\times$b) + (a$\times$c), then it satisfies which of the following properties of Rational numbers?

ABCD is a parallelogram. DK is perpendicular to BA produced at K and DM is perpendicular to BC produced at M. Find the measure of $\angle KDM.$

The adjacent angles of a parallelogram are in the ratio 2:1. Find the measures of all the angles.

Question 5

The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table.



$\begin{array}{cc}\text{Length(in mm)}& \text{Number of leave}\\ 118-126& 8\\ 127-135& 10\\ 136-144& 12\\ 145-153& 17\\ 154-162& 7\\ 163-171& 5\\ 172-180& 3\end{array}$



Draw a histogram to represent the data above.

In an objective type paper of 150 questions; John got 80% correct answers and Mohan got 64% correct answers. (i) How many correct answers did each get ? (ii) What percent is Mohan's correct answers to John's correct answers ?

The total surface area of a solid cylinder is 462 CM square. if its curved surface area is one by third of the total surface area. find the volume of the cylinder

If you win Rs. 10,000 and pay 25% on taxes, how much do you take home?

In $\Delta$ ABC, DE is parallel to BC. Prove that area of ∆DOB= area of ∆EOC.

A bus conductor collected Rs 2916 from passengers of the bus. Each passenger paid an amount equal to number of passengers in the bus. What is the fare paid by each passenger?

A garrison has sufficient provisions for $480$ men for $12$ days. If the number of men is reduced by $160$, find how long will the provisions last.

Question 12

Ram put some buttons on the table. There were 4 blue, 7 red, 3 black and 6 white buttons in all. All of a sudden, a cat jumped on the table an knocked out one button on the floor. What is the probability that the button on the floor is blue?

(a) $\frac{7}{20}$

(b) $\frac{3}{5}$

(c) $\frac{1}{5}$

(d) $\frac{1}{4}$

Simplify the expression: $\frac{1}{\frac{\sqrt{66}}{\sqrt{2}\times \sqrt{3}}+\sqrt[4]{4144}}$

In the given figure, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. The measure of $\angle DAC$ is