Explore topic-wise InterviewSolutions in .

Question 92 (xxix)

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

$8a^3-2a$

If $3^x=27$, what is $x$?

Question 143(i)

Use the propeties of exponents to verify that each statement is true.

$\frac{1}{4}\left(2^n\right)=2^{n-2}$

Question 85 (xiii)

Expand the following, using suitable identities.

$(a^2+b^2{)}^2$

Find the integer m in the following:

(i) m + 6 = 8; (ii) m + 25 = 15; (iii) m − 40 = − 26; (iv) m + 28 = −49.

Construct a frequency table with equal class intervals froin the following data on the monthly wages (in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210-230 (230 not included): 220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

From the following Receipts and Payments Account of Mumbai Club, prepare Income and Expenditure Account for the year ended 31-12-2012 and its balance Sheet as on that date.

RECEIPTS AND PAYMENT ACCOUNT

for the year ending on 31st December, 2012

$\begin{array}{cccc}\text{Receipts}& \text{Amount}& \text{Payments}& \text{Amount}\\ & \left(\text{Rs}\right)& & \left(\text{Rs}\right)\\ \text{Cash in Hand}& 4,000& \text{Salary}& 2,000\\ \text{Cash at Bank}& 10,000& \text{Repair Expenses}& 500\\ \text{Donations}& 5,000& \text{Purchase of Furniture}& 6,000\\ \text{Subscriptions}& 12,000& \text{Miscellaneous Expenses}& 500\\ \text{Entrance Fees}& 1,000& \text{Purchase of Investments}& 6,000\\ \text{Interest on Investments}& 100& \text{Insurance Premium}& 200\\ \text{Interest Received from Bank}& 400& \text{Billiard Table}& 8,000\\ \text{Sale of Old Newspapers}& 150& \text{Paper, Ink, etc.}& 150\\ \text{Sale of Drama Tickets}& 1,050& \text{Drama Expenses}& 500\\ & & \text{Cash in Hand}\left(\text{Closing}\right)& 2,650\\ & & \text{Cash at Bank}\left(\text{Closing}\right)& 7,200\\ & \overline{33,700}& & \overline{33,700}\end{array}$

Information :

(a) Subscriptions in arrears for 2012 Rs 900 and subscription in advance for 2013 Rs 350.

(b) Insurance premium outstanding Rs 40.

(c) Miscellaneous expenses prepaid Rs 90. (d) 50$\%$ of donation is to be capitalised.

(e) Entrance fees are to be treated asrevenue income.

(f) 8$\%$ interest has accrued on investment for five months.

(g) Billiard table costing Rs 30,000 was purchased during the last year and Rs 22,000 were paid for it.

Factorise
$(x^2-2xy+y^2)-z^2$

The frequency distribution of two variables is known as

(a) Univariate Distribution

(b) Bivariate Distribution

(c) Multivariate Distribution

(d) None of the above

Question 83 (v)

Multiply the following :

$-3x^{2}y,(5y-xy)$

The perimeter of a rhombus is 260cm and one of its diagonals is 66cm. Find the area of the rhombus and its other diagonal.

Question 109(i)

Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using

$x=1,y=\frac{-1}{2}$ and $z=\frac{1}{4}$

and what is the name of this property?

The total surface area of a cylinder of radius 'r' and height 'h' is _____.

Factorise:

$3+23z-8z^2$

The corresponding sides of 2 similar triangles $△ABC$ and $△PQR$ are in the ratio 4:23. $\angle R$ is___________
Given that $\angle B$=${60}^{\circ }$ and $\angle A$= ${40}^{\circ }$.

Using the identities of algebric expressions, Find the value of ${\left(4.9\right)}^2$ .

Find the square root of the following decimal numbers:

7.29

If the volume of this prism is $684$ cm${}^3$, what will be its length?

The binary operation $\square$ is defined as follows:

Write down the rational number whose numerator is the smallest four digit number and denominator is the largest five digit number.

Find the area of the pentagon shown in the figure if AD=10 cm,AG=8 cm,AH=6 cm,AF=5 cm and BF=5 cm,CG=7 cm and EH=3 cm.

A cuboidal box is of the measurement $3cm\times 2cm\times 36cm$. Find the volume and check if it is a perfect cube or not. [2 MARKS]

Simplify:

$(x^5÷x^2)\times y^2\times y^3$

The value of $k$ is if ${}^6{\text{C}}_k=\frac{6!}{\left(4\right)!\times k!}$

___ is a 3D shape whose all faces are squares.

What is the median of following data?
34, 27, 45, 55, 22, 30, 40.

Line AB of 4 cm is drawn. Another line CD which is congruent and perpendicular to AB is drawn. Length of CD is_____.

Four alternative options are given for each of the following statements. Select the correct option.

A collection of data having more than 3 modes is said to be:

A. uni-mode

B. bi-mode

C. tri-mode

D. multi-mode

Question 109(iii)

Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using

$x=\frac{-2}{7},y=\frac{-5}{6}$ and $z=\frac{1}{4}$

and what is the name of this property?