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The diagonals do not necessarily intersect at right angles in a

(a) parallelogram

(b) rectangle

(c) rhombus

(d) kite

Factorise by grouping method:

$a(a-4)-a+4$

(a+b+c)^2

The volume of a cubical tank is 1331 $m^3$. Given that it costs Rs.10 to paint per square meter. Find the cost incurred to paint its complete surface area.

An increase in salary of 5 % to his present salary will give a man an additional income of 60000 per year. What is his present annual income?

A table is sold at Rs 4995 inclusive of 7% VAT . What is the cost o the table before vat.

Rajni sold a pressure cooker at a loss of 8%.Had she bought it at 10% less and sold for Rs.176 more, she would have gained 20%.Find the cost price of the pressure cooker .

*Use x as C.P.

A positive number is 5 times another number. If 21 is added to both the numbers then one of the new numbers becomes twice the other new number. What are the numbers?

Q73. Which of the following are components of Housing for All by 2022?

1. Slum rehabilitation of Slum Dwellers

2. Credit linked subsidy

3. It is fully Centrally Sponsored Scheme.

4. Houses constructed under the mission would be allotted in the joint name of the male head of the household and his wife.

Which of the above statement(s) is/are correct?

If x = √(p+2q) +√(p-2q) / √(p+2q) - √(p-2q) , then show that qx^2 -px + q = 0

In triangle ABC, D is a point in AB such that AC = CD = DB. If $\angle B={28}^{\circ }$, then the measure of angle ACD is

What is the value of x in the following equation?

12x - 2 = 40 - 2x

Two numbers differ by 5, The sum of square of these numbers is 97. Find the product of the numbers.

The number of natural numbers between 15 and 20 is ___.

Rina and Tina went to the market to buy half a dozen apples and two chocolates one for each. What is the amount (in Rs) they spent if each apple cost Rs x and each chocolate Rs y?

Using a suitable algebraic identity, the value of ${101}^3$ is ___ .

Name a polygon that cannot have diagonals.

What amount has to be repaid on a loan of Rs.16000 for 1.5 years at 10% per annum compounded half yearly?

The L.C.M. of $9x^2+6x+1,3x^2+7x+2and2x^2+3x-2$ is $(x+a)(2x-b)(3x+c{)}^2$. Then the value of $a-b-c=?$

Question 4 (ii)
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

1989

Express ${16}^{-2}$ as a power with the base 2.

Fourth angle of the quadrilateral that has three acute angles is

(a) acute (b) right (c) obtuse (d) straight

If $(a+b)=6$, and $ab=2$, then the value of $\frac{1}{a^2}+\frac{1}{b^2}$ is equal to

Factorise : $5+7x-6x^2$

Factorizing the given expression gives:

$-4a^2+4ab-4ca$

Directions:- Study the following information carefully to answer the question given below.

Six persons - A, B, C, D, E and F - are sitting in two cars namely X and Y but not necessarily in the same order. Out of the six persons, two are driving the cars. There are three persons in each car and one person must be on the front seat beside the person who is driving the car. In car X, D is neither driving nor sitting in the back seat. F is sitting on the back seat in Car Y. C is in the driver's seat but not in the Car X. A is neither driving nor travelling in the Car Y. E is not in the driver's seat in any car.

Which of the following pairs represents the persons sitting on the front seats in the Car X and Car Y respectively?

The diagonal of a quadrilateral shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 14m. Find the area of the field(in m²).

Which of the following options is correct?

S1 : Total surface area of a cuboid is the sum of areas of 4 faces excluding top and bottom faces.

S2 : Lateral surface area of a cuboid is the sum of areas of 4 faces excluding top and bottom faces.

S3 : Volume of a cuboid is of the form xyz.

Factorize by finding common factors :

$7ab+21a^2+b$

Two numbers are respectively 20 percent and 50 percent of a third number. What percent is the second of the first ?

Question 2(iv)

State True or False.
There is no perfect cube which ends with 8.

$\text{The given figure shows a rhombus ABCD in which angle}BCD={180}^{\circ }.\text{Find angle s x and y.}$

Question 2 (vii)

The following number is obviously not a perfect square. Give reasons.

222000

Question 8(ii)
Compare the following numbers:
(ii) $4\times {10}^{14};3\times {10}^{17}$

$y^2+2y-3=?\left(a\right)(y-1)(y+3)\left(b\right)(y+1)(y-3)\left(c\right)(y-1)(y-3)\left(d\right)(y+2)(y-3)$

Consider the figure:

If $\angle$A = ${70}^{\circ }$​, $\angle$ACD = ${120}^{\circ }$​, then find the value of $\angle$B (in degrees).

___

If $a+\frac{1}{a}$ = 4 , then $a^{}+\frac{1}{a^2}$ = ____________

The cost of a notebook is $Rs.3a^2-4ab+6b^2$. How much would $5a^2{b}^2$ notebooks cost?

Question 1 (iii)
What will be the unit digit of the squares of the following number:

799