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If (x – 1, y + 1 ) = (5, 6), then the value of x and y is given by

In the adjoining figure, $\Delta QPR$ is right-angled at Q in which QR = 6 cm and PQ = 7 cm. Find the area of $\Delta QSR$, given that PS is parallel to QR.

For a cube of side 'a' and a cuboid of length 'l', breadth 'b' and height 'h', match the following.

An ice cream cone has base radius 6 cm and altitude 8 cm. The total surface area of 21 such cones is

Evaluate each of the following using identities:

(i) $(399{)}^2$

(ii) $(0.98{)}^2$

(iii) $991\times 1009$

(iv) $117\times 83$

Factorise
$x^3+27$

Which of the following statements are incorrect?

The mean of 15 numbers is 27. If each number is multiplied by 4, what will be the mean of the new numbers?

If 2x+3y=13 and xy=6 find the value of 8x³+27y³.

1. 8

Which of the following should be the FIRST sentence after rearrangement?

Three coins were tossed 30 times. Each time the number of heads occurring was noted down as follow
0 1 2 2 1 2 3 1 3 0
1 3 1 1 2 2 0 1 2 1
3 0 0 1 1 2 3 2 2 0
Prepare a frequency distribution table for the data given above.

Evaluate each of the following using identities :

(i) ${(2x-\frac{1}{x})}^2$

(ii) $(2x+y)(2x-y)$

(iii) $(a^{2}b-b^{2}a{)}^2$

(iv) $(a-0.1)(a+0.1)$

(v) $(1.5x^2-0.3y^2)(1.5x^2+0.3y^2)$

Question 165

Find two repeater machines that will do the same work as a $(\times 81)$ machine.

I. 2x + 3y = 14

II. 4x + 2y = 16

Solve the following pair of equations:
$\frac{5}{x-1}+\frac{1}{y-2}=2$
$\frac{6}{x-1}-\frac{3}{y-2}=1$
(where $x\ne 1,y\ne 2)$

Solution set of the inequality
$\frac{1}{2^x-1}>\frac{1}{1-2^{x-1}}is$

Shreya, Karan and Gautam started a business in partnership by investing Rs. 20,000. At the end of one year, Shreya, Karan and Gautam received Rs. 600, Rs. 1200 and Rs. 200 respectively as profit share. The amount of capital Shreya invested in the business was Rs. 6000. Is this statement true?

Total surface area of a hemisphere with radius ${}^{\prime }{r}^{\prime }$ units, will be equal to

100ml 0.1M HCI is mixed with 100 ml 0.1M NaOH. Identify the correct statement (s)

The solution of a linear equation is not affected when

Any linear equation of the form y = mx will pass through

The number of tables available is 1/4 of 2 times the number of chairs ($x$) decreased by 5. The expression to find the number of tables is .

If p and q are integers, which of the following can be correct for $\frac{p}{q}$ to be a rational number?

The sides of a triangle are in the ratio of 13 : 14 : 15 and its perimeter is 84 cm. The area of the triangle will be equal to

If we start at (0,0) on a rectangular coordinate system and move 5 right and 3 up, where are we?

Question 33

State whether the given statements are true (T) or false (F).

If b : a = c : d, then a, b, c and d are in the proportion

Question 46

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

The standard from of $\left(\frac{1}{100000000}\right)$ is ___

Two figures are said to be congruent if they have:

You were given with random five digits 0, 5, 3, 7 and 2. You were just thinking how many five digit numbers you can form using these digits. You thought there can be so many numbers that can be formed, but you want to find the greatest five digits and the smallest five digit number that can be formed by using them. What can be the two numbers? ( Without repeating the digits)