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x = 5, y = 2 is the solution of the linear equation:

At what point does the line x + y = 5 meet a line which is parallel to the y-axis at a distance 2 units from the origin and in the positive direction of x-axis?

Question 71(ii)

It is given that l varies directly as m.

Find the constant of proportion (k), when l is 6, then m is 18.

In the given figure, ΔABC is congruent to ΔPQR.

What is the value of (x + 2y + 3z)?

Maximum numbers of points that can lie on a line are:

The surface area of a cuboid is $1372c{m}^2$. If its dimensions are in the ratio $4:2:1,$ then its breadth is

A, B, C are three points such that. Do they lie on a straight line?

Question 3

The compound interest on Rs 50000 at 4% per annum for 2 yr compounded annually is
(a) Rs 4000
(b) Rs 4080
(c) Rs 4280
(d) Rs 4050

Replace the underlined word with a modal auxiliary showing necessity.

David needs to rush to the airport to catch his flight on time.

Question 1 (vi)

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$3x^2-x-4$

Why do we group data?

In the given figure, if ∠DOB = 2x - 5° and ∠AOC = 85° , then x = ___.

In the above figure, ABCD is a square and BCE is an equilateral triangle. Find the measure of angle DEC.

Which of the following irrational numbers is represented by CE on the given number line?

Find the volume of a cubical box whose surface area is 13.50 cm².

Which of the following rational number lies between $\frac{7}{3}$ and $\frac{8}{5}$?

What is the average amount of money spent by Satish if he has spent ₹250, ₹350 and ₹300 in 3 days?

Find the decimal expansion of 2\15

Question 8(i)
Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 Litres of water.Vidya consumed $\frac{2}{5}$ of the water. Pratap consumed the remaining water.
(i) How much water did vidya drink?

Question 5

In the given figure, PR > PQ and PS bisects $\angle$QPR. Prove that $\angle$PSR > $\angle$PSQ

.

If a line that passes through the origin also passes through the points that can be denoted as (3k,k), then what is the equation of the line. Also find the point whose abscissa is 6. [4 MARKS]

A fruit grower has $150$ acres of land available to raise two crops, $A$ and $B$. It takes one day to trim an acre of crop $A$ and two days to trim an acre of crop $B$, and there are $240$ days per year available for trimming. It takes $0.3$ day to pick an acre of crop $A$ and $0.1$ day to pick an acre of crop $B$, and there are $30$ days per year available for picking. Fruit grower planted the crops in order to maximize his profit, then his maximum profit is $($assuming that the profit is $140$ per acre for crop $A$ and $235$ per acre for crop $B)$

Question 6

$\Delta ABC$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that $\angle BCD$ is a right angle.

What
is 'I' in these lines?

Rohit borrowed ₹45,000 at simple interest and rate is 8.5% per annum. How much money will he pay at the end of 4 years to clear his debt?

The circumference of a circle is 44 cm. What is its area?

168 sq cm

145 sq cm

1.54 sq m

154 sq cm

In the given figure, O is the centre of a circle, $\angle AOBand\angle BDC,\text{find}\angle OBC.$

In $\Delta ABCand\Delta DEF$, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B, and C are joined to vertices D, E and F respectively ( see the given figure).

Question 2 (iii)

Find the LCM and HCF of 336, 54 and verify that LCM $\times$ HCF = product of the two numbers.

If $lo{g}_2(4^{x+1}+4)lo{g}_2(4^x+1)=lo{g}_{2}8,$ then x equals

Compute the length of the diagonal of a square of side 10 metres, correct to centimetres.