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If the fourth and seventh terms of a G.P are 10 and 80 respectively, then find the tenth term.

One hundred and fifty articles of the same kind were bought by a supplier for Rs 12,570 and Rs 12.50 per article was spent on its packing, transportation, etc. If 60% of the articles were sold for Rs 115 each and the remaining for Rs 120 each; find the profit he made.

If A (4, -3) & B (-8, 6) have respective coordinates

A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is

If ∪ = {2, 4, 6, 8, 10, 12, 14, 17}, where ∪ is Universal set and some set A = {1, 4, 6, 9, 11, 12}, Then, set A^C is

The area of a trapezium is 126 sq. cm. The height of the trapezium is 14 cm. If one of its parallel sides is 8 cm longer than the other side, find the lengths of the parallel sides.

The line $ax+by=a^2{b}^2$, will meet the x- axis at ____.

Find the number of terms in each of the following APs:

(i) $7,13,\mathrm{19....},205$

(ii) $18,\frac{31}{2},13,...-47$

Simplify the following equation and determine if the simplified equations are linear

$\frac{1}{x}$ + $\frac{3}{y}$ = 1

$\frac{6}{x}$ - $\frac{12}{y}$ = 2

In Fig., if $AB=AC$, prove that $BE=EC$ [2 MARKS]

A hollow cylinder of radius r and height h is wrapped by an aluminium foil till its radius becomes R. The thickness of the foil wrapped around the cylinder is:

The area of the curve $x^2+y^2=2ax$ is

If a train travelled 9 km/hr slower, it would take one hour more to travel 410 km. The equation representing this situation is :

The value of cos² 17^o – sin² 73^o is

In the given figure, ABC is a triangle. DE is parallel to BC and $\frac{AD}{DB}=\frac{3}{2}$. If the area of $\Delta DEF$ is $81c{m}^2$. The area of $\Delta CFB$ is

In $\Delta ABC,AB=12cm,\angle A={45}^{\circ },\angle B={30}^{\circ }.$ Then the area of the triangle ABC is

Which of the following represents the radian measure of ${45}^{\circ }$ ?

In $\Delta$ ABC, if D is a point on side AB such that $\frac{AB}{AD}=3$. Find $\frac{AD}{DB}$.

Which among the following are classifications of triangular matrices?

A bag has white ,red, and black balls only . A ball is drawn at random from the bag . If the probability of getting a white ball is 3/18 & that of black ball is 2/5 then find the probability of getting red ball. If bag contains 20 black balls then find total number of balls in bag.

What is the diffence between Euclid's division lemma and Euclid's division Algorithm? With an example.

Draw a histogram for the marks of students given below:

$\begin{array}{cccccc}Marks:& 0-10& 10-30& 30-45& 45-50& 50-60\\ No.ofstudents& 8& 32& 18& 10& 6\end{array}$

Shikha buys shares at the par value of Rs 20 in a company, paying $12\%$ dividend. Find the number of shares bought by her, if she receives an annual income of Rs 5760.

The fourth proportional to 5, 8, 15 is ____________

If one root of the equation 4x²− 2x + (λ−4) = 0 be the reciprocal of the other, then find the value of λ .

Is the answer: 8

The term "Quadri" means "four". For example quadrilateral which has four sides. But quadratic equations denotes equation with highest power of two. -- Explain why?

Statements

Some cups are plates.

Some plates are jugs.

Conclusions

I. Some cups are jugs.

II. All cups are jugs.

In the given figure ∠ABC=∠BDC=90^o each. Choose the correct similarity from the given choices.

Sides of two similar triangles are in the ratio 4: 9. What is the ratio of the area of these triangles?

Median of the data represented below is

A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. The probability that it bears a two digit number is:

In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If $\angle$ APQ = ${58}^o$ then the measure of $\angle$ PQB is

(a) ${32}^o$ (b) ${58}^o$ (c) ${122}^o$ (d) ${132}^o$

In ∆ ABC, AB = 12cm, / B = 58^o, the perpendicular from A to BC meets it at D. The bisector of /ABC meets AD at E. Calculate correct to one decimal place,

Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

The line 3 + 4y = 12 is cut by the x – axis & y – axis at points A & B respectively. Find co-ordinates of the point which divides AB in the ratio 2 : 3

A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides (Fig). Find the radius of the inscribed circle and the area of the shaded part.

In Fig, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. $(Use\pi =3.14)$

In $\Delta ABC$, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4 = 3.2 cm, DE= 2cm and BC= 5cm, find BD and CE.

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:
$\begin{array}{cccccccccc}1& 6& 2& 3& 5& 12& 5& 8& 4& 8\\ 10& 3& 4& 12& 2& 8& 15& 1& 17& 6\\ 3& 2& 8& 5& 9& 6& 8& 7& 14& 12\end{array}$
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5- 10. [2 MARKS]

a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then, the least prime factor of (a + b) is

(a) 2 (b) 3 (c) 5 (d) 8

Question 24

If a and b are two integers, then which of the following may not be an integer?

(a) $a+b$
(b) $a-b$
(c) $a\times b$
(d) $a÷b$

Solve each of the following quadratic equations:
$\frac{a}{(x-b)}+\frac{b}{(x-a)}=2,x\ne b,a$

In a $△ABC,\angle A=x^{\circ },\angle B=(3x-2{)}^{\circ },\angle C=y^{\circ }and\angle C-\angle B=9^{\circ }$.Find the three angles.