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In the figure, the ratio of AD to DC is 3 to 2. If the area of $\Delta$ ABC is $40c{m}^2$, what is the area of $\Delta BDC$?

Factorise $x^2+\frac{1}{x^2}-11$

Angle formed in minor segment of a circle is

Arrange the following surds in ascending order of their values from top to bottom.

Write $(625{)}^{\frac{-1}{4}}$ in decimal form.

Find the value of k for which (x -1) is a factor of $(2x^3+9x^2+x+k)$.

Find five different solutions of each of the following equations:

(a) 2x - 3y = 6

(b) $\frac{2x}{5}+\frac{3y}{10}=3$

(c) 3y = 4x

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the field. Also, find the cost of ploughing the field at Rs 5 per $m^2,$

How many pairs of adjacent angles are formed.when two lines intersect in a point ?

The total surface area of a solid cylinder is $231c{m}^2$ and its curved surface area is $\frac{2}{3}$ of the total surface area. Find the volume of the cylinder.

If ${27}^x=\frac{9}{3^x}$, find x.

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of $\Delta PQR$ is double the perimeter of $\Delta ABC$.

Given below is frequency distrigution of wages (in Rs ) of 30 workers in certain factory:

$\begin{array}{cccccccc}\text{Wages (in Rs)}& 110-130& 130-150& 150-170& 170-190& 190-210& 210-230& 230-250\\ \text{No.of workers}& 3& 4& 5& 6& 5& 4& 3\end{array}$

A worker is selected at random. Find the probability that his wages are:

(i) less than $Rs.150$ (ii) at least $Rs.210$ (iii) more than or equal to $150$ but less than $Rs.210$.

Construct a right triangle ABC whose base BC is 6 cm and the sum of hypotenuse AC and other side AB is 10 cm.

In $\Delta ABC,$ if bisectors of $\angle ABC$ and $\angle ACB$ intersect at O at angle of ${120}^{\circ }$ , then find the measure of $\angle A.$

In figure given below, O is the centre of circle and $\angle AQR={35}^{\circ }$ and $\angle PAQ={120}^{\circ }$ then $\angle SPR$ is equal to :

A plane left 30 minutes later than its scheduled time. In order to reach the destination which is 1500 km away on time, it has to increase its speed by 250 km/hr. Find its original speed.

Factorization: $(a+b{)}^2-2(a^2-b^2)+(a-b{)}^2$

Which of the following relations are correct?

2x(a-b) + 3y(5a-5b) + 4z(2b -2a)

In what time will $Rs.1600$ amount to $Rs.1768$ at $6\%$ per annum simple interest?

A, B, C and D are the only possible outcomes of a trial. So if P(A) + P(D) = 0.75, then P(C) + P(B) =

x - y = 0, is a line:

The angles of a triangle are in the ratio 2:3:4.So, the degree measures of the angles are

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A U B ) ?

AB is a chord of a circle. AB divides the circumference of the circle into ____ arcs and the arc with longer length is called ____ and the arc with shorter length is called_____.

If the mean a, b, c, d and e is 28, mean of a, c and e is 24 and mean of b and d is $n^2-2$, then the value of n is $\pm k$, where k is

The value of machinery is Rs.20000. The value is depreciating by 10% every year. What will be the value of the machinery after 3 years?

Meena borrowed ₹ 40,000 at 10 % p.a simple interest. She immediately invested this money at 10 % p.a compounded half- yearly.Calculate Meena's gain in 18 months

Instructions for Ques 21 - Ques 23: Refer the figure below and answer the questions that follow. In the figure, line l is parallel to m

In the figure, the line which is transversal is

A metallic prism of height 35 cm has a base as a right angled triangle. The triangle has a base length of 24cm and altitiude 10cm. It is melted and drawn into a cylindrical wire of radius 0.35 cm. What will be the length of wire drawn in metres?

Find the remainder using the remainder theorem (⁴ - 5³ + ² - 2 + 6) ÷ ( + 4)

A linear polynomial is a polynomial of degree ……….

If the base of a triangle is 24cm and height is 48cm.What will be the area of the triangle in $c{m}^2$?

Factorize the polynomial x⁴ + 3x² + 2

Which of the following statements is incorrect

If x-2 is a factor of ax²-x-6 , so what should be the value of a?

Solutions of the equation 2x + 5y = 0 is:

In the figure, O is the centre of the circle. If $\angle$OBC = 25${}^{\circ }$, then $\angle$BAC in degree is equal to:

In the figure D, E and F are the mid points of sides BC, CA and AB respectively of triangle ABC.

Then

The value of the x and y intercept of the following graph is

If $\frac{5-\sqrt{3}}{2+\sqrt{3}}=x+y\sqrt{3},$ then

If $x=\sqrt{6}+\sqrt{5},$ then $x^2+\frac{1}{x^2}-2=$

If the polynomials $a{x}^3+3x^2$ - 13 and $2x^3$ - 5x + a, when divided by (x-2), leave the same remainders, find the value of a.