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Two cars start together in same direction from the same place the first goes with uniform speed of 10km/h . The second goes at a speed of 8km/h n the first hour and increases the speed by by 1/2km/h in each succeeding hour . After how many hours will the second car overtake the first ? If both cars go non - stop.

Under which condition can a secant to a circle be called a tangent?

In the given figure, the length of $BC$ is

(a) $7cm$ (b) $10cm$ (c) $14cm$ (d) $15cm$

Lateral surface area of a cylinder is 1056 sq. cm and radius is 14 cm. Find the height of the cylinder.

1. 3

A ${60}^{\circ }$ angle is constructed with arc radius as 4 cm. Find the area of the $△BOC$.

300 chocolates are distributed equally among a certain number of students. Had there been 10 more students, each would have received one chocolate less. The number of students is ___ .

Classify the following equations into pure and adfected quadratic equation.

(1) x² + 2 = 6

(2) a² + 3 = 2a

(3) p (p − 3) = 1

(4) 2m² = 72

(5) k² − k = 0

(6)

Record the following transactions in the Journal of Shyam Sunder & Sons :

Question 4 (vii)

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(vii) 0, - 4, - 8, - 12 …

A toy is in the form of a cone of radius 3.5 cm mounted on a hemipshere of same radius.The total height of the toy is 15.5 cm.Find the total surface of the toy.

A square matrix $A$ is said to be orthogonal if $A^{\prime }A=A{A}^{\prime }=I_n,A^{\prime }$ is transpose of $A.$

If $A$ and $B$ are orthogonal matrices, of the same order, then which one of the following is an orthogonal matrix

Show all the prime factors of 1778700

What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm ?

Solve the following quadratic equation by factorization.
$\frac{a}{x-a}+\frac{b}{x-b}=\frac{2c}{x-c}$

A school has three sections of Class 10. They need to have enough books in the class library so that they can be distributed equally in the three sections . What is the minimum number of books required if the number of students in section A , B and C are 30, 32 and 36 respectively?

Prove that √x + √y is irrational, where x and y are primes.

Show that N=1010101...101 is not a prime except when N is 101.

Based on the statements given below, choose the correct option.
S1 : Total surface area of a cuboid is the sum of areas of four of its faces, leaving the top and bottom faces.
S2 : Lateral surface area of a cuboid is the sum of areas of four of its faces, leaving the top and bottom faces.
S3 : Area of a face of a cuboid is of the form $xy,$ where $x$ and $y$ are the length and breadth of that face respectively.

Dinesh bought an article of Rs. 374, which include a discount of 15% on the marked price and a sales tax of 10% on the reduced price. Find the marked price on the article.