Question 5

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, – 4) and B (8, 0).

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Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

- Q:-
How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
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A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?

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The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

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The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

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Three coins are tossed. Describe

(i) Two events which are mutually exclusive.

(ii) Three events which are mutually exclusive and exhaustive.

(iii) Two events, which are not mutually exclusive.

(iv) Two events which are mutually exclusive but not exhaustive.

(v) Three events which are mutually exclusive but not exhaustive.

- Q:-
If is the A.M. between

*a*and*b*, then find the value of*n*. - Q:-
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

- Q:-
Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

- Q:-
2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

- NCERT Chapter