If ABCD be a rhombus, AC is its smallest diagonal and $\angle ABC$ = $60^{0}$ ,find length of a side of the rhombus when AC = 6 cm.1). 6 cm2). 3 cm3). $6\sqrt{2}$ cm4). $3\sqrt{3}$ cm
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1. In the class of 180 students, 50 passed in History and Geography, 50 in History and Sociology, 30 in Sociology and Geography, and 10 students passed in all the three subjects. No students have failed in all the 3 subjects. Find the total number of students who passed in History only, Geography only, and Sociology only.
2. What approximate value should come in place of the question mark (?) in the following questions? You are not expected to calculate the exact value.
3. Find the unit digit of 833933! × 777223! × 838123! × 525111!.
4. The two lines 3x – 8y = 16 and 2x + 4y = 6 intersect at (a, b). Find the value of a2 – 4b2.
5. The unit’s digit is nine times the ten’s digit in a two-digit number. If 72 is added to the number, the digits interchange their places. Find the original number?
6. The sum of the ages of brother and sister at present is 21. Five years ago the product of their ages was 28. What is the age of the brother and the sister?
7. Twice the difference between two numbers is equal to their sum. If one number is 15, find the other number.
8. O is the orthocentre of $\triangle ABC$. Then $\angle BOC+\angle BAC$ is equal to
9. In a three- digit number if the extreme digits are replaced then the number remains the same and the sum of digits is 17 and difference between first and second number is 4. Find the 3-digit number.
10. Given f(x) = 5x3 + 14x2 – 10x + 9. Given the divisor is (x + 1), what should be added or subtracted from f(x) so as to make it exactly divisible by the divisor?
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