CRPF PUBLIC SCHOOL, ROHINI. EIGHTH INTRA School Mathematics Olympiad 2017 CLASS - XI

Size: px

Start display at page:

Download "CRPF PUBLIC SCHOOL, ROHINI. EIGHTH INTRA School Mathematics Olympiad 2017 CLASS - XI"

Clara Burke
6 years ago
Views:

1 CRPF PUBLIC SCHOOL, ROHINI EIGHTH INTRA School Mathematics Olympiad 7 CLASS - XI Max. Marks: 5 Time: hour 3 minutes General Instructions:. Q- (Section- A) is based on NCERT Textbook. Each MCQ carry mark.. Q-5 (Section -B) is based on logical reasoning. Each MCQ carries marks. 3. Q6- (Section- C) is based on higher order thinking skills (HOTS). Each MCQ carries marks. 4. Q-5 (Section -D) is based on Non-Routine challenging questions. Each question carries 4 marks. 5. THERE IS A NEGATIVE MARKING. 5% marks will be deducted for each wrong answer. 6. Each MCQ question has five choices (A, B, C, D or E). Select the correct answer to each question and darken the corresponding circle in the Answer Sheet provided to you. SECTION A (NCERT BASED). If the system of equations, y 7sin x 3cos x, y 7cos x 3sin x is solved simultaneously for x π then the value of y must be : (A) 4 (B) 5 (C) 5 (D). Solve for x: x x. (A) (-, ) (B) ( -, -) (, ) (C) (, ) (D) (-, -) 3. The number of two digit numbers which leaves a remainder when divided by 4 is: (A) (B) (C) (D) 3 4. The number of the values of x in the interval [,5π] satisfying the equation 3sin x 7sin x is: (A) (B) 5 (C) 6 (D) 5. The value of cos cos cos cos is: (A) (B) (C) 3 (D) - Eighth Intra School Mathematics Olympiad - Class XI Page

6. If cot and lies in second quadrant, then the value of sin cos is: 5 7 (A) 3 7 (B) 3 (C) 7 3 (D) 3 7 7. If x 3, then the value of x 4 4x 8x 35 is: (A) (B) 3 (C) (D) 8.

2 6. If cot and lies in second quadrant, then the value of sin cos is: 5 7 (A) 3 7 (B) 3 (C) 7 3 (D) If x 3, then the value of x 4 4x 8x 35 is: (A) (B) 3 (C) (D) 8. The letters of the M O T H E R are written in all possible orders, and these words are written out as in a dictionary, then the rank of the word M O T H E R is: (A) 6 (B) 6! (C) 39 (D) The altitude of the triangle with vertices A(-4,-3) B(,) C(5,5) are concurrent, the point of concurrence is: (A) (B) (C) (D). The solution of x 3x, where [ ] denotes the greatest integer function is: (A) (, 3) (B) [, 3] (C) (,3] (D) [,3) SECTION B (LOGICAL REASONING). Look at the venn diagram given below. Which of the following statements is true for (A) All honest European swimmers (B) All honest advocates who are not swimmers (C) All non European advocates who are honest swimmers (D) All non Europeans who are honest swimmers Eighth Intra School Mathematics Olympiad - Class XI Page

Select a figure from the options that fits in the given figure to complete its original design. 3. In the addition shown, each of X, Y and Z represents a digit. What is the value of X+Y+Z?

3 Select a figure from the options that fits in the given figure to complete its original design. 3. In the addition shown, each of X, Y and Z represents a digit. What is the value of X+Y+Z? (A) (B) 5 (C) (D) (E) 8 4. Each of the three cards is labeled with three numbers. Which of the following groups of three cards has the properties that the first and second cards have exactly one number in common, the first and third cards have exactly one number in common, and the second and third cards have exactly one number in common? 5. An cockroach has six legs, a squirrel has four legs and a spider has eight legs. At a local zoo, if the total number of legs were counted to be 6, which came from an equal number of each of these animals. How many animals there are in the zoo? (A) 34 (B) 35 (C) (D) 5 Eighth Intra School Mathematics Olympiad - Class XI Page 3

4 SECTION C (HIGHER ORDER THINKING SKILLS) 6. If a be the A.M. between b and c and G.M s are G and G then G is equal to: 3 3 G (A) abc (B) abc (C) 3abc (D) 4abc 7. In the diagram, P lies on y axis Q has coordinates (4, ) and PQ passes through the point R(,4). What is the area of OPQ? (A) 8 (B) (C) 3 (D) 4 (E) 6 8. The value of (A) cos cos84 cos56 cos3 is: (B) (C) - (D) 8 (E). 9. A five digit number is divisible by 3 is to be formed using the numbers,,,3,4 and 5 without repetition. The total number of ways this can be done is: (A) 6 (B) 4 (C) 35 (D) 6 (E) 5. The domain of the function f defined by f ( x) 4 x x is: (A),,4 (B),,4 (C),,4 (D),,4 SECTION D (NON-ROUTINE QUESTIONS). Two lines with slopes 4 and 4 5 intersect at (,). What is the area of the triangle formed by these two lines and the vertical line x 5 (A) 5 (B) (C) 8 (D) (E) 5 Eighth Intra School Mathematics Olympiad - Class XI Page 4

. A point is equidistant from the coordinate axis if the vertical distance from the point to the x axis is equal to the horizontal distance from the point to the y axis.

5 . A point is equidistant from the coordinate axis if the vertical distance from the point to the x axis is equal to the horizontal distance from the point to the y axis. The point of intersection of the vertical line x = a with the line with equation 3x 8y 4 is equidistant from the coordinate axis. what is the sum of all possible values of a? (A) (B) 44 (C) 55 4 (D) 5 (E) 8 3. Determine all pairs (a, b) of real numbers that satisfy the following system of equations: a b 8 and log a log b (A) (C) 8 6, 8 6 (B) 6 8, , (D) 8 6, In the diagram, line segments AC and DF are tangent to the circle at B and E, respectively. Also AF intersects the circle at P and R and intersects BE at Q as shown. If CAF 35, DFA 3 and FPE 5 Determine the measure of PEQ. (A) 3 (B) 65 (C) 3.5 (D) 5 (E) The sum of four different positive integers is. The largest of these four integers is n. The smallest possible value of n is : (A) 6 (B) 5 (C) 8 (D) 7 (E) 94 ****************************************************************************** NOTE: The Solution Key of this paper will be available on School s blog today after 6 pm. The Result will be declared on 3 November 7(Thursday) and will be available on School s blog. Eighth Intra School Mathematics Olympiad - Class XI Page 5

Unit 7 Number System and Bases. 7.1 Number System. 7.2 Binary Numbers. 7.3 Adding and Subtracting Binary Numbers. 7.4 Multiplying Binary Numbers

Contents STRAND B: Number Theory Unit 7 Number System and Bases Student Text Contents Section 7. Number System 7.2 Binary Numbers 7.3 Adding and Subtracting Binary Numbers 7.4 Multiplying Binary Numbers