10th CBSE Maths APEX
INSTITUTE FOR IIT-JEE / MEDICAL |H.O. -62 Nitikhand-III, Indirapuram; | Contact: 0120-4331180, 9990495952 | Web: www.ape b: www.apexiit.co.in/
sin A 1 + cos A = 2 cosec A. + 1 + cos A sin A cot(90° − θ ) cos ec(90° − θ ). sin θ = sec2θ. 23. Prove that: + tan θ tan(90° − θ ) 22. Prove that:
24. 200 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows. No. of letters 1 – 5 5 – 10 10 – 15 15 – 20 20 – 25 20 60 80 32 8 No. of surnames Find the median. Section D
25. Draw the graph of the pair of equa tions 2x + y = 4 and 2x – y = 4. Write the ver tices of the triangle formed by these lines and the y a xis. Also shade this triangle. 26. The annual incomes of A and B are in the ratio 3 : 4 and their an nual expenditures are in the ratio 5 : 7. If each saves Rs 15 ,000 annually, find their annual in comes. 27. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. 28. State and prove converse of Pythagoras Theorem. 29. Evaluate:
sin 2 41° + sin 2 49° 3 sec 31° − 2 . cos ec59° tan 2 30°
tan A cot A = 1 + sec A cosec A. + 1 − cot A 1 − tan A If cosecθ - sinθ = m and sec θ - cosθ = n, prove that (m2n)2/3 + (mn2)2/3 = 1. Show that the square of any positive integer is of the form 3q or 3q+1 for some integer q. The following distribution gives the production yield per hectare of wheat of 100 farms of a village. Change the distribution to a more than type distribution, and draw its ogive. Production yield 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 80 in kg/hectare No. of farms 2 8 12 24 38 16 If the median of the following data is 525, find the values of x and y if the sum of the frequencies is 100. Class Interval 0 – 100 100 – 200 200 – 300 300 – 400 400 – 500 Frequency 2 5 12 17 x
Mathematics SA – 1 (Aug, 2016)
33.
34.
----------
APEX
Class X
Time allowed: 3 hours : General Instructions
Maximum Marks: 90
(i) All questions questions are compulsory. (ii) The question paper consists of of 34 questions divided into four sections sections A, B, C and D. Section - A comprises of 8 questions of 1 mark each, section - B comprises of 6 questions of 2 marks each, section - C comprises of 10 questions of 3 marks each and section - D comprises 10 questions of 4 marks each. (iii) Question numbers 1 to 8 in section section - A are multiple choice questions questions where you are to select one correct option out of the given four. (iv) (iv) There is no overall choice. However, internal choice have been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the a lternatives in all such questions. calculator is not permitted. permitted. (v) Use of calculator -----------------------------------------------------------------------------------
30. Prove that: 31. 32.
Mega Test – 2
Section
A
B
C
D
Q. No.
1 – 8
9 – 14
15 – 24
25 – 34
Marks
1
2
3
4
----------------------------------------------------------------------------------Section A
1.
Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. The value of x in the factor tree is:
----------
INSTITUTE FOR IIT-JEE / MEDICAL |H.O. -62 Nitikhand-III, Indirapuram; |
(A) 30 APEX
(B) 150
(C) 100
(D) 50
INSTITUTE FOR IIT-JEE / MEDICAL |H.O. -62 Nitikhand-III, Indirap
|
10th CBSE Maths
2.
The sum and the product of the zeroes of a quadratic polynomial are
−
2
10th CBSE Maths
Section C
and 1
2 3. 4.
5.
6.
(A) 2x2 + x + 1 (B) 2x2 – x + 1 (C) 2x2 – x – 1 (D) 2x2 + x – 1 The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0 have: (a) unique solution (b) many solutions (c) no solution (d) exactly two solutions If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively: (a) 3 and 5 (b) 5 and 3 (c) 3 and 1 (d) -1 and -3 If the ratio of the corresponding sides of two similar triangles is 2 : 3, then the ratio of their corresponding altitude is: (a) 3 : 2 (b) 16:81 (c) 4:9 (d) 2:3 If tanA =
5
12
8.
is an irrational number.
2+ 3
16. Show that 4n can never end with the digit zero for any natural number n. 17. If α and β are the zeroes of the polynomial x2 – 5x + 6, then find the polynomial whose zeroes are 1
α
and
1
β
.
y 8 x 3 y 5 = ; + =− 3 3 2 4 2 19. In the given figure, two triangles ABC an d DBC are on the same base BC in which ∠A = ∠D = 90°. If CA and BD meet each other at E, show that AE × CE = BE × DE. 18. Solve for x and y: 4x +
, the value of (sinA + cosA) × secA is:
6
(A)
7.
15. Prove that
respectively, then the polynomial is:
7
(B)
17
(C)
12
(D)
13 12 12 17 (4 tan2A – 4 sec2A) is equal to : (A) –1 (B) – 4 (C) 0 (D) 4 The mean and median of same data are 2 4 and 26 respectively. The value of mode is: (A) 23 (B) 26 (C) 25 (D) 30
20. In the given fig., ABE ≅ ACD. Prove that ADE
ABC
:
Section B
9.
The ages of employees in a factory are as follows. Find the mean age. Age in Years 17 – 23 23 – 29 29 – 35 35 – 41 41 – 47 47 – 53 No. of Employees 2 5 6 4 2 1 10. Divide (2x2 – x – 20) by (x + 3) and verify the result by division algorithm. 11. Form a quadratic polynomial whose one of the zeroes is -15 and sum of the zeroes is 42. 12. In figure below, ABCD is a rectangle. Find the values of x and y.
21. Find the mode of the following data: Marks No. of Students Less than 10 3 Less than 20 8 Less than 30 24 Less than 40 36 Less than 50 49 Less than 60 69 Less than 70 75 Less than 80 80
13. If the areas of two similar triangles are equal, prove that they are congruent. 14. Find the value of sin 60° geometrically. APEX
INSTITUTE FOR IIT-JEE / MEDICAL |H.O. -62 Nitikhand-III, Indirap
|
APEX
INSTITUTE FOR IIT-JEE / MEDICAL |H.O. -62 Nitikhand-III, Indirap
|
