10th Maths Model Question Bank: 10-ஆம் வகுப்பு கணக்கில் சதம் சாத்தியம்தான்; எப்படி? இதோ மாதிரி வினாத்தாள்!

10ஆம் வகுப்பு தமிழ், ஆங்கில பாடங்களுக்கான மாதிரி வினாத்தாள் வெளியிடப்பட்டது. இன்று கணிதப் பாடத்துக்கான மாதிரி வினாத்தாளை இந்தக் கட்டுரையில் காணலாம். 

மாணவர்கள் | கோப்புப்படம்

தமிழ்நாடு முழுவதிலும் இருக்கும் அர்ப்பணிப்பு மிக்க அரசுப் பள்ளி ஆசிரியர்களைக் கொண்டு உருவாக்கிய பொதுத் தேர்வுக்கான 10, 12ஆம் வகுப்பு மாதிரி வினாத்தாள் வங்கியை ABP Nadu சார்பில் தினந்தோறும் வெளியிட்டு வருகிறோம். அந்த வகையில் 10ஆம் வகுப்பு தமிழ், ஆங்கில பாடங்களுக்கான மாதிரி வினாத்தாள் வெளியிடப்பட்டது. இன்று கணிதப் பாடத்துக்கான மாதிரி வினாத்தாளை இந்தக் கட்டுரையில் காணலாம். 

STANDARD : 10                               SUBJECT : MATHEMATICS 
TIME : 3 Hours                                 MARKS : 100

 

                                 PART – I
Note: (i) Answer all the 14 questions.
(ii) Choose the most suitable answer from the given four alternatives and write the 
option code with the corresponding answer. (14 x 1 = 14)
1) If  AXB  = 6 and  A= {1, 3} then, n(B)
is 
(A) 1 (B) 2 (C) 3 (D) 6 

2) If the ordered pairs (a + 2, 4) and  (5, 2a +b) are equal then (a , b) is 
(A) 2, −2 (B) 5, 1 (C) 2, 3 (D) 3, −2

3)The least number that is divisible by all the numbers from 1to 10 (both inclusive) is
(A) 2025 (B) 2520 (C) 5025 (D) 5220

4) Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the  possible reminders are 
(A) 0, 1, 8 (B) 1, 4, 8 (C) 0, 1, 3 (D) 1, 3, 5 

5) Graph of a linear poynomial is
(A)Parabola (B)Hyperbola (C)circle (D) straight line

6) Transpose of a column matrix is
(A) column matrix (B) row matrix
 (C) unit matrix (D) diagonal matrix

7)The two tangents from external points P to a circle with center at O are PA and PB. If angle APB=70° then the value of angle AOB is
(A) 120° (B)130°  (C) 100° (D)110°

8) A tangent is perpendicular to the radius at the

(A)center (B) chord (C) point of contact (D)infinity

9)The area of triangle formed by the points (-5,0)(0,-5) and (5,0) is

(A)0.sq.units(B) 5 sq.units (C) 25 sq.units (D)none of these

10) If the ratio of the height of a tower and the length if its shadow is √3:1, then the angle of elevation of the sun has measure

(A) 90°(B)60° (C)45° (D)30°

11) A shuttle cock used for playing badminton has the shape of the combination of
(A)frustum of a cone and a hemisphere  (B) a cylinder and a sphere (C)a sphere and a cone (D) a hemisphere and a cone

12)The range of the data 8, 8, 8, 8, 8.....8 is
(A) 8 (B) 3 (C) 1 (D) 0

13)The standard deviation of a data is 3.If each value is multiplied by 5 then the new variance is

(A)15 (B)225 (C) 3 (D) 5

14)If (5,7) (3,p) and (6,6) are collinear, then the value of p is (A)9 (B) 12 (C)3 (D) 6.

PART – II
Note: (i) Answer only 10 questions.
(ii) Question Number 28 is compulsory. 
(10 x 2 = 20)

15) If 𝐵 × 𝐴 = {(−2,3), (−2,4), (0,3), (0,4)(3,3), (3,4)} then find A and B. 
16) A Relation R is given by the set
 {(𝑥, 𝑦) / 𝑦 = 𝑥 + 3, 𝑥 ∈ {0,1,2,3,4,5}}. Determine its domain and range.
17) A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over. 
18) Which term of the A.P 21, 18, 15, … is −81?19) Find the square root of the expression 
 256(x – a)⁸ (x – b)⁴ (x – c)¹⁶ (x – d)²⁰
20) Determine the nature of roots for the following quadratic equations x² − x − 20 = 0.
21) In ∆ABC, D and E are points on the sides AB and AC respectively. If AB = 12 cm, AD = 8 cm, AE=12 cm and AC = 18 cm. Show that DE | | BC 
22) Find the area of the triangle formed by the points (–10, – 4), (–8,–1) and (–3, –5) 
23) Find the slope of a line joining the given points (−6, 1) and (– 3, 2)
24) A kite is flying at a height of 75 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
25)The volume of a solid right circular cone is 11088 cm³. If its height is 24 cm then find the radius of the cone
26) Two coins are tossed together. What is the probability of getting different faces on the coins? 
27) What is the probability that a leap year selected at random will contain 53 saturdays. 
28)From the figure, AD is the bisector of ∠𝐀. If BD=4 cm,  DC=3 cm and AB= 6 cm, find AC. 

Part -- C

Note: (i) Answer only 10 questions.
(ii) Question Number 42 is compulsory.  (10 x 5 = 50)

29) Given A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4} and D = {1, 3, 5}, check if 
(A ∩ C) × (B ∩ D) = (A × B) ∩ (C × D) is true ? 
30) Represent each of the given relations by (a) an arrow diagram, (b) a graph and (c) a set in roster form, wherever possible. 
{(x, y) | y = x + 3, x, y are natural numbers
x,y< 10} 
31) Find the HCF of 396, 504, 636. 
32) The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms. 
33) Is it possible to design a rectangular park of perimeter 320 m and area 4800 m² ? If so find its length and breadth. 
34) Find the values of m and n if the following expression is a perfect square.
 x⁴ – 8x³ + mx² + nx + 16. 
35) ABCD is a quadrilateral in which AB = AD, the bisector of ∠BAC and ∠CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF | | BD. 
36) State and prove Pythagoras theorem. 
37) Find the area of the quadrilateral whose vertices are (– 4, – 2), (– 3, −5), (3, – 2) and (2, 3)
38) From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be 30° and 60°. If the height of the lighthouse is h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is 4ℎ/√3
39) From the top of a 12 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower. 
40) The frustum shaped outer portion of the table lamp has to be painted including the top part. Find the total cost of painting the lamp if the cost of painting 1sq.cm is Rs.2. 
41) From a well shuffled pack of 52 cards, one card is drawn at random. Find the probability of getting (i) red card (ii) heart card (iii) red king (iv) face card (v) number card
42) If 𝛼, 𝛽 and are the roots of the equation 3𝑥²− 4𝑥 + 1 = 0 , form a quadratic equation whose roots are  𝛼²/𝛽 and 𝛽² /𝛼.

Part --IV                           2x8=16

43) (a) Take a point 11cm away from the centre of a circle of radius 4cm, and draw two tangents to the circle from the points. Measure their lengths  (or)
(b) Construct a triangle similar to a given triangle PQR with its sides equal to 
3/5 of the corresponding sides of 
 the triangle PQR (scale factor 3/5 < 1) 

44) (a) Draw the graph of 𝑦 = 𝑥²+ 3𝑥 − 4 and hence use it to solve 𝑥²+ 3𝑥 − 4 = 0. (or)
(b) Draw the graph of xy=24. From the graph find the value of (i) x when y=6 (ii) y when
 x=2

மாதிரி வினாத்தாள் உருவாக்கம்

- ஆசிரியர் பத்மாவதி (A3 குழு), 

ஏ.ஜே.எஸ். நிதி மேல்நிலைப் பள்ளி, 
ஆலந்தூர், சென்னை.

இதையும் வாசிக்கலாம்: 10th Tamil Question Bank: 10ஆம் வகுப்பு தமிழ் பாடத்தில் எளிதாக சதம் அடிக்கலாம்; மாதிரி வினாத்தாள் இதோ! https://tamil.abplive.com/education/tn-10th-tamil-question-bank-with-answers-2023-tamil-nadu-sslc-important-questions-tamil-subject-101574