Haryana Board (HBSE) Class 10 Maths SAT-1 Question Paper 2024 PDF Download. SAT (Students Assessment Test). HBSE Class 10 Mathematics SAT Question Paper 2024. Haryana Board Class 10 Maths Students Assessment Test 2024. HBSE Class 10th Maths SAT 2024 Answer. Haryana Board Class 10 Students Assessment Test. Haryana Board Class 10 Maths SAT Paper 2024 Solution. हरियाणा बोर्ड कक्षा 10 गणित SAT पेपर 2024.
HBSE Class 10 Maths SAT-1 Question Paper 2024 Answer Key
Instructions :
• All questions are compulsory.
• Questions (1-11) carry 1 mark each.
• Questions (12-14) carry 2 marks each.
• Questions (15-17) carry 3 marks each.
• Questions (18-19) carry 5 marks each.
• Question (20) case study, carry 4 marks.
1. निम्नलिखित में से कौन-सी एक अपरिमेय संख्या नहीं है?
Which of the following is not an irrational number ?
(a) 5 + √2
(b) 3 – √3
(c) 2 + √9
(d) 4 – √8
Answer : (c) 2 + √9
2. बहुपद p(x) = ax2 + bx + c के अधिकतम शून्यक होंगे, जहां a ≠ 0.
Polynomial p(x) = ax2 + bx + c, a ≠ 0 has maximum number of zeros.
(a) 1
(b) 2
(c) 3
(d) 4
Answer : (b) 2
3. वर्ग अंतराल 20-60 का वर्ग चिह्न होगा :
The Class Mark of class interval 20-60 will be :
(a) 42
(b) 45
(c) 35
(d) 40
Answer : (d) 40
4. यदि P(E) = 0.03 है, तो P(not E) का मान है :
If P(E) = 0.03, then the value of P(not E) will be :
(a) 0.97
(b) 0.7
(c) 0.03
(d) 0
Answer : (a) 0.97
P(E) + P(not E) = 1
5. यदि 26 और 91 का HCF = 13 है, तो उनका LCM होगा :
If HCF of 26 and 91 is 13, then their LCM is :
(a) 26
(b) 91
(c) 182
(d) 2366
Answer : (c) 182
LCM × HCF = Product of two numbers
6. निम्नलिखित में से कौन सा द्विघात समीकरण है?
Which of the following is a quadratic equation?
(a) (x + 1)2 = 2(x – 3)
(b) (x + 4)3 = 3x(x + 1)
(c) 4x² + 5 = (2x + 7)2
(d) (x – 2)(x + 1) = (x – 1)(x + 3)
Answer : (a) (x + 1)2 = 2(x – 3)
7. एक द्विघात बहुपद ज्ञात कीजिए, जिसके शून्यकों का योग और गुणनफल क्रमशः 3 और 1 है।
Find a quadratic polynomial, whose sum and product of zeroes is 3 and 1 respectively.
Answer : α + β = 3, αβ = 1
Quadratic Polynomial = x2 – (α+β)x + αβ = x2 – 3x + 1
8. प्रथम पाँच प्राकृत संख्याओं का माध्य क्या होगा?
What would be the mean of the first five natural numbers?
Answer : (1+2+3+4+5)/5 = 15/5 = 3
9. ………….. और अपरिमेय संख्याएँ सामूहिक रूप से वास्तविक संख्याएँ बनाती हैं।
…………….. and irrational numbers collectively form real numbers.
Answer : Rational number
10. मूल के निर्देशांक ………… हैं।
Coordinates of origin are ………….
Answer : (0, 0)
11. अभिकथन (A): √5 अपरिमेय संख्या का एक उदाहरण है।
कारण (R) : सभी धनात्मक पूर्णांकों का वर्गमूल अपरिमेय संख्याएँ हैं।
Assertion (A) : √5 is an example of Irrational number.
Reason (R) : The square root of all positive integers are irrational numbers.
Answer : Assertion (A) is true but Reason (R) is false.
12. हल करे : x + y = 14, x – y = 4
Solve: x + y = 14, x – y = 4
Answer : x + y = 14 ………(i)
x – y = 4 ……….(ii)
Adding eqn.(i) and (ii), we get
2x = 18
x = 18/2 = 9
Put x = 9 in eqn.(i), we get
9 + y = 14
y = 14 – 9 = 5
Hence, x = 9 and y = 5
13. k के किस मान के लिए द्विघात समीकरण x2 – kx + 9 = 0 के मूल बराबर हैं?
For what value of k the roots of the quadratic equation x2 – kx + 9 = 0 are equal?
Answer : Here, a = 1, b = –k, c = 9
Discriminant (D) = b2 – 4ac = 0
(–k)2 – 4(1)(9) = 0
k2 – 36 = 0
k2 = 36
k = √36
k = ±6
14. 52 पत्तों की अच्छी तरह से फेटी गई गड्डी में से एक पत्ता निकाला जाता है। प्राप्त करने की प्रायिकता ज्ञात कीजिए :
(i) लाल रंग का बादशाह
(ii) एक फेस कार्ड
One card is drawn from a well shuffled pack of 52 cards. Find the probability of getting :
(i) a king of red colour
(ii) a face card
Answer :
(i) P(E) = 2/52 = 1/26
(ii) P(E) = 12/52 = 3/13
15. दो क्रमागत धनात्मक पूर्णांक ज्ञात कीजिए, जिनके वर्गों का योग 365 है।
Find two consecutive positive integers, sum of whose squares is 365.
Answer : Let two consecutive positive integers are x and x + 1.
ATQ,
x2 + (x + 1)2 = 365
x2 + x2 + 2x + 1 – 365 = 0
2x2 + 2x – 364 = 0
x2 + x – 182 = 0 (Dividing by 2 on both sides)
x2 + 14x – 13x – 182 = 0
x(x + 14) – 13(x + 14) = 0
(x + 14)(x – 13) = 0
x + 14 = 0 or x – 13 = 0
x = –14 or x = 13
But x = –14 is not possible.
Take x = 13, then x + 1 = 13 + 1 = 14
Hence, the required consecutive positive integers are 13 and 14.
16. सिद्ध कीजिए कि √5 एक अपरिमेय संख्या है।
Prove that √5 is an irrational number.
Answer : Let us assume that √5 is a rational number.
Now, √5 = p/q where p and q are co-prime integers and q ≠ 0
p = √5q
Squaring both sides, we get
p2 = 5q2 ……..(i)
5 divides p2 then 5 also divides p
Put, p = 5m in eqn.(i),
(5m)2 = 5q2
25m2 = 5q2
5m2 = q2
5 divides q2 then 5 also divides q
Hence p, q have a common factor is 5 . This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
Hence √5 is an irrational number.
17. द्विघात बहुपद x2 – 9x + 20 के शून्यक ज्ञात करें और शून्य तथा गुणांक के बीच संबंध सत्यापित करें।
Find the zeros of the quadratic polynomial x2 – 9x + 20 and verify the relationship between zeros and coefficients.
Answer : Here a = 1, b = –9, c = 20
x2 – 9x + 20 = 0
x2 – 5x – 4x + 20 = 0
x(x – 5) – 4(x – 5) = 0
(x – 5)(x – 4) = 0
x – 5 = 0 or x – 4 = 0
x = 5, x = 4
so, α = 5 and β = 4
α + β = 5 + 4 = 9 = –b/a = –(–9)/1 = 9
αβ = 5 × 4 = 20 = c/a = 20/1 = 20
Thus, the basic relationship is verified.
18. यदि हम अंश में 1 जोड़ते हैं और हर में से 1 घटाते हैं, तो भिन्न घटकर 1 हो जाती है। यदि हम हर में केवल 1 जोड़ते हैं तो यह 1/2 हो जाता है। भिन्न ज्ञात कीजिए.
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. Find the fraction.
Answer : Let Numerator = x and Denominator = y
Fraction = x/y
ATQ, (x+1)/(y–1) = 1
x + 1 = y – 1
x – y + 2 = 0 ……….(i)
ATQ, x/(y+1) = 1/2
2(x) = y + 1
2x – y – 1 = 0 ……….(ii)
Subtract eqn.(i) from eqn.(ii), we get
x = 3
Put x = 3 in eqn.(i),
3 – y + 2 = 0
5 – y = 0
y = 5
so, Fraction = x/y = 3/5
19. पाँच वर्ष पहले, नूरी की उम्र सोनू से तीन गुना थी। दस साल बाद, नूरी की उम्र सोनू से दोगुनी हो जाएगी। नूरी और सोनू की उम्र कितनी है?
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Answer : Let the present age of Nuri = x
And, the present age of Sonu = y
5 years ago, age of Nuri = x – 5
5 years ago, age of Sonu = y – 5
ATQ,
x – 5 = 3(y – 5)
x – 3y = – 10 ……….(i)
10 years later, age of Nuri = x + 10
10 years later, age of Sonu = y + 10
ATQ,
x + 10 = 2(y + 10)
x – 2y = 10 …….(ii)
Subtract eqn.(i) from eqn.(ii), we get
y = 20
Put y = 20 in eqn.(ii),
x – 2(20) = 10
x – 40 = 10
x = 10 + 40 = 50
Hence, the age of Nuri (x) = 50 years and the age of Sonu (y) = 20 years.
20. कताई के खेल में एक तीर को घुमाना होता है जो 1, 2, 3, 4, 5, 6, 7, 8 में से किसी एक संख्या पर इंगित करते हुए रुक जाता है और ये समान रूप से संभावित परिणाम होते हैं। इसकी क्या संभावना है कि यह इंगित करेगा :
(i) 8?
(ii) एक विषम संख्या?
(iii) 2 से बड़ी संख्या?
(iv) 9 से कम संख्या?
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at :
(i) 8?
(ii) an odd number?
(iii) a number greater than 2?
(iv) a number less than 9?
Answer :
(i) P(E) = 1/8
(ii) P(E) = 4/8 = 1/2
(iii) P(E) = 6/8 = 3/4
(iv) P(E) = 8/8 = 1