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Q. (1–3): In each of the following questions, two equations are given. You have to solve them and give answer.
निम्नलिखित प्रश्नों में दो समीकरण (I) और (II) दिये गये है दोनों समीकरण हल कीजिए और उत्तर दीजिए-
Q.1. I. p2 + 16p + 63 = 0
II. q2
+ 13q + 42 = 0
(1) If p > q (2) If p ≤ q
(3) If p ≥ q
(4) If p < q
(5) If p = q or relationship cannot be established/यदि p = q या सम्बन्ध स्थापित नहीं किया जा सकता है।
Q.2. I. p2 –
12p + 32 = 0 II.
q2 – 7q + 12 = 0
(1) If p > q
(2) If p ≤ q
(3) If p ≥ q
(4) If p < q
(5) If p = q or relationship cannot be established/यदि p = q या सम्बन्ध स्थापित नहीं किया जा सकता है।
(2) If p ≤ q
(3) If p ≥ q
(4) If p < q
(5) If p = q or relationship cannot be established/यदि p = q या सम्बन्ध स्थापित नहीं किया जा सकता है।
Q.3. I. 2p2 + 11p
+ 12 = 0 II. q2 + 4q + 3 = 0
(1) If p > q
(2) If p ≤ q
(3) If p ≥ q
(4) If p < q
(5) If p = q or relationship cannot be established/यदि p = q या सम्बन्ध स्थापित नहीं किया जा सकता है।
(2) If p ≤ q
(3) If p ≥ q
(4) If p < q
(5) If p = q or relationship cannot be established/यदि p = q या सम्बन्ध स्थापित नहीं किया जा सकता है।
Q.4. The length of a room floor exceeds its breadth by 25 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 8 m. The area of the roof is-
कमरे की फर्श की लम्बाई फर्श की चौड़ाई से 25 मी. अधिक है। यदि फर्श की लम्बाई 10 मी. कम कर दी जाये और चौड़ाई 8 मी. बढ़ा दी जाये, तो फर्श का क्षेत्रफल अपरिवर्तित रहता है, छत का क्षेत्रफल है-
(1) 5400 m.2/मी.2
(2) 5600 m.2/मी.2
(3) 4800 m.2/मी.2
(4) 5100 m.2/मी.2
(5) None of these/इनमें से कोई नहीं
Q.5. In how many different arrangements the letters of the word 'UNITED' be arranged so that all the vowels come together?
'UNITED' शब्द के अक्षरों को कितने विभिन्न प्रकार से व्यवस्थित किया जा सकता है ताकि सभी स्वर एक साथ आ जाए?
(1) 120
(2) 360
(3) 720
(4) 240
(5) None of these/इनमें से कोई नहीं
Q.6. By selling an article for Rs.376 losses 20% then what price it should to be sold to earn 20% profit?
एक वस्तु को 376 रु. में बेचने पर 20 % की हानि होती है । 20% लाभ हेतु इसी वस्तु को कितने रु. में बेचना चाहिए?
(1) Rs./रु.564
(2) Rs./रु.364
(3) Rs./रु.570
(4) Rs./रु.580
(5) Rs./रु.576
Q.7. Two trains x and y starts from station A and B towards B and A respectively. After passing each other they take 4 hours 48 minutes and 3 hours 20 minutes to reach B and A respectively. If train x is moving at 60 km/hr. Then find the speed of train y ?
दो रेलगाड़ियों x तथा y दो स्टेशनों A और B से एक दूसरे की तरफ चली। एक दूसरे को पार करने के बाद उन्हें B और A तक पहुँचने में क्रमशः 4 घण्टे 48 मिनट तथा 3 घण्टे 20 मिनट लगे। यदि रेलगाड़ी की गति 60 किमी./घण्टे हो तो रेलगाड़ी y की गति ज्ञात कीजिए ?
(1) 64 km. /hr. / (किमी. /घण्टा)
(2) 48 km. /hr. / (किमी. /घण्टा)
(3) 72 km. /hr. / (किमी. /घण्टा)
(4) 68 km. /hr. / (किमी. /घण्टा)
(5) None of these/इनमें से कोई नहीं
Q.(8–10). What approximate value will come in place of question mark (?) in the following questions?
निम्नलिखित प्रश्नों में प्रश्नचिह्न (?) के स्थान पर आसन्न्तः क्या मान आयेगा ?
Q.8. 34.799% of 4872 + 59.766% of 8005 = ?
(1) 7500
(2) 6500
(3) 5000
(4) 6000
(5) 5800
Q.9. 
(1) 5472
(2) 5276
(3) 5346
(4) 5800
(5) 6000
Q.10. (876.324 × 54.987) – (36.42 × 500.11) = ?
(1) 35000
(2) 25000
(3) 30000
(4) 32000
(5) 24000
ANSWER KEY:
Q1. (2) I. p2
+ 16p + 63 = 0
p2
+ 9p + 7p + 63 = 0p (p + 9) + 7 (p + 9) = 0
(p + 9) (p + 7) = 0
p = – 9, p = – 7
II. q2 + 13q + 42 = 0
q2 + 7q + 6q + 42 = 0
q (q + 7) + 6 (q + 7) = 0
(q + 7) (q + 6) = 0
q = – 7, q = –6
q ≥ p
Q2. (3) I. p2
– 12p + 32 = 0
p2
– 8p – 4p + 32 = 0p (p – 8) – 4 (p – 8) = 0
(p – 8) (p – 4) = 0
p = 8, p = 4
II. q2 – 7q + 12 = 0
q2 – 4q – 3q + 12 = 0
q (q – 4) – 3 (q – 4) = 0
(q – 4) (q – 3) = 0
q = 4, q = 3
p ≥ q
Q3. (5) I. 2p2 + 11p + 12 = 0
2p2 + 8p
+ 3p + 12 = 02p (p + 4) + 3 (p + 4) = 0
(p + 4) (2p + 3) = 0
p = – 4, p = –
II. q2
+ 4q + 3 = 0
q2 + 3q + q + 3 = 0
q (q + 3) + (q + 3) = 0
(q + 3) (q + 1) = 0
q = – 3, q = – 1
Relationship cannot be established/ सम्बन्ध स्थापित नहीं किया जा सकता है।
q2 + 3q + q + 3 = 0
q (q + 3) + (q + 3) = 0
(q + 3) (q + 1) = 0
q = – 3, q = – 1
Relationship cannot be established/ सम्बन्ध स्थापित नहीं किया जा सकता है।
Q4. (4) Let the breadth of floor be b m./माना फर्श की चौड़ाई b मी. है ।
Then, length of the floor be (b + 25) m./तो, फर्श की लम्बाई (b + 25) होगी ।
Area/क्षेत्रफल = (b + 25) × b
According to the question/प्रश्नानुसार,
(b + 15) (b + 8) = (b + 25) × b
b2 + 8b + 15b + 120 = b2 + 25b
2b = 120
b = 60
l = b + 25 ⇒ 60 + 25 ⇒ 85
Area of the roof/छत का क्षेत्रफल = 85×60 = 5100
Q5. (4) Required number of ways/अभीष्ट तरीकों की संख्या = 5! × 2! = 240
Q6. (1) Selling price/विक्रय मूल्य = 
= Rs./रु.564
= Rs./रु.564
Q7. (3) 
According to the question/प्रश्नानुसार,
S2 = 72
Q8. (2) 
1705.2 + 4800 = ?
? = 6505.2
9. Sol. (3) 123×44 = ? + 66
5412– 66 = ?
? = 5346
Q10. (3) 876×55 – 36.4×500 = ?
48180 – 18200
? = 29980 
30000
30000
