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Q-1 Find
the H.C.F. of x3 – x2 – x – 15 and x3 – 3x2
– 3x + 9.
x3
– x2 – x – 15 और x3
– 3x2 – 3x + 9 का म.स.प. ज्ञात कीजिए।
(A) (x+3)
(B) (x-5)
(C) (x-3)
(D) (x+5)
Q-2 The rate of depreciation of a car is 10% per annum. Its present worth is Rs.81000. What was its worth 2 years ago?
एक कार की अवमूल्यन दर 10% वार्षिक है। इसका वर्तमान मूल्य 81000 रू. है। 2 वर्ष पहले इसका मूल्य क्या था?
(A) 99000
(B) 100000
(C) 112000
(D) 6561
Q-3 A man sold his article a loss of 5%. Had he sold it for Rs.1800 more, he would have made a profit of 4%. Find the cost price of the article.
एक आदमी अपनी वस्तु को 5% हानि पर बेचता है, अगर वह इसे 1800 रू. अधिक में बेचे तो उसे 4% का लाभ प्राप्त होता है। वस्तु का क्रय मूल्य ज्ञात कीजिए।
(A) 20000
(B) 12000
(C) 15000
(D) 17500
Q-4 Seats of Maths, Physics and Chemistry are in the ratio of 5:7:8 respectively. There is a proposal to increase these ratio by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
गणित, भौतिकी और रसायन विज्ञान की सीट क्रमशः 5:7:8 के अनुपात में है। एक प्रस्ताव के अनुसार इनके अनुपात में क्रमशः 40%, 50% और 75% की वृद्धि कर दी जाती है। बढ़ी हुई सीटो का सापेक्षतः अनुपात क्या होगा?
(A) 5:3:2
(B) 3:1:2
(C) 2;4:3
(D) 2:3:4
Q-5 Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.
एक 50 मीटर लम्बे और 44 मीटर चौड़े टैंक में एक 14 सेमी. व्यास वाले पाइप से 5 किमी/घंटा की दर से पानी निकल रहा है। टैंक में पानी का तल 7 सेमी. ऊपर उठने में कितना समय लगेगा?
(A) 1.25 hours/घंटे
(B) 2 hours/घंटे
(C) 1 hours/घंटे
(D) 3 hours/घंटे
Q-6 Two trains of lengths 130 m and 110 m running on parallel tracks, when running in the same direction the faster train crosses the slower one in 20 seconds. When running in opposite direction at same speeds as their earlier speeds they pass each of other completely in 12 seconds. Find the speed of faster train.
130 मी. और 110 मी. लम्बी दो रेलगाड़ी एक समान्तर ट्रैक पर चल रही है। जब ये समान दिशा में चलती है तो तेज गाति वाली रेलगाड़ी धीमी गति वाली रेलगाड़ी को 20 सेकेण्ड में पार करती है। जब ये दोनों अपनी उसी समान चाल से विपरीत दिशा में चलती है तो वे एक दूसरे को 12 सेकेण्ड में पूर्णतया पार करती है। तेज गति वाली रेलगाड़ी की चाल ज्ञात कीजिए।
(A) 15 m/s मी./से.
(B) 16 m/s मी./से.
(C) 12 m/s मी./से.
(D) 30 m/s मी./से.
Q-7 553
+ 173 - 723 + 201960 is equal to :
553
+ 173 - 723 + 201960 किसके बराबर है?
(A) 10
(B) 0
(C) -10
(D) 100
Q-8 If
x = k3 – 3k2 and y = 1 – 3k, then for what value of k,
will be x = y?
यदि x = k3 – 3k2
और y = 1 – 3k, तो k के किस मूल्य के लिए x = y होगा?
(A) 4
(B) 1
(C) 2
(D) 3
Q-9 The
value of sin265o + sin225o + cos235o
+ cos255o is:
sin265o
+ sin225o + cos235o + cos255o
का
मान हैः
(A) 2
(B) 1
(C) 4
(D) 3
Q-10 If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be.
यदि दो शंकुओं के आयतनों का अनुपात 2 : 3 है और उनके आधारों की त्रिज्याओं का अनुपात 1 : 2 है, तो उनकी ऊँचाईयों का अनुपात होगा:
(A) 5:2
(B) 7:5
(C) 8:5
(D) 8:3
ANSWER KEY:-
Q1-(C) Let/माना P (x) = x3 – x2 – x -
15
= x2 (x – 3) + 2x (x – 3) +5 (x – 3)
= (x – 3) (x2 + 2x + 5)
= (x – 3) (x2 + 2x + 5)
And/और Q (x) = x3 - 3x2 – 3x +
9
= x2 (x – 3) – 3 (x – 3) = (x – 3) (x2 – 3)
Required H.C.F/ अभीष्ट म.स.प. = (x – 3)
= x2 (x – 3) – 3 (x – 3) = (x – 3) (x2 – 3)
Required H.C.F/ अभीष्ट म.स.प. = (x – 3)
Q2-(B)
Q3-(A)
Q4-(D)
Q5-(B)
Q6-(B)
Q7-(B) 553 + 173 - 723 + 201960
55 + 17 - 72 = 0
553 + 173 - 723 + 201960 = 0
553 + 173 - 723 + 201960 = 0
Q8-(B) x = k3 – 3k2,
y = 1- 3k
k3 – 3k2 = 1 – 3k
k3 – 3k2 + 3k – 1 = 0
k3 – 1 – 3k(k – 1) = 0
(k – 1)3 = 0
k = 1
k3 – 3k2 + 3k – 1 = 0
k3 – 1 – 3k(k – 1) = 0
(k – 1)3 = 0
k = 1
Q9-(A) sin265o + sin225o
+ cos235o + cos255o
= sin265o + sin2(90o-65o)
+ cos2(90o- 55o) + cos255o= sin265o + cos265o + sin255o + cos255o
= 1+1
= 2
Q10-(D)