दसवी की परीक्षाओं के बाद सवाल खडा उठता है अपने सब्जेक्ट चूस करने का....चाह्हे वो साईंस हो या कामर्स....आर्ट्स हो या हिउमानीटीज.....लक्स ये निर्धारित करें की कोइसा भी विसय चुने,,उसमे बाज़ी मारे.....
खैर...जो भी हो.....कुछ बच्चो ने तो अपनी आई.आई.टी. की प्रिप्रेसन तो नौवी कक्षा से ही सुरवात कर दी होगी.....दो साल की लगातार जी-तोड़ महनत का नतीजा....है...जो हर युवा के सपनो में बस गया है....आई.आई.टी में सेलेक्ट होना...जो की बड़ी ही आत्मसम्मान एवं गौरव की बात है....इसी सुनहरे सपनो को साकार करने के लिए आवस्यक हे...की आप यहाँ प्रतिज्ञा लेंगे की आज से हम निष्ठां एवं इमानदारी से अपनी पढ़ाई करे,,इस ध्येय से की चाहे ये दुनिया इधर की उधर ही क्यों ना हो जाए...हम अपने टेबल कुर्सी से नही हटेंगे,,,और निरंतर अभ्यास करते रहेंगे.....
चलिए बढ़ते हैं हम अपने आई.आई.टी जे.ई.ई सेक्सन की ओर........इसमें कुछ मामूली से सवाल हैं...जिनपर आई.आई.टी. ने १९९२ एवं १९९७ में पूछे गए.....किन्ही भी तीन सवालों को हल करने की कोसिस करें....और चेक करें की आपकी प्रिप्रेसन का लेवल कहा तक पंहुचा हे.....
Passage 1
When heat is added to a gas, the temperature increases and the gas expands. If the gas is in a rigid container, then the volume remains constant and the pressure increases. If the gas in in a container that can expand (for example a cylinder with a vertical piston), then the pressure remains constant but the volume expands.
The amount of energy required to increase the temperature of one mole of gas is called the specific heat; there is a specific heat for constant pressure (Cp) and a specific heat for constant volume ((Cv).
Q. 1 Let X be the energy needed to raise the temperature of 5 moles of nitrogen held at constant pressure by one degree. Let Y be the energy needed to raise 5 moles of carbon monoxide by one degree with the pressure held constant. What is the ratio X:Y?
a) 5:7
b) 1:1
c) 7:5
d) 7:9
Q. 2 The difference Cp - Cv is a constant. This constant is often called R, the universal gas constant. Which of the following is true given the data?
Q. 3 How much energy would be required to heat two moles of methane by one degree if the gas is kept at constant volume?
a) 6.5 calories
b) 8.5 calories
c) 11 calories
d) 13 calories
PASSAGE 2 --
Three metal rods are located relative to each other as shown in the figure where L1 + L2 = L3. Values of density and Young’s modulus for the three materials are:
d1 = 2.7 ´ 103 kgm-3, Y1 = 7 ´ 1010 Nm-2
d2 = 11.3 ´ 103 kgm-3, Y2 = 1.6 ´ 1010 Nm-2
d3 = 8.8 ´ 103 kgm-3, Y3 = 11 ´ 1010 Nm-2
If L3 = 1.5 m, what must be the ratio L1/L2 be if a sound wave is to travel the length of the rods 1 and 2 in the same time required to travel the length of rod 3? If the frequency of the source is 4000hz, determine the phase difference between the wave traveling along rods 1 and 2 and the one traveling along rod 3.
a) For a monoatomic gas, Cp = 3/2 R
b) For a diatomic gas, Cp = 3/2 R
c) For a monoatomic gas, Cv = 3/2 R
d) For a diatomic gas, Cv = 3/2 R
PASSAGE 3 ---
Consider the shown arrangement in which a thin rope ‘A’ with a linear density mA is connected to a thick rope ‘B’ with linear mass density mB. The thick rope passes over a pulley and is connected to a heavy block of mass M. The separation of fixed support S from a pulley is L. A stationary wave is setup in this composite string such that the joint remains a node. Given that mb = 4 kg/m, ma = 0.4 kg/m, M = 1 kg and L = 4l = 1 m. Under these conditions, find:
The least possible frequency of vibration
The total energy of vibration if the amplitude for both the string is A = 1 mm and the string vibrates at the frequency obtained in (a).
Q. 6 Let l, a Î R, find all the set of all values of l for which the set of linear equations has a non-trivial solution.
lx + (sin a) y + (cos a) z = 0
x + (cos a) y + (sin a) z = 0
-x + (sin a) y - (cos a) z = 0
If l = 1, find all values of a.
lx + (sin a) y + (cos a) z = 0
x + (cos a) y + (sin a) z = 0
-x + (sin a) y - (cos a) z = 0
If l = 1, find all values of a.
