Find the largest subset of R on which the function :f R → R defined as:
is continuous.
See Answer → If y=em sin -1 X, then show that . Hence using Leibnitz’s formula, find the value of
.
Find the condition for the curves, ax2 by2 =1 and a x2 + b y 2 = 1 intersecting orthogonally.
See Answer →Find the length of the cycloid x = α(θ −sinθ),y = α 1( − cosθ) and show that the line θ = 2π/3 divides it in the ratio 1 : 3.
See Answer →Trace the curve y2 (x+1) = x2 (3-x) clearly stating all the properties used for tracing it.
See Answer →If the revenue function is given by being the input, find the maximum revenue. Also find the revenue function R, if the initial revenue is 0.
Find the area between the curve y2(4-x) = x3 and its asymptote parallel to y-axis.
See Answer →Find all the roots of f(x) = 0.
See Answer →Find the value of αfor which f is continuous at x = − .3
See Answer →For any two sets S and T, show that:
S∪T = (S − T ) ∪ ( S ∩ T) ∪ (T − S).
Depict this situation in the Venn diagram.
See Answer →Find the least value of a² sec² x + b² cosec²x, where a > 0,b>0.
See Answer →Express as a sum of partial fractions.
If z-1+2i|= 4, show that the point z+ i describes a circle. Also draw this circle.
See Answer →The set R of real numbers with the usual addition (+) and usual multiplication (.) is given. Define () on R as:
Find the domain of the function f given by f(x) =
Which of the following statements are true or false? Give reasons for your answer in the form of a short proof or a counter-example, whichever is appropriate.
a) The set {S ∈R :x2 - 3x + 2 = 0}is an infinite set.
b) The greatest interger function is continuous on R.
c)
d) Every integrable function is monotonic.
e) a⊕b = a + b defines a binary operation on Q, the set of rational numbers.
See Answer →निम्नलिखित में से 12 दिए गए शीर्षकों में से किसी भी 10 शीर्षकों का वर्गीकरण ड्यूई दशमलव वर्गीकरण (19वें संस्करण) का उपयोग करके कीजिए।
1. कानूनी पुस्तकालय
2. बौद्ध दर्शन
3 जैन धर्म की पवित्र पुस्तकें
4. पुस्तकालय और सूचना विज्ञान का अध्ययन और शिक्षण
5. दिल्ली में राजनीतिक स्थिति
6. अमेरिका और भारत के बीच विदेशी संबंध
7. डेलनेट (भारत)
8. भारतीय पुस्तकालय संघ, नई दिल्ली
9. पंजाब लोगों की मेहमान नवाजो
10. मैकेनिकल इंजीनियरिंग का शब्दकोश
11. मानव रोग
12. हिंदी लघु कथाएँ