Find the sum of the 5th roots of unity.
See Answer →Apply De Moivre's theorem to write (√5+i) in the form a + ib, with a, b ∈ R.
See Answer →Obtain the polar and exponential representations of z₁, z₂ and z₁z₂, where z1 = 1/2 - i and z₂ = 3+i
See Answer →Express z = 2/-4-i in standard (algebraic) form. Further, give an Argand diagram in which z, Z and -z are plotted.
See Answer →Find x and y, given that (5x + y, 3x - y) = (2, 2x)∈QxQ.
See Answer →Draw a Venn diagram of sets A, B and C where A⊆B, A∩C, BOC≠ φ.B, ∩ C = φ. What is the universal set you have chosen? Justify your choice of sets in the diagram.
See Answer →For any two sets A and B, in a universal set U, prove that B ⊆ A ⇔ A U B = A.
See Answer →Which of the following statements are true? Justify your answers. (This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. For instance, to show that '{1, padma, blue} is a set' is true, you need to say that this is true because it is a well-defined collection of 3 objects.)
i) The collection of Venn diagrams is a set.
ii) (A\B) UC=A\(B∩C) for any three sets A, B and C.
iii) If ze R, then |z|=z.
iv) xm + a1 xm -1+ ....am-1 x + am = 0, ai ∈ R∀ i = 1, ..., m, has a root in R only if m is an odd number.
v) x > 0 is necessary for x+3>1.
vi) Any system of three linear equations in two variables has no solution.
vii) If a matrix has n² entries, where n∈ N, then it is a square matrix.
viii) For n > 4, the AM of the first n natural numbers is greater than n +1.
See Answer →एक श्रेणी का पहला और आखरी पद क्रमशः 4 और 76 हैं। श्रेणी का योगफल 1920 है। श्रेणी के पदों की संख्या ज्ञात कीजिए।
See Answer →f(x, y) = ax² + 2hxy+by² के लिए आइलर प्रमेय सत्यापित कीजिए।
See Answer →निम्नलिखित आँकड़ों से X और Y के बीच सहसंबंध गुणांक ज्ञात कीजिए :
| X | Y |
| 1 2 3 4 5 6 7 8 9 | 9 8 10 12 11 13 14 16 15 |
के लिए E(x) और V(x) ज्ञात कीजिए।हल कीजिए: (1-sin x tan y)dx+(cos x sec² y)dy = 0.
See Answer →चार बिंदुओं A, B, C और D के स्थिति सदिश क्रमशः 2 + 4k, 5i+3√3j+4k, - 2√3+ और 2i+k हैं। हैं। दर्शाइए कि AB, CD के समांतर है तथा CD =2/3 AB है।
See Answer →उस समतल की समीकरण ज्ञात कीजिए जो समतलों x+2y+3z = 4 और 4x+3y+2z+1=0 के प्रतिच्छेदन बिंदु से तथा मूल बिंदु से गुजरता है।
See Answer →यदि x+y = 6 है, तो x² + y² का न्यूनतम मान ज्ञात कीजिए।
See Answer →यदि x का p.d.f., f(x) = 2xk,0<x<1 है, तो k का मान और x का S.D. ज्ञात कीजिए।
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