Math Chapter Wise

EnglishTGT 2011

Q21.Every bounded sequence has a cluster point, then this theorem is known as:

ACauchy's theorem BWeierstrass theorem CBolzano-Weierstrass theorem DNone of these

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EnglishUP PCS (Pre) 1998

Q22.The sum of the series (()) n 1 1 n n 1 (n 2) ∞ = + + + + ∑ ∑ is:

A1/2 B1/4 C1 log 2 2 − Dlog 2 + 1

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EnglishUP PGT 2021 (GIC) Lecturer Exam 2015

Q23.The sum of the series ∞ 1 1 1 1 - + - +....... 1.2 2.3 3.4 4.5 is:

A1–loge2 B3–loge2–1 C2loge2–1 D2–loge3–1

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EnglishUP PCS (Pre) 1994

Q24.The series 3 4 5 2 is 2 3 4 –

Aconvergent but not absolutely convergent Bdivergent Cabsolutely convergent Doscillates finitely

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EnglishUP PCS (Pre) 1994

Q25.The series n 3 n 1 x n 1 at x 1 is–

Aconvergent Bdivergent Coscillatory Dnone of these

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EnglishUP PCS (Pre) 1994

Q26.The series 2 2 2 1 1 1 1 2 3 4 is–

Adivergent Bconvergent Coscillatory Dnone of these

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EnglishUP PCS (Pre) 1994

Q27.The series x logx + x2 log2x + _ _ _ _ _+ xn log nx + _ _ _ ∞ ∞ ∞ is convergent if –

Ax < 1 Bx ≤ 1 Cx ≥1 DNone of these

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EnglishUP PCS (Pre) 1994

Q28.The series 1 1 1 1 is: 2 3 4

Aconvergent but not absolutely convergent Boscillatory Cdivergent Dabsolutely convergent

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EnglishUP PCS (Pre) 1994

Q29.The series 1 cos is n ∑

Aconvergent Bdivergent Coscillatory Dnone of these

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EnglishUP PCS (Pre) 1995

Q30.The series p n 1 sin n is

AConvergent for all values of p BConvergent for p ≤ 1 and divergent for p ≥1 CConvergent for p > 1 and divergent for p ≤ 1 DDivergent for all values of p

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EnglishUP PCS (Pre) 1995

Q31.The series whose general term (n 1) n is + −

AConvergent BDivergent COscillates finitely DOscillates infinitely

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EnglishUP PCS (Pre) 1995

Q32.The absolutely convergent series is–

An 1 1 1 1 1 1...... (1)... − − + − + − + + − Bn 1 1 1 1 1 (1) 1...... 2 3 4 5 n Cn 1 1 1 1 1 (1) 1...... 2 3 4 5 n Dn 1 2 2 2 2 2 1 1 1 1 (1) 1...... 2 3 4 5 n

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EnglishUP PCS (Pre) 1996

Q33.The infinite series 1 + 2x + 3x2 + 4x3 + …… converges for:

Ax ≥ 1 Bx ≤ 1 C|x| < 1 Dfor negative values of x only

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EnglishUP PCS (Pre) 1999

Q34.The divergent series is:

A1 n n 1 2 1 ∞ = + ∑ B3 n 1 n 4n 2 ∞ = − ∑ Cn 1 1 sin n ∞ = ∑ D2 n 1 1 sin n ∞ = ∑

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EnglishUP PCS (Pre) 1999

Q35.For an infinite series n n 1 u, ∞ = ∑ the true statement is:

An lim u 0 →∞ = is necessary condition but not a sufficient condition for the convergence of the series n u ∑ Bn lim u 0 →∞ = is sufficient condition but not a necessary condition for the convergence of the series n u ∑ Cn lim u →∞ = 0 is necessary and sufficient condition for the convergence of the series n u ∑ Dn lim u →∞ = 0 is neither a necessary condition nor a sufficient condition for the convergence of n u ∑

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EnglishUP PCS (Pre) 2000

Q36.The infinite series 3 3 3 1 1 1 cos1 cos cos cos...... 2 3 4 + + + + + + + + + + + + + + + +

Ais convergent Bis divergent Cis oscillatory Dhas a finite sum

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EnglishUP PCS (Pre) 2000

Q37.Series 3 5 x 1 x 1.3 x...... 1 2 3 2.4 5 + + + + + + + + + + + + is convergent for:

Ax2 = 1 Bx2/< 1 Cx2/> 1 DNone of these

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EnglishUP PCS (Pre) 2000

Q38.The series (()))p 1 n logn ∑ ∑ is:

Aconvergent if p > 0 Bconvergent if p > 1 Cdivergent if p > 1 Dconvergent if 0 < p < 1

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EnglishUP PCS (Pre) 2001

Q39.The series:

A2 n n=1 n=1 π sin and cos are both 2n 2 convergent ∞ ∞ ∑ ∑ B2 n n=1 n=1 π sin and cos are both 2n 2 divergent ∞ ∞ ∑ ∑ C2 n=1 n n=1 π sin is divergent and 2n π cos is convergent 2 ∞ ∑ D2 n=1 π sin is convergent and 2n ∞ ∑ n n=1 π cos is divergent 2 ∞ ∑

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EnglishUP PCS (Pre) 2003

Q40.The series 1 n 2 n is logn

Aconvergent Bdivergent Coscillatory Dnone of the above

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