Free Printable Test - 2_B.A./B.Sc. 2nd Semester 2021, Dev Samaj College

1.

Name of Student

4 lines

2.

Class of Student

a)

B.A. 2nd Semester (ARTS)

b)

B.Sc. 2nd Semester (NON - MEDICAL)

c)

B.Sc. 2nd Semester (COMPUTER SCIENCE)

3.

Roll No. of Student

4 lines

4.

Mark your Attendance

a)

Present

b)

Absent

5.

A reduction formula for an integral is a formula which connects an integral with another integral of the same type but of lower degree.

a)

True

b)

False

6.

Reduction formula for $I_n=\int x^{n\ }\ e^{ax\ }\ dx$

a)

$I_n=\frac{x^ne^{ax}}{a}+\frac{n}{a}\ I_{n-1}$

b)

$I_n=\frac{x^ne^{ax}}{a}-\frac{n}{a}\ I_{n-1}$

c)

$I_n=\frac{x^ne^{ax}}{a^2}-\frac{n}{a}\ I_{n-1}$

d)

$I_n=\frac{x^ne^{ax}}{a}-\frac{n}{a^2}\ I_{n-1}$

7.

Reduction Formula for $I_{m,\ n}=\int x^m\ \left(\log\ x\right)^n\ \ dx$

a)

$I_{m,\ n}=\frac{x^{m+1}\left(\log\ x\right)^n}{m+1}+\frac{n}{m+1}\ I_{m,\ n-1}$

b)

$I_{m,\ n}=\frac{x^m\left(\log\ x\right)^n}{m+1}-\frac{n}{m+1}\ I_{m,\ n-1}$

c)

$I_{m,\ n}=\frac{x^{m+1}\left(\log\ x\right)^n}{m+1}-\frac{n}{m+1}\ I_{m,\ n-1}$

d)

$I_{m,\ n}=\frac{x^{m+1}\left(\log\ x\right)^n}{m+1}-\frac{n}{m}\ I_{m,\ n-1}$

8.

$\ Evaluate\ \ \int_0^{\frac{\pi}{2}}\sin^7x\ \ dx$

a)

$\frac{16}{34}$

b)

$\frac{16}{37}$

c)

$\frac{16}{39}$

d)

$\frac{16}{35}$

9.

$\ Evaluate\ \ \int_0^{\frac{\pi}{10}}\sin^85x\ \ dx$

a)

$\frac{7\pi}{256}$

b)

$\frac{7\pi}{255}$

c)

$\frac{7\pi}{254}$

d)

$\frac{9\pi}{256}$

10.

$Evaluate\ \int_0^{\infty}\frac{dx}{\left(1+x^{2\ }\right)^{\frac{7}{2}}}$

a)

$\frac{8}{13}$

b)

$\frac{7}{15}$

c)

$\frac{8}{5}$

d)

$\frac{8}{15}$

11.

$\ Evaluate\ \ \int_0^{\frac{\pi}{2}}\sin^4x\ \cos^6x\ \ dx$

a)

$\frac{3\pi}{513}$

b)

$\frac{3\pi}{515}$

c)

$\frac{3\pi}{512}$

d)

$\frac{3\pi}{511}$

12.

$\ Evaluate\ \ \int_0^{\frac{\pi}{4}}\sin^22x\ \cos^62x\ \ dx$

a)

$\frac{5\pi}{513}$

b)

$\frac{5\pi}{515}$

c)

$\frac{3\pi}{512}$

d)

$\frac{5\pi}{512}$

13.

$Evaluate\ \ \int_0^a\ x^{4\ }\sqrt{a^2-x^2}\ dx$

a)

$\frac{\ \pi a^6}{32}$

b)

$\frac{\ \pi a^6}{31}$

c)

$\frac{\ \pi a^8}{32}$

d)

$\frac{\ \pi a^4}{32}$

14.

$\ \$ $If\ \ I_n=\int_0^{\frac{\pi}{2}}x\ \sin^{n\ }x\ \ dx,\ n>1$ $\ and\ \ \ I_n=\frac{n-1}{n}I_{n-2}+\frac{1}{n^2}.$ $Hence\ evaluate\ \ I_3$

a)

$\frac{7}{8}$

b)

$\frac{7}{19}$

c)

$\frac{7}{10}$

d)

$\frac{7}{9}$

Test - 2_B.A./B.Sc. 2nd Semester 2021, Dev Samaj College

Total questions: 14

Worksheet time: 32mins

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