NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.5
Page No 322:
Question 1:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7634/NCERT_Solution_Math_Chapter_7_final_html_m55126bc.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7634/NCERT_Solution_Math_Chapter_7_final_html_mdc04adc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7634/NCERT_Solution_Math_Chapter_7_final_html_mdc04adc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7634/NCERT_Solution_Math_Chapter_7_final_html_m16112759.gif)
Equating the coefficients of x and constant term, we obtain
A + B = 1
2A + B = 0
On solving, we obtain
A = −1 and B = 2
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7634/NCERT_Solution_Math_Chapter_7_final_html_m4848e6b0.gif)
Question 2:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7636/NCERT_Solution_Math_Chapter_7_final_html_m68b00263.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7636/NCERT_Solution_Math_Chapter_7_final_html_m28ec0239.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7636/NCERT_Solution_Math_Chapter_7_final_html_m28ec0239.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7636/NCERT_Solution_Math_Chapter_7_final_html_m28783f7d.gif)
Equating the coefficients of x and constant term, we obtain
A + B = 0
−3A + 3B = 1
On solving, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7636/NCERT_Solution_Math_Chapter_7_final_html_535f7aa7.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7636/NCERT_Solution_Math_Chapter_7_final_html_m3d20aa7e.gif)
Question 3:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7637/NCERT_Solution_Math_Chapter_7_final_html_47ceee9b.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7637/NCERT_Solution_Math_Chapter_7_final_html_m4f1e46cd.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7637/NCERT_Solution_Math_Chapter_7_final_html_m4f1e46cd.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7637/NCERT_Solution_Math_Chapter_7_final_html_26acb356.gif)
Substituting x = 1, 2, and 3 respectively in equation (1), we obtain
A = 1, B = −5, and C = 4
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7637/NCERT_Solution_Math_Chapter_7_final_html_m4450a170.gif)
Question 4:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7638/NCERT_Solution_Math_Chapter_7_final_html_m604be94a.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7638/NCERT_Solution_Math_Chapter_7_final_html_71020d43.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7638/NCERT_Solution_Math_Chapter_7_final_html_71020d43.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7638/NCERT_Solution_Math_Chapter_7_final_html_m1762d17b.gif)
Substituting x = 1, 2, and 3 respectively in equation (1), we obtain ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7638/NCERT_Solution_Math_Chapter_7_final_html_1d01d669.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7638/NCERT_Solution_Math_Chapter_7_final_html_1d01d669.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7638/NCERT_Solution_Math_Chapter_7_final_html_m3e97765a.gif)
Question 5:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7640/NCERT_Solution_Math_Chapter_7_final_html_67c72223.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7640/NCERT_Solution_Math_Chapter_7_final_html_md82450c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7640/NCERT_Solution_Math_Chapter_7_final_html_md82450c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7640/NCERT_Solution_Math_Chapter_7_final_html_51425d46.gif)
Substituting x = −1 and −2 in equation (1), we obtain
A = −2 and B = 4
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7640/NCERT_Solution_Math_Chapter_7_final_html_44d773ed.gif)
Question 6:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_m283b87e2.gif)
Answer:
It can be seen that the given integrand is not a proper fraction.
Therefore, on dividing (1 − x2) by x(1 − 2x), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_m6d6cb64.gif)
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_37abe9b6.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_37abe9b6.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_7abf94a2.gif)
Substituting x = 0 and
in equation (1), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_m5a4d85ce.gif)
A = 2 and B = 3
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_m633e2bc7.gif)
Substituting in equation (1), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7643/NCERT_Solution_Math_Chapter_7_final_html_m5ef621d.gif)
Question 7:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7646/NCERT_Solution_Math_Chapter_7_final_html_4c300254.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7646/NCERT_Solution_Math_Chapter_7_final_html_48d3a42d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7646/NCERT_Solution_Math_Chapter_7_final_html_48d3a42d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7646/NCERT_Solution_Math_Chapter_7_final_html_m4f316a86.gif)
Equating the coefficients of x2, x, and constant term, we obtain
A + C = 0
−A + B = 1
−B + C = 0
On solving these equations, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7646/NCERT_Solution_Math_Chapter_7_final_html_1512cd64.gif)
From equation (1), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7646/NCERT_Solution_Math_Chapter_7_final_html_m657b90b0.gif)
Question 8:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7648/NCERT_Solution_Math_Chapter_7_final_html_33a31e6c.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7648/NCERT_Solution_Math_Chapter_7_final_html_m50fcae82.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7648/NCERT_Solution_Math_Chapter_7_final_html_m50fcae82.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7648/NCERT_Solution_Math_Chapter_7_final_html_4f0f5909.gif)
Substituting x = 1, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7648/NCERT_Solution_Math_Chapter_7_final_html_m16a77e49.gif)
Equating the coefficients of x2 and constant term, we obtain
A + C = 0
−2A + 2B + C = 0
On solving, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7648/NCERT_Solution_Math_Chapter_7_final_html_m620277b2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7648/NCERT_Solution_Math_Chapter_7_final_html_58e6a15b.gif)
Question 9:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7649/NCERT_Solution_Math_Chapter_7_final_html_15b962ca.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7649/NCERT_Solution_Math_Chapter_7_final_html_4a16e570.gif)
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7649/NCERT_Solution_Math_Chapter_7_final_html_33f40317.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7649/NCERT_Solution_Math_Chapter_7_final_html_33f40317.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7649/NCERT_Solution_Math_Chapter_7_final_html_m7cd0d550.gif)
Substituting x = 1 in equation (1), we obtain
B = 4
Equating the coefficients of x2 and x, we obtain
A + C = 0
B − 2C = 3
On solving, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7649/NCERT_Solution_Math_Chapter_7_final_html_m643a66d1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7649/NCERT_Solution_Math_Chapter_7_final_html_m4e34711f.gif)
Question 10:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7651/NCERT_Solution_Math_Chapter_7_final_html_7dfa52ef.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7651/NCERT_Solution_Math_Chapter_7_final_html_mcf89333.gif)
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7651/NCERT_Solution_Math_Chapter_7_final_html_3f730617.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7651/NCERT_Solution_Math_Chapter_7_final_html_3f730617.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7651/NCERT_Solution_Math_Chapter_7_final_html_48a2f765.gif)
Equating the coefficients of x2 and x, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7651/NCERT_Solution_Math_Chapter_7_final_html_m4ee3b74.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7651/NCERT_Solution_Math_Chapter_7_final_html_6a680da4.gif)
Question 11:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7653/NCERT_Solution_Math_Chapter_7_final_html_meef6cee.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7653/NCERT_Solution_Math_Chapter_7_final_html_7f58a1eb.gif)
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7653/NCERT_Solution_Math_Chapter_7_final_html_mad7d3e3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7653/NCERT_Solution_Math_Chapter_7_final_html_mad7d3e3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7653/NCERT_Solution_Math_Chapter_7_final_html_m3492ed42.gif)
Substituting x = −1, −2, and 2 respectively in equation (1), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7653/NCERT_Solution_Math_Chapter_7_final_html_5b116a13.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7653/NCERT_Solution_Math_Chapter_7_final_html_m4654c7c5.gif)
Question 12:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7655/NCERT_Solution_Math_Chapter_7_final_html_m7e9bdf6f.gif)
Answer:
It can be seen that the given integrand is not a proper fraction.
Therefore, on dividing (x3 + x + 1) by x2 − 1, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7655/NCERT_Solution_Math_Chapter_7_final_html_m70e87107.gif)
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7655/NCERT_Solution_Math_Chapter_7_final_html_6649a66d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7655/NCERT_Solution_Math_Chapter_7_final_html_6649a66d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7655/NCERT_Solution_Math_Chapter_7_final_html_m3d304e42.gif)
Substituting x = 1 and −1 in equation (1), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7655/NCERT_Solution_Math_Chapter_7_final_html_m117d1cc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7655/NCERT_Solution_Math_Chapter_7_final_html_9b89357.gif)
Question 13:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7657/NCERT_Solution_Math_Chapter_7_final_html_1b0b274d.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7657/NCERT_Solution_Math_Chapter_7_final_html_31515503.gif)
Equating the coefficient of x2, x, and constant term, we obtain
A − B = 0
B − C = 0
A + C = 2
On solving these equations, we obtain
A = 1, B = 1, and C = 1
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7657/NCERT_Solution_Math_Chapter_7_final_html_m6a802ca2.gif)
Question 14:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7659/NCERT_Solution_Math_Chapter_7_final_html_1d0293db.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7659/NCERT_Solution_Math_Chapter_7_final_html_m151d55ff.gif)
Equating the coefficient of x and constant term, we obtain
A = 3
2A + B = −1 ⇒ B = −7
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7659/NCERT_Solution_Math_Chapter_7_final_html_m46af344a.gif)
Question 15:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7662/NCERT_Solution_Math_Chapter_7_final_html_m63e2a732.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7662/NCERT_Solution_Math_Chapter_7_final_html_m23dc4fc1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7662/NCERT_Solution_Math_Chapter_7_final_html_1b491979.gif)
Equating the coefficient of x3, x2, x, and constant term, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7662/NCERT_Solution_Math_Chapter_7_final_html_m712c361.gif)
On solving these equations, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7662/NCERT_Solution_Math_Chapter_7_final_html_m4d8f1b57.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7662/NCERT_Solution_Math_Chapter_7_final_html_a36f335.gif)
Question 16:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7663/NCERT_Solution_Math_Chapter_7_final_html_m5f37d30f.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7663/NCERT_Solution_Math_Chapter_7_final_html_m5f37d30f.gif)
Multiplying numerator and denominator by xn − 1, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7663/NCERT_Solution_Math_Chapter_7_final_html_m202e0f7f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7663/NCERT_Solution_Math_Chapter_7_final_html_m25513d6a.gif)
Substituting t = 0, −1 in equation (1), we obtain
A = 1 and B = −1
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7663/NCERT_Solution_Math_Chapter_7_final_html_m1437c43a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7663/NCERT_Solution_Math_Chapter_7_final_html_m3402fc01.gif)
Question 17:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7665/NCERT_Solution_Math_Chapter_7_final_html_6343aea2.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7665/NCERT_Solution_Math_Chapter_7_final_html_40e59867.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7665/NCERT_Solution_Math_Chapter_7_final_html_1c3aabf6.gif)
Substituting t = 2 and then t = 1 in equation (1), we obtain
A = 1 and B = −1
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7665/NCERT_Solution_Math_Chapter_7_final_html_1bd280c7.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7665/NCERT_Solution_Math_Chapter_7_final_html_m62760a7e.gif)
Page No 323:
Question 18:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7668/NCERT_Solution_Math_Chapter_7_final_html_63cc9e04.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7668/NCERT_Solution_Math_Chapter_7_final_html_67db95a0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7668/NCERT_Solution_Math_Chapter_7_final_html_14356613.gif)
Equating the coefficients of x3, x2, x, and constant term, we obtain
A + C = 0
B + D = 4
4A + 3C = 0
4B + 3D = 10
On solving these equations, we obtain
A = 0, B = −2, C = 0, and D = 6
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7668/NCERT_Solution_Math_Chapter_7_final_html_473e50ca.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7668/NCERT_Solution_Math_Chapter_7_final_html_591d2419.gif)
Question 19:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7669/NCERT_Solution_Math_Chapter_7_final_html_29c714c8.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7669/NCERT_Solution_Math_Chapter_7_final_html_29c714c8.gif)
Let x2 = t ⇒ 2x dx = dt
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7669/NCERT_Solution_Math_Chapter_7_final_html_709f9dff.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7669/NCERT_Solution_Math_Chapter_7_final_html_m740aa2df.gif)
Substituting t = −3 and t = −1 in equation (1), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7669/NCERT_Solution_Math_Chapter_7_final_html_693a6469.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7669/NCERT_Solution_Math_Chapter_7_final_html_m68da9ac5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7669/NCERT_Solution_Math_Chapter_7_final_html_2c43a007.gif)
Question 20:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7671/NCERT_Solution_Math_Chapter_7_final_html_12c7d30a.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7671/NCERT_Solution_Math_Chapter_7_final_html_12c7d30a.gif)
Multiplying numerator and denominator by x3, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7671/NCERT_Solution_Math_Chapter_7_final_html_36624ea7.gif)
Let x4 = t ⇒ 4x3dx = dt
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7671/NCERT_Solution_Math_Chapter_7_final_html_6efe54f8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7671/NCERT_Solution_Math_Chapter_7_final_html_m40c17f5.gif)
Substituting t = 0 and 1 in (1), we obtain
A = −1 and B = 1
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7671/NCERT_Solution_Math_Chapter_7_final_html_5a5b384f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7671/NCERT_Solution_Math_Chapter_7_final_html_m4c782b7a.gif)
Question 21:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7672/NCERT_Solution_Math_Chapter_7_final_html_m15581dd.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7672/NCERT_Solution_Math_Chapter_7_final_html_m15581dd.gif)
Let ex = t ⇒ ex dx = dt
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7672/NCERT_Solution_Math_Chapter_7_final_html_m5058b23.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7672/NCERT_Solution_Math_Chapter_7_final_html_16b2ac81.gif)
Substituting t = 1 and t = 0 in equation (1), we obtain
A = −1 and B = 1
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7672/NCERT_Solution_Math_Chapter_7_final_html_237dc92f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7672/NCERT_Solution_Math_Chapter_7_final_html_m4e47628f.gif)
Question 22:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m3f6b4c23.gif)
A. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_43f7504b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_43f7504b.gif)
B. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m681c71ec.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m681c71ec.gif)
C. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m39ce394b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m39ce394b.gif)
D. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m490a77c6.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m490a77c6.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m1a39d92a.gif)
Substituting x = 1 and 2 in (1), we obtain
A = −1 and B = 2
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7673/NCERT_Solution_Math_Chapter_7_final_html_m1da97f65.gif)
Hence, the correct answer is B.
Question 23:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_3ee528b8.gif)
A. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_35fa78c3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_35fa78c3.gif)
B. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_m7a7a9492.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_m7a7a9492.gif)
C. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_m6b55e11f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_m6b55e11f.gif)
D. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_m48481895.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_m48481895.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_1c4b44d7.gif)
Equating the coefficients of x2, x, and constant term, we obtain
A + B = 0
C = 0
A = 1
On solving these equations, we obtain
A = 1, B = −1, and C = 0
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7674/NCERT_Solution_Math_Chapter_7_final_html_6b082199.gif)
Hence, the correct answer is A.