Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

41. Without expanding, prove that

open vertical bar table row 9 cell space space space space 9 end cell cell space space 12 end cell row 1 cell space space minus 3 end cell cell space space minus 4 end cell row 1 cell space space space space 9 end cell cell space space 12 end cell end table close vertical bar space equals 0 space

72 Views

42. Without expanding, prove that the following determinants vanish :

open vertical bar table row 5 cell space space 15 end cell cell space space minus 25 end cell row cell 7 space space end cell cell space space 21 end cell cell space space space space space space 30 end cell row 8 cell space space 24 end cell cell space space space space space 42 end cell end table close vertical bar

67 Views

43. Without expanding, prove that the following determinants vanish :

open square brackets table row 6 cell space space 0 space end cell cell space space 2 end cell row 9 cell space 1 end cell cell space space 3 end cell row 15 cell space 2 end cell cell space space 5 end cell end table close square brackets

108 Views

44. Without expanding, prove that the following determinants vanish :

open vertical bar table row 43 cell space space space 1 end cell cell space space space space 6 end cell row 35 cell space space space 7 end cell cell space space space space 4 end cell row 17 cell space space space 3 end cell cell space space space 2 end cell end table close vertical bar space

106 Views

45. Without expanding, prove that the following determinants vanish :

open square brackets table row 102 cell space 18 end cell cell space space 36 end cell row 1 cell space 3 end cell cell space 4 end cell row 17 cell space 3 end cell cell space 6 end cell end table close square brackets

71 Views

46. Without expanding, prove that the following determinants vanish :

open vertical bar table row 43 cell space space 1 end cell cell space space space 6 end cell row 28 cell space space 7 end cell cell space space space 4 end cell row 14 cell space space 3 end cell cell space space space 2 end cell end table close vertical bar

72 Views

47. Without expanding, prove that the following determinants vanish :

open vertical bar table row 2 cell space space space 7 end cell cell space space 65 end cell row 3 cell space space space 8 end cell cell space space 75 end cell row 5 cell space space space 9 end cell cell space 86 end cell end table close vertical bar

68 Views

48. Without expanding, prove that the following determinants vanish :

open vertical bar table row straight x cell space space space straight a end cell cell space space space straight x plus straight a end cell row straight y cell space space space straight b end cell cell space space straight y plus straight b end cell row straight z cell space space space straight c end cell cell space space straight z plus straight c end cell end table close vertical bar space equals 0

68 Views

49. Without expanding, prove that the following determinants vanish :

open vertical bar table row cell straight x plus straight y end cell cell space space space straight y plus straight z end cell cell space space space straight z plus straight x end cell row straight z straight x straight y row 1 1 1 end table close vertical bar

115 Views

Let space space increment space equals space space open vertical bar table row 1 cell space space straight a end cell cell space space straight b plus straight c end cell row 1 cell space space straight b end cell cell space space straight c plus straight a end cell row 1 cell space space straight c end cell cell space space straight a plus straight b end cell end table close vertical bar space equals space space open vertical bar table row 1 cell space space straight a plus straight b plus straight c end cell cell space space straight b plus straight c end cell row 1 cell space space straight a plus straight b plus straight c end cell cell space space straight c plus straight a end cell row 1 cell space space straight a plus straight b plus straight c end cell cell space space straight a plus straight b end cell end table close vertical bar space comma by space straight C subscript 2 space plus straight C subscript 3 Taking space out space common space straight a space plus space straight b space plus space straight c space from space straight C subscript 2 equals left parenthesis straight a plus straight b plus straight c right parenthesis space cross times space 0 space space space space space space space space space space space space space space space space space space space space space open square brackets table row cell because space straight C subscript 1 comma straight C subscript 2 space are space identical end cell end table close square brackets equals space 0

68 Views