Dpp 12th Maths WA.pdf
PARTICE TEST PAPER-1.pdf
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PART-A Q.1 Find the number of real solution(s) of the equation logx9 – log3x2 = 3. [3] Q.2 Simplify: cos x · sin(y – z) + cos y · sin(z – x) + cos z · sin (x – y) where x, y, z R. [3] Q.3 If logx–3(2x – 3) is a meaningful quantity then find the interval in which x must lie. [3] Q.4 If x = 1 and x = 2 are solutions of the equation x3 + ax2 + bx + c = 0 and a + b = 1, then find the value of b. [3] Q.5 tan = 1 2 + 1 2 + 1 where (0, 2), find the possible value of . [3] 2 + cos12 cos 72 Q.6 Find the exact value of sin 72 + sin12 . [3] Q.7 If the tangent of DAB is expressed as a ratio of positive integers a b in lowest term, then find the value of (a + b). [3] 12 A Q.8 If sin A = 13 . Find the value of tan 2 . [3] Q.9 Let x = (0.15)20. Find the characteristic and mantissa in the logarithm of x, to the base 10. Assume log102 = 0.301 and log103 = 0.477. [3] Q.10 The figure (not drawn to scale) shows a regular octagon ABCDEFGH with diagonal AF = 1. Find the numerical value of the side of the octagon. [3] PART-B cos3 + cot(3 + ) sec( 3) cosec 3 Q.11 Simplify tan2 ( ) sin( 2) . [4] Q.12 Find the sum of the solutions of the equation 2e2x – 5ex + 4 = 0. [4] Q.13 Prove the identity cot A + cosec A 1 = cot A . [4] cot A cosec A +1 2 Q.14 If log (log ( log x)) = log (log ( log y)) = 0 then find the value of (x + y). [5] 1 2 1 Q.15 If log25 = a and log 225 = b, then find the value of log + log in terms of a and b 9 2250 (base of the log is 10 everywhere). [5] Q.16 Prove that the expression sin2 + sin2(120° + ) + sin2(120° – ) remains constant R. Find also the value of the constant. [5] y Q.17 Suppose that x and y are positive numbers for which log9x = log12y = log16(x + y). If the value of x = 2 cos , where (0, 2) find . [6] tan 1 cot Q.18 If tan tan 3 = 3 , find the value of cot cot 3 . [6] 2 3 4 Q.19 Let S = sec 0 + sec + sec + sec + sec and P = tan · tan 2 · tan 4 then prove 5 5 5 5 9 9 9 S + P = 2 2 sin 7 [6] 12
PARTICE TEST PAPER-1.pdf
- CLASS : XI (J1 & J2) This paper held on 04.06.07 for Bulls Eye. PART-A Q.1 Findthenumberofreal solution(s)oftheequation logx9 – log3x2 = 3. [3] Q.2 Simplify: cos x · sin(y– z) + cos y· sin(z – x) + cos z · sin (x – y) where x, y, z R. [3] Q.3 If logx–3(2x –3) isameaningful quantitythenfind theinterval inwhich xmust lie. [3] Q.4 If x = 1 and x = 2 are solutions of the equation x3 + ax2 + bx + c = 0 and a + b = 1, then find the value of b. [3] Q.5 tan = 2 1 2 1 2 1 where (0, 2), find the possible value of . [3] Q.6 Find the exact value of 12 sin 72 sin 72 cos 12 cos . [3] Q.7 If the tangent of DAB is expressed as a ratioof positive integers b a in lowest term, then find the value of (a+ b). [3] Q.8 If sinA= 13 12 . Find the value of tan 2 A . [3] Q.9 Let x = (0.15)20. Find the characteristic and mantissa in the logarithm of x, to the base 10.Assume log102 = 0.301 and log103 = 0.477. [3] Q.10 The figure (not drawn to scale) shows aregular octagonABCDEFGH withdiagonalAF=1. Findthenumerical valueof the side of the octagon. [3] PART-B Q.11 Simplify ) 2 sin( ) ( tan 2 3 cosec ) 3 sec( ) 3 cot( 2 cos 2 3 . [4] Q.12 Findthesum ofthesolutionsoftheequation 2e2x – 5ex + 4 = 0. [4]
- Q.13 Prove the identity 1 A cosec A cot 1 A cosec A cot = 2 A cot . [4] Q.14 If x) log ( log log 3 2 2 = y) log ( log log 2 3 2 = 0 then find the value of (x + y). [5] Q.15 If log25 = a and log 225 = b, then find the value of 2 9 1 log + 2250 1 log in terms of a and b (base of the logis 10 everywhere). [5] Q.16 Prove that the expression sin2 + sin2(120° + ) + sin2(120° – ) remains constant R. Find also the valueof theconstant. [5] Q.17 Suppose that x and yare positive numbers for which log9x = log12y= log16(x + y). Ifthe value of x y = 2 cos , where 2 , 0 find . [6] Q.18 If 3 tan tan tan = 3 1 , find the value of 3 cot cot cot . [6] Q.19 Let S = sec 0 + sec 5 + sec 5 2 + sec 5 3 + sec 5 4 and P = 9 tan · 9 2 tan · 9 4 tan then prove S + P = 12 7 sin 2 2 [6]