CBSE Set Qa1 Maths Class X 1999 Sample Test Papers For Class 10th for students online

Section - A

Q1) Evaluate without using trignometric table:
cos 75^o/sin 15^o + sin 12^o/cos 78^o - cos 18^o/sin 72^o  (Marks 2)
Ans1)  cos 75^o/sin 15^o + sin 12^o/cos 78^o - cos 18^o/sin 72^o  
= sin (90^o - 75^o)/sin 15^o + cos (90^o - 12^o)/cos 78^o - sin (90^o - 18^o)/sin 72^{o   .}.^. sin (90^o - ) = cos ,  
= sin 15^o/sin 15^o + cos 78^o/cos 78^o - sin 72^o/sin 72^o                                     cos (90^o - ) = sin
= 1 + 1 - 1
= 1

Q2) Evaluate (sec² - 1)(1 - cosec² )  (Marks 2)
Ans2) (sec² - 1)(1 - cosec² )
= (tan² )(-cot² )   ^..^. 1 + tan² = sec² , 1 + cot² = cosec²
= (tan² )(1/-tan² )
= -1

Q3) If tan A = b/a where a and b are real numbers, find the value of sin² A  (Marks 2)
Ans3) tan A = b/a
= P (perpendicular) = b, B (Base) = a

In a rt PQR  Hypotenuse2 = Perpendicular2 + Base2  (Pythagoras Theorem) = b2 + a2 = H = (b2 + a2) sin2 A = P2/H2 = b2/(a2 + b2)

Q4) A cricketer has mean score of 58 runs in nine innings. Find out how many runs are to be scored in the tenth innings to raise the mean score to 61.  (Marks 2)
Ans4) 58 = sum of the runs scored in nine innings / 9
= 522 = sum of the runs scored in nine innings
61 =  sum of the runs scored in ten innings / 10
= 610 = sum of the runs scored in ten innings
.^.. Score required in the tenth inning = 610 - 522 = 88 runs.

Q5) Find the mean of the following data:
46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92
If in the data, the observation 92 is replaced by 19, determine the new median.  (Marks 2)
Ans5)  Arranged data:
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
n = 11 (odd number)
Median = ((n + 1) / 2)^th term
= 6^th term
= 58 
When 92 is replaced by 19
Arranged data:
19, 33, 35, 41, 46, 55, 58, 64, 77, 87, 90
n = 11 (odd number)
Median = ((11 + 1) / 2)^th term
= 6^th term
= 55

Q6) Harshad purchased a motorcycle for Rs. 42,952 which includes the amount of sales tax. If the tax charged is 12% of the list price, find the list price of the motorcycle.  (Marks 2)
Ans6) Let the list price of the motor cycle be Rs. x
rate of sales tax = 12%
According to the question
x + 12/100 . x = 42952
= 112/100 x = 42952
= x = 42952 x 100 / 112 = Rs. 38,350
.^.. List price of the motor cycle = Rs. 38,350

Q7) The circumference of the edge of a hemispherical bowl is 132 cm. Find the capacity of the bowl ( = 22/7)  (Marks 2)
Ans7) circumference = 2r = 132
= r = (132 x 7)/(2 x 22) = 21 cm
Capacity of the bowl = 2/3r³ = 2/3 x 22/7 x 21 x 21 x 21
= 19404 cm³

Q8) Find the value of c for which the quadratic equation 4x² - 2(c + 1)x + (c + 4) = 0 has equal roots.  (Marks 2)
Ans8) Equal roots
= D = 0
= b² - 4ac'  where a = 4, b = -2(c + 1), c' = c + 4
= [-2(c + 1)]² - 4(4)(c + 4) = 0
= 4c² - 8c - 60 = 0
= c² - 2c - 15 = 0
= (c - 5)(c + 3) = 0
= c = 5 or c = -3

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