A Fair Die Is Tossed Repeatedly Until A Six Is Obtained Let X Denote The Number Of Tosses Conditional Probability That X Gte 6 Given X Gt 3 Equals 1) 125/216 2) 25/216 3) 5/36 4) 25/36 Solution: Option (4) 25/36. P[(X ≥ 6)/X>3] = [P[(X>3)/(X ≥ 6)].P(X ≥ 6) / P(X ≥ 6) =... View Article
A Fair Die Is Tossed Repeatedly Until A Six Is Obtained Let X Denote The Number Of Tosses Required The Probability That X Gte 3 Equals 1) 125/216 2) 25/36 3) 5/36 4) 25/216 Solution: Option (2) 25/36 P(X ≥ 3) = 1- [P(X=1) + P(x= 2)] P(X ≥ 3) = 1-[(⅙) +(⅙)(⅚)] P(X ≥... View Article
A Fair Die Is Tossed Repeatedly Until A Six Is Obtained Let X Denote The Number Of Tosses Required The Probability That X Equals 3 Equals 1) 25/216 2) 25/36 3) 5/36 4) 125/216 Solution: Option (1) 25/216 P(X= 3) = (â…š)(â…š)(â…™) P(X= 3) = 25/216.... View Article
Let U1 And U2 Be Two Urns U1 Contains 3 White And 2 Red Balls U2 Contains Only 1 White Ball The Probability That Head Appeared On The Coin 1) 17/23 2) 11/23 3) 15/23 4) 12/23 Solution: Option (4) 12/23 P(H) = ½, P(T) = ½, Let W be the event of drawing white ball form U2... View Article
Let U1 And U2 Be Two Urns U1 Contains 3 White And 2 Red Balls U2 Contains Only 1 White Ball Probability Of The Drawn Ball From U2 Being White 1) 13/30 2) 23/30 3) 19/30 4) 11/30 Solution: Option (2) 23/30 (i) Head - one white from U1, white from U2 = (½)(⅗)(2/2) = 3/10... View Article
A Box Contains 24 Identical Balls Of Which 12 Are White 12 Are Black The Probability That A White Ball Is Drawn For The 4th Time On The 7th Draw Is 1) 5/64 2) 27/32 3) 5/32 4) 1/2 Solution: Option (3) 5/32 Given that a box contains 24 identical balls, of which 12 are white and 12... View Article
A Dice Is Thrown 2n Plus 1 Times The Probability Of Getting 1 3 Or 4 At Most N Times Is 1) 1/2 2) 1/3 3) 1/4 4) None of these Solution: Option (1) ½ Let p be the probability of getting 1, 3 or 4 = 3/6= ½ q= 1-p=½ By... View Article
If A Straight Line Is Tangent To One Point And Normal To Another Point 1) x - y = √2 2) √2x - y = [(89 √2) / 27] + 1 3) x - y = 89√2 4) None of these Solution: (2) √2x - y = [(89 √2) / 27] + 1... View Article
Which One Of The Following Curves Cuts The Parabola 1) x2 + y2 = a2 2) y = e-x/2a 3) y = ax 4) x2 = 4ay Solution: (4) x2 = 4ay For y2 = 4ax, y-axis is tangent at (0, 0), while for x2... View Article
The Number Of Solutions Of The Equation 1) 0 2) 1 3) 2 4) 3 Solution: (1) 0 f (x) = x3 + 2x2 + 5x + 2 cos x f’ (x) = 3x2 + 4x + 5 - 2 sinx = 3 [(x + (2 / 3))2 + (11 /... View Article
A Cylindrical Gas Contained Is Closed At The Top And Open At The Bottom 1) 2 / 3 2) 1 / 2 3) 4 / 5 4) 1 / 3 Solution: (3) 4 / 5 Let h be the thickness of sides. Then that of the top will be 5h / 4. S... View Article
The Maximum Value Of X 2 X 1 X 2 X 1 For Real Values Of X Is 1) 1 / 2 2) 1 3) 2 4) 3 Solution: (4) 3 y = [x2 - x + 1] / [x2 + x + 1] y = [x2 - x + 1 + x - x] / [x2 + x + 1] y = 1 - [2x /... View Article
The Equation E X 8 2x 17 0 Has 1) one real root 2) two real roots 3) eight real roots 4) four real roots Solution: (1) one real root ex – 8 + 2x − 17 = 0 The... View Article
The Point On The Curve Y 2 X The Tangent At Which Makes An Angle Of 45 1) (1 / 2, 1 / 4) 2) (1 / 2, 1 / 2) 3) (2, 4) 4) (1 / 4, 1 / 2) Solution: (4) (1 / 4, 1 / 2) The slope of the tangent at that... View Article
The Points Of Contact Of The Tangent Drawn From 0 0 To The Curve 1) x2 - y2 = xy 2) x2 + y2 = x2y2 3) x2 - y2 = x2y2 4) None of these Solution: (3) x2 - y2 = x2y2 Let the tangent be drawn at the... View Article
The Angle At Which The Curve Y Ae Ax Intersects The Y Axis Is 1) tan-1 (a2) 2) sin-1 (1 / √1 + a4) 3) cot-1 (a2) 4) sin-1 (√1 + a4) Solution: (3) cot-1 (a2) y = aeax dy / dx = a2eax The... View Article
The Function Sin X Alpha Sin X Beta Has No Maximum Or Minimum If 1) β - ɑ = Kπ 2) β - ɑ ≠Kπ 3) β - ɑ = 2Kπ 4) None of these Solution: (2) β - ɑ ≠Kπ f (x) = [sin (x + ɑ)] / [sin (x + β)] f’ (x)... View Article
The Minimum Value Of Root E X 2 1 Is 1) 1 2) 0 3) 2 4) None of these Solution: (2) 0 f (x) = √ex^2 - 1 f’ (x) = [(2x) ex^2] / [ex^2 - 1] f’ (x) > 0, if x > 0... View Article
The Set Of All X For Which Log 1 X X Is 1) (0, ∞) 2) (-1, ∞) 3) (-∞, ∞) 4) (1, ∞) Solution: (2) (-1, ∞) Let f (x) = log (1 + x) - x f’ (x) = 1 / [1 + x] - 1 = - x / [1... View Article
Let F X X 1 A If X 1 2x 3 If X 1 If F X Has Local Minimum 1) a = 7 2) a = 8 3) a = 9 4) a ≤ 5 Solution: (4) a ≤ 5 Clearly f (x) = 1 - x + a if x ≤ 1 Since y = 1 - x + a is decreasing... View Article
