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1 g. Lim x APTITUDE TEST FOR B.Sc. GRADUATE IN ENGINEERING ³ÖµÖÖÓ ÖÛúß Öë ²Öß. ÃÖÃÖß. à ÖÖŸÖÛúÖë Ûêú»Ö ³Ö¹ý Ö Ö üßõöþö ( cos (x )) x exists and it equals exists and it equals does not exist because x 0 does not exist because left hand limit is not equal to right hand limit. The classes of the type, 6 0,, 6 0,... are called discrete classes inclusive classes exclusive classes none of these. The function f(x) = log e ( + ax) log e ( bx) x is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0, is a b a + b log e a log e b none of these. A function is defined as f(x) = x ; x < x ; x > The function is continuous at x = differentiable at x = continuous but not differentiable at x = none of these. The locus of the mid point of a chord of the circle x + y = which subtends a right angle at the origin is x + y = x + y = x + y = x + y =. Lim x ( cos (x )) x ÖÖî Öæ ü üæüÿöö Æîü ¾Ö µöæü Ûêú ²Ö üö²ö ü Æîü ÖÖî Öæ ü üæüÿöö Æîü ¾Ö µöæü Ûêú ²Ö üö²ö ü Æîü x 0 Ûêú ÛúÖ üþö ÖÖî Öæ ü ÖÆüà üæüÿöö ÖÖî Öæ ü ÖÆüà üæüÿöö ŒµÖÖë Ûú ¾ÖÖ ÖÖ¾ÖŸÖá ÃÖß ÖÖ ü õöþöö¾öÿöá ÃÖß ÖÖ Ûêú ÃÖ ÖÖ Ö ÖÆüà ÆüÖêŸÖß. ÁÖê ÞÖµÖÖë Ûêú üö Ö, 6 0,, 6 0,... ÛúÖê ŒµÖÖ ÛúÆüŸÖê Æïü? ÃÖÓŸÖŸÖ ÁÖê ÞÖµÖÖÑ ÃÖ ÖÖ¾Öê Öß ÁÖê ÞÖµÖÖÑ Ö¾ÖÙ ÖŸÖ ÁÖê ÞÖµÖÖÑ. x = 0 Ö ü ±ú»ö Ö f(x) = log e ( + ax) log e ( bx) x Ö ÖÖÔ üÿö ÖÆüà ÆüÖêŸÖÖ ¾ÖÆü ÖÖ Ö ÛúÖî Ö ÃÖÖ Æîü ÖÃÖê x = 0 Ö ü f ÛúÖê üß ÖÖ ŸÖÖ Ûú µöæü x = 0 Ö ü ÃÖÓŸÖŸÖ ÆüÖê ÖÖ? a b a + b log e a log e b. Ûú ±ú»ö Ö ÛúÖê f(x) = x ; x < x ; x > ºþ Ö Öë Ö ÖÖÔ üÿö ÛúµÖÖ ÖÖŸÖÖ Æîü µöæü ±ú»ö Ö Æîü x = Ö ü ÃÖÓŸÖŸÖ P-8 x = Ö ü ¾ÖÛú»Ö ÖßµÖ x = Ö ü ÃÖÓŸÖŸÖ»Öê Ûú Ö ¾ÖÛú»Ö ÖßµÖ ÖÆüà. ¾Öé Ö x + y = Ûúß Öß¾ÖÖ Ö µö-ø²ö ãü ÛúÖ Ø²Ö ãü Ö Ö ÛúÆüÖÑ Æîü ÖÖê ˆ ËüÝÖ Ö Ö ü ÃÖ ÖÛúÖêÞÖ ÛúÖê ÓŸÖ üÿö Ûú üÿöö Æîü? x + y = x + y = x + y = x + y =

2 6. To plot a frequency polygon, we must have a Continuous distribution Ungrouped distribution Grouped distribution Discrete distribution 7. The equation of the directrix of the parabola y + y + x + = 0 is x = x = x = / x = / 8. The equation of the circle passing through (, ) and the point of intersection of x + y + x y = 0 and x + y + x 7y = 0 is x + y 0x 0y = 0 x + y + 0x y = 0 x + y 7x 0y + = 0 9. For qualitative type data, which is most suitable average? mode mean deviation standard deviation median 6. Ö¾Öé Ö ²ÖÆãü³Öã Ö ÓÛú Ö Ûêú»Ö, Æü ÖÖ êü ÖÖÃÖ ÆüÖê ÖÖ ÖÖ Æü Ûú ÃÖÓŸÖŸÖ ¾ÖŸÖ üþö ¾ÖÝÖáÛéúŸÖ ¾ÖŸÖ üþö ¾ÖÝÖáÛéúŸÖ ¾ÖŸÖ üþö ÃÖÓŸÖŸÖ ¾ÖŸÖ üþö 7. Ö ü¾ö»öµö y + y + x + = 0 Ûêú ÖµÖÓŸÖÖ ÛúÖ ÃÖ ÖßÛú üþö Æîü x = x = x = / x = / 8. (, ) ÃÖê ÝÖã Ö ü Öê ¾ÖÖ»Öê ¾Öé Ö ÛúÖ ÃÖ ÖßÛú üþö ¾Ö x + y + x y = 0 Öî ü x + y + x 7y = 0 ÛúÖ ÖÏ ŸÖ êû ü ²Ö ãü Æîü x + y 0x 0y = 0 x + y + 0x y = 0 x + y 7x 0y + = 0 9. ÝÖãÞÖÖŸ ÖÛú ÖÏÛúÖ ü Ûêú êü üö Ûêú»Ö, ÃÖ¾ÖÖÔ ÖÛú ˆ ÖµÖãŒŸÖ ÖîÃÖŸÖ ÛúÖî Ö ÃÖÖ Æîü? ÖÖê ü ÖÖ µö ¾Ö Ö»Ö Ö ÖÖ ÖÛú ¾Ö Ö»Ö Ö ÖÖ µöûúö /. 0. The value of. 0 0 dx + tan x is 0. /. dx. + tan x 0 0 ÛúÖ ÖÖ Ö Æîü / / / / P-8

3 .. The value of. (ax + bx + c) dx depends on the values of a and b a and c b only c only. The solution of the equation x dy dx = x + xy + y is tan y x = log x + c tan x y = log x + c tan x y = log y + c tan y x = log y + c. The equation of the curve passing through (, 9) which satisfies the differential equation dy dx = x + x is 6xy = x 6x +9 6xy = x 9x +6 6xy = x + 9x 6. Standard deviation is affected by change of origin scale both origin and scale none of these. A curve y = f(x) passes through the point (, ) and the normal to the curve at that point happens to be a tangent to the circle x + y =. The value of f ' () is... (ax + bx + c) dx ÛúÖ ÖÖ Ö ÛúÃÖÛêú ÖÖ Ö Ö ü Ö³ÖÔ ü Æîü? a ¾Ö b a ¾Ö c Ûêú¾Ö»Ö b Ûêú¾Ö»Ö c. ÃÖ ÖßÛú üþö x dy dx = x + xy + y ÛúÖ Æü»Ö ŒµÖÖ Æî?ü tan y x = log x + c tan x y = log x + c tan x y = log y + c tan y x = log y + c. (, 9) ÃÖê ÝÖã Ö ü Öê ¾ÖÖ»Öê ¾ÖÛÎú ÛúÖ ÃÖ ÖßÛú üþö ÛúÖî Ö ÃÖÖ Æîü ÖÖê ¾ÖÛú»Ö Ö ÃÖ ÖßÛú üþö dy dx = x + x ÛúÖê ÃÖÓŸÖã ü Ûú üÿöö Æîü? 6xy = x 6x +9 6xy = x 9x +6 6xy = x + 9x 6. ÖÖ ÖÛú ¾Ö Ö»Ö Ö ÛúÃÖÛêú Ö ü¾öÿöô Ö ÃÖê ÖϳÖÖ ¾ÖŸÖ ÆüÖêŸÖÖ Æîü? Öæ»Ö ÃÛêú»Ö Öæ»Ö ¾Ö ÃÛêú»Ö. Ûú ¾ÖÛÎú y = f(x) Ø²Ö ãü (, ) ÃÖê ÝÖã Ö üÿöö Æîü Öî ü ˆÃÖ ²Ö ãü Ö ü ¾ÖÛÎú Ûêú»Ö ²Ö¾ÖŸÖ ŸÖ ÖÖ ¾ÖÆü ²Ö ãü ¾Öé Ö x + y = Ûúß Ã Ö ÖÔ êüüöö ÆüÖêŸÖß Æîü f ' () ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? P-8

4 6. If x + y =, where x, y R, then minimum value of x + y is 7. The formula for quartile deviation is Q Q (Q Q ) / Q / (Q Q )/ (Q + Q ) 8. Which is unitless measure of dispersion? Range Quartile deviation Coefficient of variation Standard deviation 9. The variance of first n natural numbers is (n + )/ (n ) / (n ) / (n + ) / 0. If x =, the value of cos (cos x + sin x) is 6. µö ü x + y = ÆüÖê ÖÆüÖÑ x, y R ÆüÖê, ŸÖÖê x + y ÛúÖ µöæ ÖŸÖ Ö ÖÖ Ö ÛúŸÖ ÖÖ Æîü? 7. ÖŸÖã ÖÔÛú ¾Ö Ö»Ö Ö Ûêú»Ö ÃÖæ Ö ŒµÖÖ Æîü? Q Q (Q Q ) / Q / (Q Q )/ (Q + Q ) 8. ÖÏÛúßÞÖÔ Ö ÛúÖ ÛúÖ Ô ü ÆüŸÖ ÖÖ Ö ŒµÖÖ Æîü? ëü Ö ÖŸÖã ÖÔÛú ¾Ö Ö»Ö Ö Ö ü¾öÿöô Ö ÛúÖ ÝÖãÞÖÖÓÛú ÖÖ ÖÛú ¾Ö Ö»Ö Ö 9. ÖÆü»Öß n ÖÏÖÛéú ŸÖÛú ÃÖÓܵÖÖ ÛúÖ ÖÏÃÖ üþö ŒµÖÖ Æîü? (n + )/ (n ) / (n ) / (n + ) / 0. µö ü x = ÆüÖê, ŸÖÖê cos (cos x + sin x) ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü?. If u and u are solutions of Laplace equation, then u u is also a solution c u + c u is also a solution where c, c R u /u is also a solution. µö ü u ¾Ö u»öö»ööãö ÃÖ ÖßÛú üþö Ûêú Æü»Ö ÆüÖê, ŸÖÖê u u ³Öß Ûú Æü»Ö Æîü c u + c u ³Öß Ûú Æü»Ö Æîü, ÖÆüÖÑ c, c R u /u ³Öß Ûú Æü»Ö Æîü 6 P-8

5 . In a triangle ABC, B = and C =. Let D divide BC internally in the ratio sin BAD : then is equal to sin CAD 6. The mean of first n-natural numbers is (n + ) n(n + ) n. If A and B are two independent events with P = 0.6, P = 0., then P (A' B') is equal to Answer Q. to 9 after reading the given statement : Three newspapers A, B and C are published in a certain city. It is estimated from a survey that 0% read A, 6% read B, % read C, 8% read A and B, % read A and C, % read B and C and % read all the three newspapers. What is the probability that a normally chosen person. Ö³Öã Ö ABC Öë, B = ¾Ö C = Æîü ÖÖ ÖÖ BC ÛúÖê D ÖÓŸÖ üûú ºþ Ö ÃÖê : Öã ÖÖŸÖ sin BAD Öë ¾Ö³ÖÖ ÖŸÖ Ûú üÿöö Æîü, ŸÖÖê sin CAD ÛúÃÖÛêú ²Ö üö²ö ü Æîü? 6. ÖÏ Ö Ö n- Ö Ö ÖæÞÖÔ ÃÖÓܵÖÖ ÛúÖ ÖÖ µö Æîü (n + ) n n(n + ). µö ü P = 0.6, P = 0. Ûêú ÃÖÖ Ö A ¾Ö B üöê, þ֟ÖÓ Ö Ö ü ÖÖ Ñ ÆüÖë, ŸÖÖê P (A' B') ÛúÃÖÛêú ²Ö üö²ö ü Æîü? ÃÖ Ûú Ö Ö ÛúÖê ÖœÌü Öê Ûêú ²ÖÖ ü ÖÏ Ö ÃÖê 9 ÛúÖ ˆ Ö ü ëü : Ûú ÖÆü ü ÃÖê ŸÖß Ö ÃÖ ÖÖ ÖÖ ü Ö Ö A, B ¾Ö C ÖÏÛúÖ ÖŸÖ ÆüÖêŸÖê Æïü Ûú ÃÖ¾Öì ÛúÖ Öã ÖÖ Ö Æîü Ûú 0% A ÖœÌüŸÖê Æïü, 6% B ÖœÌüŸÖê Æïü, % C ÖœÌüŸÖê Æïü, 8% A ¾Ö B ÖœÌüŸÖê Æïü, % A ¾Ö C ÖœÌüŸÖê Æïü, % B ¾Ö C ÖœÌüŸÖê Æïü Öî ü % ŸÖß ÖÖë ÃÖ ÖÖ ÖÖ ü Ö Ö ÖœÌüŸÖê Æïü ÃÖ ²ÖÖŸÖ Ûúß ÛúŸÖ Öß ÃÖÓ³ÖÖ¾Ö ÖÖ Æîü Ûú Ûú ÃÖÖ ÖÖ µö ÖµÖ ÖŸÖ ¾µÖ ŒŸÖ. does not read any paper ÛúÖê Ô ÃÖ ÖÖ ÖÖ ü Ö Ö ÖÆüà ÖœÌüŸÖÖ P-8 7

6 6. does not read C reads A but not B reads only one of these papers reads only two of these papers A three digit number is written down by random choice of the digits to 9 (repetition allowed). The probability that at least one of the digits chosen is a perfect square is None of these. A and B throw a dice each. The probability that A s throw is not greater than B s throw is C ÖÆüà ÖœÌüŸÖÖ A ÖœÌüŸÖÖ Æïü»Öê Ûú Ö B ÖÆüà Ö Öë ÃÖê Ûêú¾Ö»Ö Ûú ÃÖ ÖÖ ÖÖ ü Ö Ö ÖœÌüŸÖÖ Æîü Ö Öë ÃÖê Ûêú¾Ö»Ö üöê ÃÖ ÖÖ ÖÖ ü Ö Ö ÖœÌüŸÖÖ Æîü ŸÖß Ö ÓÛúÖë Ûúß ÃÖÓܵÖÖ ÃÖê 9 ŸÖÛú ( Öã Ö üö¾öé Ö Öã ÖŸÖ) µöö ü ûûú ºþ Ö ÃÖê»ÖÜÖß ÖÖŸÖß Æîü ÃÖ ²ÖÖŸÖ Ûúß ÛúŸÖ Öß ÃÖÓ³ÖÖ¾Ö ÖÖ Æîü Ûú Öã ÖÖ ÝÖµÖÖ Ûú Ö ÃÖê Ûú Ö Ûú ÓÛú ÖæÞÖÔ ¾ÖÝÖÔ ÆüÖê? A ¾Ö B Ûú- Ûú ÖÖÃÖÖ ±ëúûúÿöê Æïü ÃÖ ²ÖÖŸÖ Ûúß ÛúŸÖ Öß ÃÖÓ³ÖÖ¾Ö ÖÖ Æîü Ûú A Ûúß ±ëúûú B Ûúß ±ëúûú ÃÖê ÖÛú ÖÆüà Æîü? 7 6. If α, β and γ are distinct real numbers, then points with position vectors α^i + β^j + γ^k, β^i + γ^j + α^k, γ^i + α^j + β^k are collinear form an equilateral triangle form a scalene triangle form a right angled triangle. µö ü α, β ¾Ö γ ¾Ö Ö ü ¾ÖÖÃŸÖ ¾ÖÛú ÃÖÓܵÖÖ ÆüÖë, ŸÖÖê Ã Ö ŸÖ ¾ÖêŒ ü ü α^i + β^j + γ^k, β^i + γ^j + α^k, γ^i + α^j + β^k Ûêú ÃÖÖ Ö Ø²Ö ãü ÃÖÓ êüüö Æîü ÃÖ Ö²ÖÖÆãü Ö³Öã Ö ²Ö ÖÖŸÖê Æïü ¾ÖÂÖ Ö ²ÖÖÆãü Ö³Öã Ö ²Ö ÖÖŸÖê Æïü ÃÖ ÖÛúÖêÞÖ Ö³Öã Ö ²Ö ÖÖŸÖê Æïü 8 P-8

7 . If a, b and c are three non-coplanar vectors, then ( a + b + c). [( a + b) ( a + c )] equals 0 [ a, b, c] [ a, b, c] [ a, b, c]. µö ü a, b ¾Ö c ŸÖß Ö ÃÖ ÖŸÖ»ÖßµÖ ¾ÖêŒ ü ü ÆüÖë, ŸÖÖê ( a + b + c). [( a + b) ( a + c)] ÛúÃÖÛêú ²Ö üö²ö ü Æïü? 0 [ a, b, c] [ a, b, c] [ a, b, c]. The value of a ^i + a ^j + a ^k if ( a = a) is a a a None. The Laplace equation u x + u = 0 has solution y u = x y u = log (x + y ) u = cos kx sin hy All of the above. µö ü ( a = a) ÆüÖê ŸÖÖê, a ^i + a ^j + a ^k ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? a a a ÖÆüà.»ÖÖ»ÖÖÃÖ ÃÖ ÖßÛú üþö u x + u y = 0 ÛúÖ Æü»Ö Æîü u = x y u = log (x + y ) u = cos kx sin hy ˆ Ö üöêœÿö ÃÖ³Öß 6. If A and B are co efficients of x r and x n r in the expansion (+ x) n, then A = λb for some λ ( ) A = B A B 7. For a positively skewed distribution, which of the following is true? Mean = Mode = Median Mean > Mode > Median Mean < Median < Mode Mean > Median > Mode 6. µö ü A ¾Ö B ÖÏÃÖÖ ü (+ x) n Öë x r ¾Ö x n r Ûêú ÝÖãÞÖÖÓÛú ÆüÖë, ŸÖÖê Ûãú û λ ( ) Ûêú»Ö, A = λb P-8 9 A = B A B 7. ÃÖÛúÖ üöÿ ÖÛú ºþ Ö ÃÖê ¾ÖÂÖ Ö ²ÖÓ ü Ö Ûêú»Ö, Ö ÖÖÓ ÛúŸÖ Öë ÃÖê ÛúÖî Ö ÃÖÖ ÃÖÆüß Æîü? ÖÖ µö = ²ÖÆãü»ÖÛú ( ÖÖê ü) = ÖÖ µöûúö ÖÖ µö > ²ÖÆãü»ÖÛú ( ÖÖê ü) > ÖÖ µöûúö ÖÖ µö < ÖÖ µöûúö < ²ÖÆãü»ÖÛú ÖÖ µö > ÖÖ µöûúö > ²ÖÆãü»ÖÛú

8 8. Which is the best measure of homogeneity of a series? Arithmetic mean Standard deviation Quartile deviation Median 8. Ö ÖÖÓ ÛúŸÖ Öë ÃÖê ÀÖÓéÜÖ»ÖÖ Ûúß ÃÖ ÖÖÓÝÖŸÖÖ ÛúÖ ÃÖ²ÖÃÖê ûö ÖÖ Ö ÛúÖî Ö ÃÖÖ Æîü? ÓÛúÝÖ ÞÖŸÖßµÖ ÖÖ µö ÖÖ ÖÛú ¾Ö Ö»Ö Ö ÖŸÖã ÖÔÛú ¾Ö Ö»Ö Ö ÖÖ µöûúö 9. n C r + n C r is equal to 9. n C r + n C r ÛúÃÖÛêú ²Ö üö²ö ü Æîü? n C r n+ C r n+ C r None n C r n+ C r n+ C r ÛúÖê Ô ÖÆüà 0. d dx tan x x x is equal to + 9x 9 + x sec x + x 0. d dx tan x x + 9x 9 + x sec x + x x ÛúÃÖÛêú ²Ö üö²ö ü Æîü?. For f(x) = (x ) / the mean value theorem is applicable in the interval [0, ] [, ] Any finite interval. If o = m and o = n, then the number of relations from A to B is mn m+n m + n mn. f(x) = (x ) / Ûêú»Ö ÖÖ µö ÖÖ Ö ÖÏ ÖêµÖ, ÓŸÖ üö»ö Öë»ÖÖÝÖæ ÆüÖêŸÖÖ Æîü [0, ] [, ] ÛúÖê Ô Ö ü ÖŸÖ ÓŸÖ üö»ö. µö ü o = m ¾Ö o = n ÆüÖê, ŸÖÖê A ÃÖê B ŸÖÛú ÃÖÓ²ÖÓ ÖÖë Ûúß ÃÖÓܵÖÖ ÛúŸÖ Öß Æîü? mn m+n m + n mn. If Z and Z are two non zero complex numbers such that Z + Z = Z + Z, then Arg Z Arg Z is equal to 0. µö ü Z ¾Ö Z üöê Öæ µöêÿö ü Ö ü»ö ÃÖÓܵÖÖ ÃÖ ŸÖ üæü ÆüÖë Ûú Z + Z = Z + Z ÆüÖê, ŸÖÖê Arg Z Arg Z ÛúÃÖÛêú ²Ö üö²ö ü Æîü? 0 0 P-8

9 . If Z is a complex number, then Z + = Z represents circle hyperbola ellipse straight line. µö ü Z ÃÖ ÖÁÖ ÃÖÓܵÖÖ ÆüÖê, ŸÖÖê Z + = Z ÛúÃÖÛúÖê ü ÖÖÔŸÖÖ Æîü? ¾Öé Ö ŸÖ Ö ü¾ö»öµö üß ÖÔ¾Öé Ö ÃÖß Öß êüüöö = e e e = e e e 6. 7 th term of the sequence, 0, is 0 7. If A = a a 0, then the value of 0 0 a A Adj A is a 7 a 9 a a 6 8. If y = x x + x x +. then x is e y log ( + y) e y + e y 9. If A = i 0 0 i 0 i i , n N, then A n equals 6. ÖãÛÎú Ö, 0, ÛúÖ ÃÖÖŸÖ¾ÖÖÑ Ö ü ÛúÖî Ö ÃÖÖ Æîü? 0 7. µö ü A = a a a ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æî?ü a 7 a 9 a a 6, ÆüÖê, ŸÖÖê A Adj A 8. µö ü y = x x + x x +. ÆüÖê, ŸÖÖê x Æîü e y log ( + y) e y + e y 9. µö ü A = i 0 0 i ÛúÃÖÛêú ²Ö üö²ö ü Æîü? 0 i i , n N ÆüÖê, ŸÖÖê A n P-8

10 0. The 9 th term of an A.P. is 99 and 99 th term is 9. The term which is equal to zero is: 0 th 0 th 08 th None of the above. The area bounded by the curve y = 8x and x = 8y is The derivative of sin x with respect to cos x is equal to tan x cot x cot x tan x. The integrating factor of the differential equation dy dx (x log x) + y = log x is given by log (log x) e x log x x. The line x a + y b = touches the curve y = be x/a at the point ( a, ba) (a, a/b) (a, b/a) None. Co-efficient of x in the expansion x x e x is 0. A.P. ÛúÖ Ö¾ÖÖÑ Ö ü 99 Æîü Öî ü 99¾ÖÖÑ Ö ü 9 Æîü, ÖÖê Ö ü Öæ µö Ûêú ²Ö üö²ö ü Æîü ¾ÖÆü Æîü 0 th 0 th 08 th. ¾ÖÛÎú y = 8x ¾Ö x = 8y «üö üö Ö²Ö ü õöê Ö Æîü cos x Ûêú ÃÖÓ²ÖÓ Ö Öë sin x ÛúÖ ¾µÖãŸ Ö Ö ÛúÃÖÛêú ²Ö üö²ö ü Æîü? tan x cot x cot x tan x. ¾ÖÛú»Ö Ö ÃÖ ÖßÛú üþö dy dx (x log x) + y = log x ÛúÖ ÃÖ ÖÖÛú»Ö Ö ÝÖãÞÖÛú ÛúÃÖÃÖê ü ÖÖÔµÖÖ ÝÖµÖÖ Æîü? log (log x) e x log x x. êüüöö x a + y b = ¾ÖÛÎú y = be x/a Ö ü ÛúÃÖ Ø²Ö ãü Ö ü æûÿöß Æîü? ( a, ba) (a, a/b) (a, b/a) ÛúÖê Ô ÖÆüà. ÖÏÃÖÖ ü x x e x Öë x ÛúÖ ÝÖãÞÖÖÓÛú ÛúŸÖ ÖÖ Æîü? P-8

11 6. The area between the curve y = x and x-axis is 7. If one root of the equation ax + bx + c = 0, a 0, be reciprocal of the other, then b = c a = c b = 0 a = 0 6. ¾ÖÛÎú y = x Öî ü x- õö Ûêú ²Öß Ö õöê Ö ÛúŸÖ ÖÖ Æîü? 7. µö ü ÃÖ ÖßÛú üþö ax + bx + c = 0, a 0 ÛúÖ Ûú Öæ»Ö µö Öë ÃÖê ¾µÖãŸÛÎú Ö ÆüÖê, ŸÖÖê b = c a = c b = 0 a = 0 8. If α and β be the roots of the equation (x a)(x b) = c, c 0, then the roots of the equation (x α)(x β) + c = 0 are a + b, b + c a, b b, c a, c 9. The value of the expression 7 C + j C is equal to j= C C C 7 C 60. Let A be an inevertiable matrix. Which of the following is not true? (A ) = (A ) A = A (A ) = (A ) 8. µö ü α ¾Ö β ÃÖ ÖßÛú üþö (x a)(x b) = c, c 0 Ûêú Öæ»Ö ÆüÖë, ŸÖÖê ÃÖ ÖßÛú üþö (x α) (x β) + c = 0 Ûêú Öæ»Ö ÆüÖëÝÖê a + b, b + c a, b b, c a, c 9. ¾µÖÓ ÖÛú 7 C + j= j C ÛúÖ ÖÖ Ö ÛúÃÖÛêú ²Ö üö²ö ü Æîü? C C C 7 C 60. ÖÖ ÖÖ Ûú A ¾µÖãŸÛÎú ÖÞÖßµÖ Öî ÒüŒÃÖ Æîü Ö ÖÖÓ ÛúŸÖ Öë ÃÖê ÛúÖî Ö ÃÖÖ ÃÖÆüß ÖÆüà Æîü? (A ) = (A ) A = A (A ) = (A ) 6. The value of.. cos x is 6... cos x ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? 0 0 P-8

12 6. The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P, then P = R P = Q Q = R 6. A weight of 0 kg is supported by two strings which make an angle of 0 and 60 with the vertical. Then the tensions in the strings are, 0, 0, 0, 6. A force of fixed magnitude and variable inclination θ to the Y axis acts in the oxy plane at a fixed point (a, b). Then the moment is minimum if θ is 6. A particle moves in a plane with constant speed, then velocity and acceleration are equal parallel perpendicular zero 66. If a man can throw a ball h metres vertically upward, then the greatest horizontal distance he can throw is h h h h 67. A particle is projected under gravity with velocity (ag) from a point at a height h above a level plane. The angle of projection α for a maximum range is given by tan a α = a tan α = a tan α = tan a α = 6. üöê ²Ö»ÖÖë P ¾Ö Q ÛúÖ Ö üþöö Öß R Æîü µö ü Q ÛúÖê ãüýöã ÖÖ ÛúµÖÖ ÖÖ ŸÖÖê ÖµÖÖ Ö üþöö Öß P Ûêú»ÖÓ²Ö¾ÖŸÖ ÆüÖêŸÖÖ Æîü, ŸÖÖê P = R P = Q Q = R 6. üöê ü ÃÃÖµÖÖë ÃÖê»Ö üûúö 0 Ûú»ÖÖê ÛúÖ ³ÖÖ ü ú ¾ÖÔ Ûêú ÃÖÖ Ö 0 ¾Ö 60 ÛúÖ ÛúÖêÞÖ ²Ö ÖÖŸÖÖ Æîü Ö ü ÃÃÖµÖÖÑ ÛúÖ ŸÖ Ö Ö ÛúŸÖ ÖÖ Æîü?, 0, 0, 0, 6. Ûú Ö ÖŸÖ Ö ü ÖÖÞÖ ÛúÖ ²Ö»Ö θ ¾Ö Y õö Ö ü Ö ü¾öÿöá Ö ÖŸÖ Ö ÖŸÖ Ø²Ö ãü (a, b) Ö oxy ÃÖ ÖŸÖ»Ö Öë»ÖÝÖÖµÖÖ ÖÖŸÖÖ Æîü ŸÖÖê Ö ÖæÞÖÔ µöæ ÖŸÖ Ö ÆüÖêŸÖÖ Æîü µö ü θ Æîü 6. ÛúÖê Ô ÛúÞÖ, ÃÖ ÖŸÖ»Ö Öë ÖµÖŸÖ ÝÖ ŸÖ ÃÖê Öæ ÖŸÖÖ Æîü, ŸÖÖê ¾ÖêÝÖ ¾Ö Ÿ¾Ö üþö Æîü ÃÖ ÖÖ Ö ÃÖ ÖÖ ÖÖÓŸÖ ü ³Ö»ÖÓ²Ö Öæ µö 66. µö ü ÛúÖê Ô ¾µÖ ŒŸÖ Ûú ÝÖë ü ÛúÖê h Öß ü ü ú Ö ü Ûúß Öê ü ±ëúûú ÃÖÛúŸÖÖ ÆüÖê, ŸÖÖê ÛúŸÖ Öß ¾ÖÆü ÖÛúŸÖ Ö õöî ŸÖ Ö æü üß ŸÖÛú ±ëúûú ÃÖÛúŸÖÖ Æîü? h h h h 67. Ûú ÛúÞÖ ÛúÖê ÝÖã¹ýŸ¾Ö Ûêú Öß Ö (ag) ¾ÖêÝÖ ÃÖê ÃÖ ÖŸÖ»Ö ÃÖê h Ñú ÖÖ Ô ŸÖÛú Ûú Ø²Ö ãü ÃÖê ÖÏõÖê ÖŸÖ ÛúµÖÖ ÖÖŸÖÖ Æîü ÖÛúŸÖ Ö ïü Ö Ûêú»Ö ÖÏõÖê ÖÞÖ ÛúÖêÞÖ α ÛúÃÖÃÖê ü ÖÖÔµÖÖ ÝÖµÖÖ Æîü? tan a α = a tan α = a tan α = tan a α = P-8

13 For Q. 68 to Q. 7, read the following and answer the succeeding questions : The first four moments of distribution about the value of the variable are, 0, 0 and The value of Arithmetic Mean is The number of nd central moment is The value of rd central moment is The value of th central moment is The value of β is The value of β is The value of γ is 0 7. The value of γ is.7.7 ÖÏ Ö 68 ÃÖê 7 Ûêú»Ö Ö Ö ÛúÖê ÖœÌêü ¾Ö ÖÝÖê Ûêú ÖÏ ÖÖë Ûêú ˆ Ö ü ëü Öæ»µÖ Ûêú ÖÃÖ ÖÖÃÖ ²ÖÓ ü Ö Ûêú ÖÆü»Öê ÖÖ ü Ö ÖæÞÖÔ, 0, 0 ¾Ö 0 Æïü 68. ÓÛúÝÖ ÞÖŸÖßµÖ ÖÖ µö ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? æüãö êüü Ö µö Ö ÖæÞÖÔ Ûúß ÃÖÓܵÖÖ ÛúŸÖ Öß Æîü? ŸÖßÃÖ êü Ö µö Ö ÖæÞÖÔ ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? ÖÖî Öê Ö µö Ö ÖæÞÖÔ ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? β ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æî?ü β ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? γ ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü? 0 7. γ ÛúÖ ÖÖ Ö ÛúŸÖ ÖÖ Æîü?.7.7 P-8