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A concave mirror form on a screen, a real image of twice the linear dimension of the object. Object and screen are then moved until the image is three times the size of the object. If the shift of the screen be 25 cm determin ...
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Straight Objective Type A wooden plank of length 1m and uniform cross section is hinged at one end to the bottom of a tank as shown in figure. The tank is filled with water up to a height of 0.5 m. Specific gravity of the pla ...
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Match for 28-31 For a triangle ABC with angles A, B and C, such that 6A=3B=2C Match the following 28) tan(B/2)tan(C/2)+tan(C/2)tan(A/2)+tan(A/2)tan(B/2) 29) 4sin(A/2)sin(B/2)sin(C/2) 30) 4cos(A/2)cos(B/2)cos(C/2) 31) ...
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Match the following for 24-27 24) \int_{-\pi }^{\pi }{xsinx}dx 25) \int_{-\pi }^{\pi }{sin^{3}xcosx}dx 26) \int_{-\pi }^{\pi }{} {sinx}dx :where {.} is the fractional part 27) \int_{-1}^{2}{[x]}dx where [.] is the integral pa ...
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*Image* In the given circuit, with steady current, the potential drop across the capacitor must be ...
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5 gm of water at 30°C and 1 gm of ice at -20°C are mixed together in a calorimeter. Find the final temperature of mixture. Water equivalent of calorimeter is negligible, specific heat of ice=0.5 cal/gm°C and latent hea ...
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*Image* An inductor of inductance L=400 mH and resistors of resistances R1=R2=2Ω are connected to a battery of emf 12V as shown in figure. The internal resistance of the battery is negligible. Switch S has been c ...
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*Image* A wide vessel is filled with three immiscible liquids. Their densities and heights are given in the figure. A small hole is produced at a height h/6 from the bottom. The initial speed of the liquid is ...
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Straight Objective Type A 2 kg block initially at rest is dropped from a height of 0.4 m onto a spring whose force constant is 2000 N/m. The maximum compression in the spring is ...
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Match for 20-23 A circle is given with centre O as x2+y2-6x+8y=0. A line x+y=4 cuts the circle is point P and Q. The tangents at P and Q meet at R Match the following 20) Area of triangle OPQ (A) 25/2 21) Area of tria ...
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f(sinx)+g(sinx)= ...
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fog(x)+gof(x)=Ï€/2 is true for x ...
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Comprehension for 17-19 f(x)=sin-1x g(x)=cos-1x given cos1=0.54 and sin1=0.84 fof(x)+gog(x) exists for x in ...
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solution matrix X is ...
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5A-1= ...
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Comprehension for 14-16 Given three equations x+2y+2z=0 2x+1y+2z=1 2x+2y+z=0 This can written in matrix form as AX=B i.e. \begin{bmatrix} 1 &2 &2 \\ 2 &1 &2 \\ 2 &2 &1 \end{bmatrix}\begin{bmatrix} x\\ y\\ z \e ...
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The plane containing the lines L2 and the shortest line between L1 and L2 is ...
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The shortest distance between the lines is ...
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Comprehension for 21-23 Consider the lines L1: (x+1)/3=(y+2)/1=(z+1)/2 , L2: (x-2)/1=(y+2)/2=(z-3)/3 and the planes P1 and P2 containing the lines L1 and L2 respectively. Also P1 and P2 never intersect. Find t ...
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The minimum area of the triangle OPQ is ...
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The locus of the midpoint of PQ is ...
asked2009-04-15 21:12:47