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If (a, b, c) is the image of the point (1,2,-3) in the line, (x+1)/2 = (y-3)/-2 = z/-1 then a+b+c is

a) 2 b) 3 c) -1 d) 1 Solution: Vector PM and (\(\begin{array}{l}2\hat{i}-2\hat{j}-\hat{k}\end{array} \)) are perpendicular. ⇒ (2λ-2)2+(1-2λ)(-2)+(3-λ) (-1) =... View Article

The value of [latex]\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{1}{1+e^{\sin x}}dx[/latex] is:

a) π/2 b) π/4 c) π d) 3π/2 Solution: I = \(\begin{array}{l}\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{1}{1+e^{\sin x}}dx\end{array} \) = \(\begin{array}{l}\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{e^{\sin... View Article

If S is the sum of the first 10 terms of the series tan^-1(1/3) + tan^-1(1/7) + tan^-1(1/13) + tan^-1(1/21) +…, then tan(S) is equal to

a) 5/11 b) 5/6 c) -6/5 d) 10/11 Solution: S = \(\begin{array}{l}\tan ^{-1}\left ( \frac{1}{1+1\times 2} \right )+\tan ^{-1}\left (... View Article

If y = y(x) is the solution of the differential equation ((5+e^x)/(2+y))(dy/dx)+e^x = 0 satisfying y(0) = 1, then a value of y(log_e13) is

a) 1 b) 0 c) 2 d) -1 Solution: ((5+ex)/(2+y))(dy/dx) = -ex ∫dy/(2+y) = ∫-e-x/(ex+5) dx ln (y+2) = -ln(ex+5)... View Article

The product of the roots of the equation 9x²-18|x|+5 = 0 is

a) 25/81 b) 5/9 c) 5/27 d) 25/9 Solution: Let |x| = t 9t2-18t +5 = 0 9t2 -15t -3t+5... View Article

If the point P on the curve, 4x²+5y² = 20 is farthest from the point Q(0, -4), then PQ² is equal to:

a) 48 b) 29 c) 21 d) 36 Solution: Given ellipse is (x2/5)+(y2/4) = 1 Let point P is (√5... View Article

Let λ∈R. the system of linear equations

Let λ∈R. the system of linear equations 2x1-4x2+λx3 = 1 x1-6x2+x3 = 2 λx1-10x2+4x3 = 3 is inconsistent for: a)... View Article

If the minimum and the maximum values of the function f: [π/4, π/2] → R defined by f(θ) = [latex]\begin{vmatrix} -\sin ^{2}\theta & -1-\sin ^{2}\theta & 1\\ -\cos ^{2}\theta &-1- \cos ^{2}\theta & 1\\ 12 & 10 & -2 \end{vmatrix}[/latex] are m and M respectively, then the ordered pair (m,M) is equal to :

a) (0,4) b) (-4,0) c) (-4,4) d) (0,2√2) Solution: f(θ) = \(\begin{array}{l}\begin{vmatrix} -\sin ^{2}\theta & -1-\sin ^{2}\theta & 1\\ -\cos... View Article

If the common tangent to the parabolas, y² = 4x and x² = 4y also touches the circle, x²+y² = c², then c is equal to:

a) 1/2 b) 1/4 c) 1/√2 d) 1/2√2 Solution: y = mx+1/m x2 = 4(mx+1/m) x2 -4mx-4/m = 0 D... View Article

If 3^{2 sin2α-1},14 and 3^{4-2 sin2α} are the first three terms of an A.P. for some α , then the sixth term of this A.P. is

a) 65 b) 81 c) 78 d) 66 Solution: 28 = 32sin2α-1+34-2 sin2α 28 = 9sin2α/3 + 81/9sin2α Let 9sin2α... View Article

If 2¹⁰+2⁹×3¹+2⁸×3²+…..+2×3⁹+3¹⁰= S-2¹¹, then S is equal to

a) 311 b) (311/2)+210 c) 2×311 d) 311-212 Solution: Let S’ = 210+29×31+ 28×32+—–+2×39+310 ..(i) 3×S’/2 = 29×31+28×32+…+310+311/2 ..(ii) Equation... View Article

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2,4,10,12,14, then the absolute difference of the remaining two observations is

a) 1 b) 4 c) 3 d) 2 Solution: Var(x) = \(\begin{array}{l}\sum \frac{x_{i}^{2}}{n}-(\bar{x})^{2}\end{array} \) 16 = (x12+ x22+ x42+ x52+... View Article

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:

a) 63 b) 54 c) 38 d) 36 Solution: C → Coffee and T → Tea n(C) = 73, n(T)... View Article

If the volume of a parallelopiped, whose coterminuous edges are given by the vectors [latex]\vec{a}=\hat{i}+\hat{j}+n\hat{k}[/latex], [latex]\vec{b}=2\hat{i}+4\hat{j}-n\hat{k}[/latex], and [latex]\vec{c}=\hat{i}+n\hat{j}+3\hat{k}[/latex] (n [latex]\geq[/latex] 0), is 158 cu. units, then: a) [latex]\vec{a}.\vec{c}=17[/latex]

a) \(\begin{array}{l}\vec{a}.\vec{c}=17\end{array} \) b) \(\begin{array}{l}\vec{b}.\vec{c}=10\end{array} \) c) n = 9 d) n = 7 Solution: \(\begin{array}{l}\begin{vmatrix} 1 & 1 &n... View Article

A galaxy is moving away from the earth at a speed of 286 km/s.

A galaxy is moving away from the earth at a speed of 286 km/s. The shift in the wavelength of... View Article

A TV transmission tower antenna is at a height of 20 m.

A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at. (i)... View Article

An infinite number of point charges, each carrying 1 μC charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m

An infinite number of point charges, each carrying 1 μC charge, are placed along the y-axis at y = 1... View Article

The projectile motion of a particle of mass 5 g is shown in the figure.

The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the... View Article

The radius of a sphere is measured to be (7.50 ± 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest integer x, is

Answer: (34) \(\begin{array}{l}V = \frac{4}{3}\pi r^{3}\end{array} \) \(\begin{array}{l}\frac{\Delta V }{V}\times 100 = 3\frac{\Delta r}{r}\times 100\end{array} \) \(\begin{array}{l}= 3\left ( \frac{0.85}{7.5}... View Article

The typical output characteristics curve for a transistor working in the common emitter configuration is shown in the figure

The estimated current gain from the figure is ………….. Answer: (200) For common emitter configuration \(\begin{array}{l}\beta =\frac{\Delta I_{c}}{\Delta I_{B}}= \frac{(4-2)mA}{(20-10)\mu... View Article

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