The value of α for which [latex]4alpha int_{-1}^{2}e^{-alpha left | x right |}dx = 5[/latex] is:
a. loge 2 b. loge √2 c. loge (4/3) d. loge (3/2) Solution: \(\begin{array}{l}4\alpha \int_{-1}^{2}e^{-\alpha \left | x \right |}dx... View Article
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The locus of mid points of the perpendiculars drawn from points on the line x = 2y to the line x = y is
a. 2x − 3y = 0 b. 3x − 2y = 0 c. 5x − 7y = 0 d. 7x... View Article
in a workshop there are five machines and the probability of any one of them to be out of service on a day is
a. 17/2 b. 4 c. 17/4 d. 17/8 Solution: P(Machine being faulty) = p = (1/4) q = 3/4 P(at... View Article
The coefficient of x^7 in the expression (1 + x)^10 + x(1 + x)^9 + x^2(1 + x)^8 + ⋯ +x^10 is
a. 420 b. 330 c. 210 d. 120 Solution: Coefficient of x7 in (1+x)10+ x(1+x)9+ x2(1+x)8+⋯ +x10 Applying sum of... View Article
Let A, B, C and D be four non-empty sets. The contrapositive statement of “If A ⊆ B and B ⊆ D then A ⊆ C ” is
a. If A ⊆ C, then B ⊂ A or D ⊂ B b. If A ⊈ C, then A... View Article
If 3x+4y =12√2 is a tangent to the ellipse (x2/a2) + (y2/9) = 1 for some a∈R then the distance between the foci of the ellipse is :
a. 2√5 b. 2√7 c. 2√2 d. 4 Solution: 3x+4y =12√2 is a tangent to the ellipse (x2/a2) + (y2/9)... View Article
A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l
A particle of mass is fixed to one end of a light spring having force constant k and unstretched length... View Article
Which of the following set of points are non-collinear
1) (1, – 1, 1), (–1, 1, 1), (0, 0, 1) 2) (1, 2, 3), (3, 2, 1), (2, 2,... View Article
If the centroid of a triangle whose vertices are (a, 1, 3), (–2, b, – 5) and (4, 7, c) be the origin, then the values of a, b, c are
1) –2, – 8, – 2 2) 2, 8, – 2 3) –2, – 8, 2 4) 7, – 1,... View Article
The points A(1, 0, 1), B(–1, 2, 3) and C(0, 1, 2) are
1) non-collinear 2) Collinear 3) Non-coplanar 4) None of the above Solution: (2) Collinear \(\begin{array}{l}\begin{array}{l} \begin{array}{l} A B=2 \sqrt{3}, B... View Article
The pairs of rectangular co-ordinate planes have equations
1) xy = yz = 0 2) x = y = z = 0 3) xyz = 0 4) None... View Article
If a line lies in the octant OXYZ and it makes equal angles with the axis, then
1) l = m = n = 1 / √3 2) l = m = n = ± 1 /... View Article
All the points on the x-axis have
1) x = 0 2) y = 0 3) x = 0, y = 0 4) y = 0, z... View Article
The direction cosines of a line equally inclined to all the three rectangular co-ordinate axis are
1) √3, √3, √3 2) 1 / √3, 1 / √3, 1 / √3 3) 1, 1, 1 4) None... View Article
The triangle formed by the points (0, 7,10), (–1, 6, 6), (–4, 9, 6) is
1) Equilateral 2) Isosceles 3) Right-angled 4) Right-angled isosceles Solution: (4) Right-angled isosceles \(\begin{array}{l}\text \ Let \ A \ be... View Article
If the points (–1, 2, – 3), (4, a, 1) and (b, 8, 5) are collinear, then a and b are respectively equal to
1) 5 and 5 2) 9 and 5 3) 5 and 9 4) –5 and 9 Solution: (3) 5 and... View Article
A vector perpendicular to the plane containing the points A (1, -1, 2), B (2, 0, -1) and C (0, 2, 1) is
1) 4i + 8j – 4k 2) 8i + 4j + 4k 3) 3i + j + 2k 4) i... View Article
If P (3, 2, 6) is a point in space and Q is a point on the line r = (i – j + 2k) + (- 3i + j + 5k). Then the value of for which the vector PQ is parallel to the plane x – 4y + 3z = 1 is
1) 1/4 2) – (1/4) 3) 1/8 4) -(1/8) Solution: (1) ¼ \(\begin{array}{l}\begin{array}{l} \text { Any point on the line... View Article
Find the distance between the planes r . (2i + j + 3k) and r . (6i – 3j + 9k) + 13 = 0.
1) 5 / 3√14 2) 10 / 3√14 3) 25 / 3√14 4) None of these Solution: (3) 25 /... View Article
The angle between the line r = (i + 2j + 3k) + λ (2i + 3j + 4k) and the plane r . (i + 2j – 2k) = 0 is
1) 0o 2) 60o 3) 30o 4) 90o 5) 45o Solution: (1) 0o \(\begin{array}{l}r=(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})+\lambda(2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k}) \text... View Article
