If θ is eliminated from the equations x = a cos(θ-α) and y = b cos(θ-β), then (x2/a2) + (y2/b2) – (2xy/ab) cos (α-β) is equal to (a) sec2(α-β) (b) cosec2(α-β) (c) cos2(-β) (d) sin2 (α-β) Solution: Given x = a... View Article
If a pair of variable straight lines x2 + 4y2+ α xy =0 (where α is a real parameter) cut the ellipse x2 +4y2 = 4 at two points A and B, then the locus of the point of intersection of tangents at A and B is (a) (2x-y)(2x+y) = 0 (b) x2-4y2+8xy = 0 (c) x2-4y2+4xy = 0 (d) (x-2y)(x+2y) = 0 Solution: Let the point of intersection of tangent A... View Article
If y(x) satisfies the differential equation y’ – y tan x = 2x sec x and y(0) = 0, then: (a) y(π/4) = π2/8√2 (b) y’(π/4) = π2/18 (c) y(π/3) = π2/9 (d) y’(π/3) = (4π/3) +... View Article
HCF and LCM of 30 and 50 Solution: Using prime factorisation 30 = 2×3×5 50 = 2×5×5 HCF is the highest common factor. The common prime... View Article
LCM of 14 and 21 by prime factorisation. Solution: LCM of 14 and 21 is the smallest number among all common multiples of 14 and 21. 14 = 21×71 21 = 31×71 LCM of 14... View Article
Square root of 800 equals (a) 2√20 (b) 20√2 (c) 40√2 (d) none of these Solution: To find the square root of 800, we will express it in terms of... View Article
Find distance of point A(2, 3) measured parallel to the line x – y = 5 from the line 2x + y + 6 = 0. Solution: Given line x - y = 5 ..(i) 2x + y + 6 = 0 ..(ii) Slope of above line is m = 1 Parallel lines have same slope. Equation line... View Article
The area of the rhombus bounded by the four lines, ax ± by ± c = 0 is (a) c2/2ab (b) 2c2/ab (c) 4c2/ab (d) ab/4c2 Solution: The four lines will form a rhombus. The coordinates of the vertices are (-c/a,... View Article
Factors of 3600 Solution: The factors of 3600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120,... View Article
Which types of isomerism are shown by 2,3-dichlorobutane? (A) Optical isomerism (B) Geomatric isomerism (C) Diastereo isomerism (D) Structural isomerism The Correct Answer is (A) Optical... View Article
CH3 – CH = CH – CH3 → H2SO4 CH3 – CH+ – CH2 – CH3 → Major product. Identify the major product formed in the following reaction. (A) CH3 - CH = CH - CH3 (B) CH3 - CH2 = CH - CH3 (C) CH3 - CH3 = CH - CH3 (D) CH3 - CH = CH2 - CH3 | OSO3H The Correct Answer is (D)... View Article
When phenyl magnesium bromide is reacted with t-Butyl alcohol it gives (A) Ph-H (B) Ph-OH (C) Ph-O-C-CH3-CH3 (D) Ph-O-C-CH3-CH3-CH3 The Correct Answer is (A) Ph-H Solution: When is reacted with t-Butyl... View Article
In the periodic table of the elements, the phrase “middle row anomaly” refers to: (A) Instability of halogen oxides (B) Stability of alkali metal oxides (C) Stability of transition metal oxides (D) Both (A) and (C) The... View Article
An ideal gas mixture filled inside a balloon expands according to the relation pV2/3 = constant.The temperature inside the balloon will be: (A) Constant (B) Decreasing (C) Increasing (D) Cannot be defined. The Correct Answer is (C) Increasing Solution: = Constant =... View Article
