If The Distance Between 2 3 And 5 2 Is Equal To The Distance Between X 2 And 1 3 Then The Values Of X Are 1) -6, 8 2) 6, 8 3) -8, 6 4) -7, 7 Solution: Option (1) -6, 8 Distance between (2, 3) and (-5, 2) = √[(-5-2)2+ (2-3)2] = √(49+1) =... View Article
The Three Distinct A At12 2at1 Bat22 2at2 And Ca0 Where A Is A Real Number Are Collinear If 1) t1t2 = - 1 2) t1t2 = 1 3) 2t1t2 = t1 + t2 4) t1 + t2 = a Solution: Option (1) t1t2 = - 1 The points A (at12, 2at1) , B(at22,... View Article
The Vertices Of Abc Are A 2 2 B4 4 And C5 8 Find The Length Of A Median Of A Triangle Which Is Passing Through The Point C 1) √65 2) √117 3) √85 4) √116 Solution: Option (3) √85 We know that the median passing through C will absolutely pass through the... View Article
If Algebraic Sum Of Distances Of A Variable Line From Points 2 0 0 2 And 2 2 Is Zero Then The Line Passes Through The Fixed Point 1) (- 1, - 1) 2) (1, 1) 3) (2, 2) 4) (0, 0) Solution: Option (4) (0, 0) The equation of the line passing through the point P(x1, y1)... View Article
The Points A 1 2 B 2 4 And C 4 8 Form A An 1) isosceles triangle 2) equilateral triangle 3) straight line 4) right-angled triangle Solution: Option (3) straight line Slope of... View Article
The Line X Plus Y 4 Divides The Line Joining The Points 1 1 And 5 7 In The Ratio 1) 2 : 1 2) 1 : 2 internally 3) 1 : 2 externally 4) None of these Solution: Option (2) 1:2 internally Given points (1, -1) and (5,... View Article
The Line Joining Ab Cos Alpha B Sin Alpha And B A Cos Beta A Sin Beta Where A Notequals B Is Produced To The Point M X Y So That Am Mb B A 1) 0 2) 1 3) - 1 4) a2 + b2 Solution: Option (1) 0 Given that AM: BM = b:a Thus, M divides AB externally in the ratio of b:a... View Article
The Equation Of The Base Bc Of An Equilateral Abc Is X Plus Y 2 And A Is 2 1 The Length Of The Side Of The Triangle Is 1) √2 2) (3/2)1/2 3) (1/2)1/2 4) (2/3)1/2 Solution: Option (4) (⅔)1/2 Given that the vertex A = (2, -1) Now, draw a perpendicular... View Article
If The Line 2x Plus Y K Passes Through The Point Which Divides The Segment Joining The Points 1 1 And 2 4 In The Ratio 3 2 Then K Is Equal To 1) 29/5 2) 5 3) 6 4) 11/15 Solution: Option (3) 6 Let A= (1, 1), and B = (2, 4) P(x1, y1) divides the line segment AB in the ratio... View Article
The Triangle Joining The Points P 2 7 Q 4 1 And R 2 6 Is 1) isosceles triangle 2) equilateral triangle 3) right-angled triangle 4) None of these Solution: Option (3) Right angled triangle... View Article
The value of [latex]tan\: [tan^{-1}\left ( \frac{1}{2} \right )- tan^{-1}\left ( \frac{1}{3} \right )][/latex] is 1) 5/6 2) 7/6 3) 1/6 4) 1/7 Answer: (4) 1/7 Solution: Let tan-1(1/2) = A tan A = 1/2 tan-1(1/3) = B tan B = 1/3 Now, tan[tan-1(1/2) -... View Article
The Value Of Tan Of Sin Inverse 3 5 Plus Cos Inverse 3 Roor13 Is 1) 6/17 2) 6/√13 3) √13/5 4) 17/6 Answer: (4) 17/6 Solution: Let sin-1(3/5) = A sin A = 3/5 Using the identity sin2x + cos2x = 1,... View Article
Cos Of Cos Inverse 1 7 Plus Sin Inverse 1 7 1) -1/3 2) 0 3) 1/3 4) 4/9 Answer: (2) 0 Solution: cos[cos-1(-1/7) + sin-1(-1/7)] We know that sin-1(x) + cos-1(x) = π/2 Thus,... View Article
If Cos Inverse X Plus Cos Inverse Y Plus Cos Inverse Z 3pi Then 1) 0 2) 1 3) 2 4) 3 Answer: (4) 3 Solution: Given, cos-1(x) + cos-1(y) + cos-1(z) = 3π We know that, 0 ≤ cos-1(x) ≤ π Thus, the... View Article
The Value Of Sin Inverse Root 3 2 Minus Sin Inverse 1 2 Is 1) 45° 2) 90° 3) 15° 4) 30° Answer: (4) 30° Solution: sin-1(√3/2) - sin-1(1/2) As we know sin 60° = √3/2 and sin 30° = 1/2. =... View Article
Sin Tan Inverse 1 Minus X Square 2x Plus Cos Inverse 1 Minus X Square 1 1) 0 2) 1 3) √2 4) 1/√2 Answer: (2) 1 Solution: Let x = tan A tan-1[(1 - x2)/2x] + cos-1[(1 - x2)/(1 + x2)] = tan-1[(1 - tan2A)/2... View Article
If Sin Inverse 3 5 Plus Cos Inverse 12 13 Sin Inverse C Then 1) 65/56 2) 24/65 3) 16/65 4) 56/65 Answer: (4) 56/65 Solution: Let cos-1(12/13) = A cos A = 12/13 Using the identity sin2x +... View Article
If 4 Sin Inverse X Plus Cos Inverse X Pi Then X Is 1) 0 2) 1/2 3) -√3/2 4) 1/√2 Answer: (2) 1/2 Solution: Given, 4 sin-1(x) + cos-1(x) = π 3 sin-1(x) + sin-1(x) + cos-1(x) = π 3... View Article
The Value Of Cos Inverse Cos 5pi 3 Plus Sin Inverse Sin 5pi 3 Is 1) 0 2) π/2 3) 2π/3 4) 10π/3 Answer: (1) 0 Solution: cos-1(cos 5π/3) + sin-1(sin 5π/3) = cos-1[cos(2π - π/3)] + sin-1[sin(2π -... View Article
If Sin Inverse A Sin Inverse B Sin Inverse C Pi Then 1) 2abc 2) abc 3) (1/2)abc 4) (1/3)abc Answer: (1) 2abc Solution: Given, sin-1(a) + sin-1(b) + sin-1(c) = π Let sin-1(a) = x,... View Article
