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- A tangent at (x1,y1) to the curve y=x3+2x2+4 and passes through origin, then (x1,y1) is Answer is C (1,7) 1
- A circle of equation x2+y2+ax+by+c= 0 passes through (0, 6) and touches y=x2 at (2, 4). Find a+c. Answer :: 16 Solution :: Given ,x²+y²+ax+by+c= 0 passes through (0, 6) Then , 0+36+0+6b+c=0 6b-+c=-36 ....(1) Touches y=x² at (2, 4) 4+16+2a... 2
- What is the general solution of sin^2 x+ sin^2 2x=sin^2 3x? Answer: x = nπ/2 or x = nπ ± π/6 , where n in mathbbZ Use the identity sin²A - sin²B = sin(A+B)sin(A-B) . Rewrite the equation as sin²3x - s... 1
- One of the diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If A and B are the points Let O be the centre of circle M be mid point of AB. Then , OM ⊥ AB ⇒ M (1,4) Since, slope of AB = 0 Equation of straight line MO is x = 1 an... 1
- consider statement-1 is a fallacy. statement-2 is a tautology (b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I Explanation: Statement I and II are... 1
- let a=j-k and c=i-j-k. then the vector b satisfying ab+c=0 and a.b=3 is Option 1 is correct -i+j-2 k Explaination:: a x b + c = 0 a x (a x b) + a x c = 0 (a.b)a - (a.a)b + a x c = 0 3a - 2b + (-2i - j - k) = 0 2b... 1
- If u , v ,w are non-coplanar vectors and p,q are real numbers, then the equality Correct option is 3) exactly one value of (p,q) Explaination: 1
- If α, β and γ are three consecutive terms of a non-constant G.P. such that the equations Correct option is 4) βγ α x² + 2β x + γ = 0 Let β = α t, γ = α t² therefore α x² + 2α tx + α t² = 0 ⇒ x² + 2tx + t² = 0 ⇒ (x + t)² = 0 ⇒ x =... 1
- The Boolean expression ∼(p⇒(∼q)) is equivalent to : Correct option is A) p^q Explaination:: ∼(p⇒(∼q)) as p⇒q \ is \ same \ as \ ∼p v q we get ∼((∼p) v(∼q)) = p^q 1
- A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the centroid of this triangle is: Correct option is 2) ( 1/3,rm 2 ) Explanation:: 1
- A plane which bisects the angle between the two given planes 2x – y + 2z – 4 = 0 and x + 2y + 2z – 2 = 0, passes through the point :0 Correct option is (4) (2, –4, 1) Explaination:: From question, the equations of planes given are: 2x – y + 2z – 4 = 0 X + 2y + 2z – 2 = 0 Th... 1
- The equation of the common tangent to the curves y^2 = 16x and xy = - 4 is Answer: (a) x - y + 4 = 0 Any tangent to the parabola y² = 16x (here 4a = 16 , so a = 4 ) with slope m is y = mx + 4/m For it to touch the h... 1
- The equation of the common tangent to the curves y^2 = 8x and xy = - 1 is Correct option is (d) y=x+2 Explaination:: tangents to the curve y²=8x is y=mx+2/m , so it must satisfy xy=-1 x(mx+2/m)=-1 mx²+2/mx+1=0 , si... 1
- The general solution of the differential equation (y^2 – x^3 )dx – xydy = 0 (x ≠ 0) is : The correct option is 2) y²+2x³+cx²=0 Detailed explaination 1
- Let a ∈ (0,π/2) be fixed. If the integral ∫ tan x + tan α/tan x - tan α dx = A(x) cos 2α + B(x) sin 2α + C, where C is a Correct option is (4) x – α and log_e|sin(x – α)| Detailed Explaination: ∫ tan x + tan α/tan x - tan α dx = ∫ sin x /cos x+ sin α/cos α/sin... 1
- Suppose that f is differentiable for all x and that f’(x) ≤ 2 for all x. If f(1) = 2 and f(4) = 8, then f(2) has the value equal to LMV Theorem for f in [1, 2] forall c in(1, 2) f(2)-f(1)/2-1 =f'(c) ≤ 2 f(2)-f(1) ≤ 2 ⇒ f(2) ≤ 4 ...(1) Again, using LMV Theorem in [2, 4] fo... 1
- The system of linear equations x + y + z = 2 , 2x + 3y + 2z = 5 , 2x + 3y + (a2 – 1)z = a + 1 Correct option is inconsistent when |a|= sqrt3 Solution:: D=beginvmatrix 1&1&1\\2&3&2\\ 2 &3 &a²-1 endvmatrix D= 1(3a²-3-6) - 1(2a²-2-4) + 1... 1
- A aeroplane is flying horizontally with speed of 432 km/hr at height h meter from ground. Its angle of elevation The correct answer is option A)1200 sqrt3 Explanation:: 1
- If A=[ 1 2 2 2 1 2 2 2 1] and A^-1 exists and A≠0 , then (A^2-4A)A^-1= The correct answer is option a) beginbmatrix -3& 2 & 2\\ 2 & -3& 2\\ 2&2&-3 endbmatrix Video explaination:: https://youtu.be/7B6Et9Lb3gw 1
- Given that x = -9 is a root of ||The other two roots are ______ and ________ . the correct answer is available here watch this video by neha mam 2
- If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 (a, b, c being distinct and different from 1 ) are concurrent, then value of The correct answer is option c) 1 if the given lines are concurrent , then beginarray|ccc|cc| a& 1 & 1 \\ 1 & b & 1\\ 1 &1 & c\\ endarray=0... 1
- Area (in sq. units) of the region outside |x|/2 + |y|/3 = 1 and inside the ellipse x^2/4 + y^2/9 = 1 is The correct answer is option c) 6( π-2 ) Explaination:: Area of Ellipse =πab=6π Area |x|over2+|y|over3=1 is =1over2(d₁d₂)=1over2(4)(6)=12 so... 1
- Evaluate int {root x^2 + a^2} dx solve this question This can be best answer possible https://youtu.be/BmCM98ymuiY This video belongs to ganit yogi if they want we can remove it from here . 2
- Find the value of A and B if int(sinx/sin(x-alpha))dx= Answer: (b) (A, B) = (cosα, sinα) Write x = (x-α) + α , so sin x = sin(x-α)cosα + cos(x-α)sinα. Dividing by sin(x-α) : sin x/sin(x-α) = cosα... 1