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If (α, β) is the point on y²= 6x, that is closest to (3, 3/2) then find 2(α+β)

a. 6b. 9c. 7d. 5Solution: Answer: (b)Equation of normal at (α, β) isy-β = (-β/2a)(x-α)⇒ 3y-3β =... View Article

The value of tan (2 tan^-1(3/5) + sin^-1(5/13)) is:

a. 220/21b. 110/21c. 55/21d. 20/11Solution: Answer: (a)tan (tan-1 (6/5)/(1-(9/5)) + tan-1 (5/12))= tan (tan-1 (15/8) + tan-1 (5/12))= ((15/8) +... View Article

In a ∆ABC, if [latex]left | overrightarrow{AB} right |=7[/latex], [latex]left | overrightarrow{BC} right |=5[/latex], and [latex]left | overrightarrow{CA} right |=3[/latex]. If the projection of [latex]overrightarrow{BC}[/latex] on [latex]overrightarrow{CA}[/latex] is n/2, then the value of n is

Answer: 5/2 cos ∠BCA5|(32+52-72)/(2.3.5)| = 5|-15/30|= 5/2... View Article

If element of matrix A = [a_ij]_(3×3) where [latex]A = \left\{\begin{matrix} (-1)^{j-i} &i<j \\ 2& i=j\\ (-1)^{i+j}& i>j \end{matrix}\right.[/latex], then the value of |3 adj(2A^-1)| is:

a. 72b. 36c. 108d. 48Solution: Answer: (c)A = |A| = 2(4-1)+1(-2+1)+1(1-2)= 2(3)+1(-1)+1(-1)= 4|3 adj(2A-1)| = 33|adj(2A-1)|= 33×|2A-1|2=... View Article

If A = [latex]\begin{bmatrix} 1 & 0\\ 0& 1 \end{bmatrix}[/latex]1[latex] and B = \sum_{r=1}^{2021}A^{r}[/latex] then value of |B| is

a. 2021b. 20212c. -2021d. 0Solution: Answer: (b)A = I, B= I+I+I+....,2021 times |B| = 20212Hence option b is the answer.... View Article

Given below are three conditions:A: If 2+4 = 7, then 3+4 = 8 and B: if 3+5 = 8, then earth is flat and C: if A and B are true, then 5+4 = 11. Choose the correct option.

a. A is true, B and C are false b. B is true, A and C are false c. C is true, A and B are false d. B is false, A and C are true Solution:... View Article

If [latex]g(t)=\begin{Bmatrix} max(t^{3}-6t^{2}+9t-3,0), & t \; belongs\: to\: [0,3] \\ 4-t & t \; belongs\: to\:(3,4) \end{Bmatrix}[/latex] then the number of points at which g(t) is non differentiable is:

a. 1b. 3c. 2d. 4Solution: Answer: (b)y = t3- 6t2 + 9t - 3y’ = 3t2-12t + 9= 3(t2- 4t + 3)So total 3 points.Hence option b is the answer.... View Article

If f(x) = (5x+3)/(6x+a) and f(f(x) = x then the value of a is:

a. -5b. 5c. 6d. -6Solution: Answer: (a)f(f(x) = (5f(x)+3)/(6f(x)+a) = x⇒ 5f(x)+3 = 6xf(x)+ax[(25x+15)/(6x+a)] + 3 = 6x((5x+3)/(6x+a)) +... View Article

If P(bar(A)cap B)+P(Acap bar(B))= 1-k and P(bar(A)cap C)+P(Acap bar(C))= 1-2k and P(bar(B)cap C)+P( bar(C)cap B)= 1-k and P(A∩B∩C) = k², k ∈(0, 1)

Question: If , , P(A∩B∩C) = k2, k ∈(0, 1). Then the value of P (at least one of A, B, C) is: a. >1/2 b. [1/8, ¼] c. < 1/4 d.... View Article

If x = ay-1 = z-2, and x = 3y-2 = bz-2 lie in same plane, then the value of a, b is

a. a = 2,b = 3b. a = 1, b = 1c. b = 1, a ∈ R-{0}d. a = 3,b = 2Solution: Answer:(c)(x/1) = (y-1/a)/(1/a) = (z-2)/1x = (y-⅔)/(⅓) =... View Article

If Re [(1+cos θ + 2i sin⁡ θ)] = 4, then the value of θ is

a. π/2b. π/3c. -π/2d. πSolution: Answer: (d)[1/(1 + cos2θ + 2i sin θ)] ×(1+cos θ - 2i sin θ)/(1 + cos... View Article

Sum of 21 terms of series [latex]log_{9^{frac{1}{2}}}x + log_{9^{frac{1}{3}}}x + log_{9^{frac{1}{4}}}x……….[/latex] is 252, then the value of x is:

a. 7b. 243c. 9d. 81Solution: Answer: (c)2 log9 x + 3 log9 x + 4 log9 x………….21 terms= (2 + 3 + 4 + 5…+ 22)... View Article

If f(x) = x+1, then find [latex]\lim_{n\to \infty }\frac{1}{n}\left [ f(0)+f(\frac{5}{n})+ f(\frac{10}{n})+…+f(\frac{5(n-1)}{n})\right ][/latex]

a. 7/2b. 3/2c. 5/2d. 1/2Solution: Answer: (a) = ∫01 f(5x)= ∫01(5x+1) dx= ((5x2/2) + x)01= (5/2) + 1= 7/2Hence option a is the answer.... View Article

Mean of 6 observations is 10 and their variance is 20/3 . If observations are 15, 11, 10, 7, a, b then |a-b| is equal to:

a. 2b. 1c. 3d. 4Solution: Answer: (b)Mean = 10(7+10+11+15+a+b)/6 = 10a + b = 17Variance = 20/3(49+100+121+225+a2+b2)/6 - 100 = 20/3a2+b2 =... View Article

The value of x satisfying the equation log_(x+1)⁡(2x²+7x+5) + log_(2x+5)⁡(x+1)²= 4 is:

a. -2b. 2c. -4d. 4Solution: Answer: (b)log(x+1) ⁡(2x+5)(x+1) + log(2x+5) (x+1)2 = 41+ log(x+1) (2x+5)⁡ + 2log(2x+5) (x+1) = 4Put log(x+1) (2x+5)... View Article

If [latex]\lim_{x\to 0}\frac{\alpha x(1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+…)-\beta (x-\frac{x^{2}}{2}+\frac{x^{3}}{3}+…)+\gamma x^{2}(1-x+\frac{x^{2}}{2!}-\frac{x^{3}}{3!}+…)}{x^{3}}=10[/latex], find the value of α + β + γ

Solution: Answer: (3) ⇒ α - β = 0⇒ α = β⇒ α + β/2 + γ = 0⇒ γ = -3β/2⇒... View Article

[latex]a_{ij}=\left\{\begin{matrix} 1 ,& i=j\\ -x ,&\left | i-j \right |=1 \\ 2x+1, & otherwise \end{matrix}\right.[/latex], A = [a_ij]_3×3. f(x) = Det(A). Then find the sum of local maximum and minimum values of fx.

a. 20/27b. −20/27c. 88/27d. -88/27 Solution: Answer: (d) = 4x3- 4x2 - 4xf’(x) = 4(3x2- 2x - 1)f’(x) = 4(x-1)(x + 1/3)f(1) =... View Article