Author admin Posted on Categories Uncategorized   Leave a comment on The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If μ and σ^2 denote the mean and variance of the correct observations respectively, then 15(μ+μ^2+σ^2 ) is equal to

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If μ and σ^2 denote the mean and variance of the correct observations respectively, then 15(μ+μ^2+σ^2 ) is equal to

Ans. (2521) Sol. Let the incorrect mean be μ’ and standard deviation be σ’ We have μ’=(Σxi)/15=12⇒Σxi=180 As per given information correct Σxi=180-10+12 ⇒μ( correct mean )=182/15 Also σ’=√((Σxi^2)/15-144)=3⇒Σxi ^2=2295 Correct Σxi ^2=2295-100+144=2339 σ^2 ( correct variance )=2339/15-(182×182)/(15×15) Required value =15(μ+μ^2+σ^2 ) =15(182/15+(182×182)/(15×15)+2339/15-(182×182)/(15×15)) =15(182/15+2339/15) =2521

Author admin Posted on Categories Uncategorized   Leave a comment on An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is : (1) 5/256 (2) 5/715 (3) 3/715 (4) 3/256

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is : (1) 5/256 (2) 5/715 (3) 3/715 (4) 3/256

Author admin Posted on Categories Uncategorized   Leave a comment on Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B. Then the distance of the point P(m,n) from the point Q(-2,-3) is (1) 10 (2) 6 (3) 4 (4) 8

Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B. Then the distance of the point P(m,n) from the point Q(-2,-3) is (1) 10 (2) 6 (3) 4 (4) 8

Author admin Posted on Format ImageCategories Uncategorized   Leave a comment on <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>f</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi>R</mi> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> <mo>+</mo> <mfrac> <mn>2</mn> <mi>x</mi> </mfrac> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi mathvariant="normal">g</mi> </mrow> <mo stretchy="false">(</mo> <mrow> <mi mathvariant="normal">x</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mfenced open="{" close="" separators="|"> <mrow> <mtable columnalign="center center" columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mo data-mjx-texclass="OP" movablelimits="true">min</mo> <mo fence="false" stretchy="false">{</mo> <mrow> <mi mathvariant="normal">f</mi> </mrow> <mo stretchy="false">(</mo> <mrow> <mi mathvariant="normal">t</mi> </mrow> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> </mtd> <mtd> <mn>0</mn> <mo><</mo> <mrow> <mi mathvariant="normal">t</mi> </mrow> <mo>≤</mo> <mrow> <mi mathvariant="normal">x</mi> </mrow> <mtext> and </mtext> <mn>0</mn> <mo><</mo> <mrow> <mi mathvariant="normal">x</mi> </mrow> <mo>≤</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo> <mrow> <mi mathvariant="normal">x</mi> </mrow> <mo>,</mo> </mtd> <mtd> <mn>1</mn> <mo><</mo> <mrow> <mi mathvariant="normal">x</mi> </mrow> <mo><</mo> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> </mfenced> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>g</mi> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>g</mi> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>x</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>g</mi> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>g</mi> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>x</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math>

f : ( 0 , 2 ) → R f ( x ) = x 2 + 2 x g ( x ) g ( x ) = min { f ( t ) } , 0 < t ≤ x  and  0 < x ≤ 1 3 2 + x , 1 < x < 2 g x = 1 g x ∈ ( 0 , 2 ) g x = 1 g x ∈ ( 0 , 2 )

Author admin Posted on Categories Uncategorized   Leave a comment on Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying <math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mi>tan</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo data-mjx-texclass="NONE">⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msup> <mi>tan</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo data-mjx-texclass="NONE">⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </math> is (1) More than 2 (2) 1 (3) 2 (4) 0

Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying tan − 1 ⁡ ( x ) + tan − 1 ⁡ ( 2 x ) = π 4 is (1) More than 2 (2) 1 (3) 2 (4) 0

Author admin Posted on Categories Uncategorized   Leave a comment on [latexpage]\[5. If A denotes the sum of all the coefficients in the expansion of (1-3x+10x^2 )^n and B denotes the sum of all the coefficients in the expansion of (1+x^2 )^n,\]

[latexpage]\[5. If A denotes the sum of all the coefficients in the expansion of (1-3x+10x^2 )^n and B denotes the sum of all the coefficients in the expansion of (1+x^2 )^n,\]

(1) (2) (3) (4) Ans. (1) Sol. Sum of coefficients in the expansion of [latexpage] \[ \]

Author admin Posted on Categories Uncategorized 2 Comments on If (a,b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and [latexpage]\[ I_1= f_a^b xsin⁡(4x-x^2 )dx, ( ) I_2=f_a^b sin⁡(4x-x^2 )dx, then 36 I_1/I_2\]is equal to :

If (a,b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and [latexpage]\[ I_1= f_a^b xsin⁡(4x-x^2 )dx, ( ) I_2=f_a^b sin⁡(4x-x^2 )dx, then 36 I_1/I_2\]is equal to :

(1) 72 (2) 88 (3) 80 (4) 66 Ans. (1) Sol. Equation of CE     orthocentre lies on the line so, Using king rule (i) + (ii) Q. If A denotes the sum of all the coefficients in the expansion of (1-3x+10x^2 )^n and B denotes the sum of all the coefficients in the expansion of (1+x^2 )^n, then : (1) A=B^3 (2) 3A=B (3) B=A^3 (4) A=3B Q. The number of common terms in the progressions 4,9,14,19,……. , … Continue reading “If (a,b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and [latexpage]\[ I_1= f_a^b xsin⁡(4x-x^2 )dx, ( ) I_2=f_a^b sin⁡(4x-x^2 )dx, then 36 I_1/I_2\]is equal to :”