Sr. Teacher Grade II Competitive Exam (Mathematics)

Q1. यदि G तथा G'क्रमशः त्रिमुजों ABC तथा A'B'C' के 4. 1 If G and G' are centroid of triangles ABC and A'B'C' respectively, then \overrightarrowAA' + \overrightarrowBB' + \overrightarrowCC' is केन्द्रक हों, तो \overrightarrowAA' + \overrightarrowBB' + \overrightarrowCC' बराबर है – equal to -
(2) \overrightarrowGG'
(2) \overrightarrowGG'
(1) 2/3\overrightarrowGG'
(1) 2/3 \overrightarrowGG'
(4) 2\overrightarrowGG'
(4) 2\overrightarrowGG'
(3) 3\overrightarrowGG'
(3) 3\overlineGG' दो रेखाओं की दिक्कोज्याएं 1 + m + n = 0 और

Q2. Direction cosines of two lines are given by 2. 2lm + 2nl - mn = 0 द्वारा दी जाती है,। इन दोनों 1 + m + n = 0 and 2Im + 2nl - mn = 0, The acute रेखाओं के मध्य न्यूनकोण है – angle between these two lines is -
(2) 75°
(2) 75° 00
(1) .
(1) 60°
(4) 30^\circ
(3) 45°
(4) 30^\circ
(3) 45° यदि S = a, b, c, d, e, तो S के ऐसे उपसमुच्चयों з.
3. If S = \a, b, c, d, e\, then the total number of की कुल संख्या, जो अवयव c रखते हैं. परंतु d नहीं, -subsets of S, which contains element c but not है – d, is -
(2) 4
(1) 6
(2) 4
(1) 6
(4) 10 \cdots
(3) 8
(4) 10
(3) 8 अवकल समीकरण
4. Complementary Function of differential
4. x² (d²y)/(dx²) - x (dy)/(dx) - 3y = x² log x equation x² (d²y)/(dx²) - x (dy)/(dx) - 3y = x² log x, is - का पूरक फलन है – पायर पायर पायर
(1) c₁ e^-3x + c₂ e^x
(2) (c₁)/(x³) + c₂ x²
(1) c₁ e^-3x + c₂ e^x
(2) (c₁)/(x³) + c₂ x .
(3) c₁ e^3x + c₂ e^-x
(4) c₁ x³ + (c₂)/(x)
(3) c₁ e^3x + c₂ e^x
(4) c₁ x³ + (c₂)/(y) यदि 3 × 3 कोटि की मैट्रिक्स A का सहखंडज 5.
5. If P = \beginbmatrix 1 & α & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 1 \endbmatrix is the adjoint of a 3 × 3 मैट्रिक्स P = \beginbmatrix 1 & α & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \endbmatrix है तथा [A]' = 4 , तो α का matrix A and |A| = 4, then value of α is - मान है ∸
(2) 4 + 1/2 :
(2) 4
(1) 5
(1) 5
(4) 11
(3) 7
(4) 11 \cdot
(3) 7 फलन f
(x) = sin (5x)/(3) + cos (3x)/(7) + tan (2x)/(7) का
6. Period of function
6. f
(x) = sin (5x)/(3) + cos (3x)/(7) + tan (2x)/(71) is - आवर्तकाल है —
(2) (7π)/(5)
(1) 42π
(2) (7π)/(5)
(1) 42π
(3) 24π
(4) 11/15 π
(4) 11/15 π
(3) 24π 07 - 4 Page 2 of 32

Q3. 4. Complementary Function of differential equation x² d^2y/dx^2 - x dy/dx - 3y = x² log x is ka puurak phalan hai –

• (a) c1 e^{-3x} + c2 e^x
• (b) c1/x^3 + c2 x²
• (c) c1 e^{3x} + c2 e^{-x}
• (d) c1 x³ + c2/x

Q4. 5. If P = [[1, α, 3], [1, 3, 3], [2, 4, 1]] is the adjoint of a 3×3 matrix A = [[1, α, 3], [1, 3, 3], [2, 4, 4]] and |A| = 4, then α is –

• (a) 5
• (b) 4.5
• (c) 7
• (d) 11

Q5. 6. f(x) = sin(5x/3) + cos(3x/7) + tan(2x/7). Period of the function is –

• (a) 42π
• (b) 7π/5
• (c) 24π
• (d) 11/15 π