Quant mock(Speed test-19) for Govt. exams(10 qns) feel Good

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Q1. If (sinθ+cosθ/(sinθ−cosθ)=3   then the numerical value of sin⁴θ−cos⁴θ is   

a.1/2  b. 2/5  c. 3/5  d. 4/5

Q2.If (sinθ+cosθ)/(sinθ−cosθ)=5/4 , then the value of (tan²θ+1)/(tan²θ−1) will be   

a.41/40   b. 40/41  c.25/16  d.41/9

Q3.ABCD is a parallelogram. P and Q are the mid-points of sides BC and CD respectively. If the area of the △ABC is 12 cm², the area of △APQ is 

a.9 cm²  b.12 cm²  c.10 cm²   d.8 cm²

Q4.Two equal maximum sized circular plates are cut-off from a circular paper-sheet of circumference 352 cm. The circumference of each circular plate is 

 a.176 cm  b.180 cm  c.165 cm  d.150 cm

Q5.Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle thus formed with the original triangle is 

a.3 : 2  b.4 : 1  c.5 : 3  d.2 : 1

Q6.A trader bought a few pens at the rate of 5 per Rs.100 and a second time bought the same number of pens at the rate of 4 per Rs.100. He mixed both the lots and then sold the pens at the rate of 9 per Rs.200. In this business he suffered a loss of Rs.300. The total number of pens he bought was  

a.540  b.545  c.1080  d.1090

Q7.A shopkeeper gains 30% while buying the goods and 20% while selling them. Find his total gain percent.  

a.50%  b.40%  c.56%  d.36%

Q8.1% of tea is wasted at the time of mixing of two kinds of tea priced at Rs.600 per kg and Rs. 800 per kg. In what ratio the two kinds of tea are to be mixed so that there will be a profit of 10% on selling mixed tea at the rate of Rs. 700 per kg?   

a.3 : 19  b.17 : 3  c.5 : 17  d.17 : 5

Q9.If a milkman sells his milk at Rs. 30 per litre he incurs losses but if he sells at Rs. 34 per litre he makes a profit. If the loss to gain ratio is 1: 3, his cost price per litre (in Rs.) was 

a.31.5  b.31  c.31.75  d.32

Q10.The ratio of savings to expenditure of a person is 2 : 3. If his savings increases by 6% while his income increases by 15% then by how much percentage did his expenditure increase?  a.21%  b.24%  c.12%  d.25%

Quant mock(Speed test-18) for Govt. exams(10 qns) Geo.Special

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Q1.The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the larger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at E. The length of line segment AD is,  

a.17 cm  b.19 cm  c.18 cm  d.20 cm

Q2.O and C are the Orthocenter and the Circumcenter of an acute angled triangle PQR respectively. The points P and O are joined and produced to meet the side QR at S. If <QCR = 130⁰ and <PQS = 60⁰ then angle RPS is, 

a.100⁰  b. 35⁰  c. 30  d. 60⁰

Q3.AD is a median of triangle ABC and O is the centroid such that AO = 10cm. Length of OD (in cm) is,  a.7  b.5  c.4  d.2

Q4.In a cyclic quadrilateral ABCD, side AB is extended to E so that BE = BC. If  angle ADC=70⁰ and angle BAD=95⁰ then angle DCE is, 

a.140⁰    b.165⁰  c.120⁰  d.110⁰

Q5.If the angle subtended by a chord at its center is 60⁰, the ratio between the lengths of the chord and the radius is,  

a.1 : 1  b.2 : 1  c.(2)^1/2 : 1  d.1 : 2

Q6.In a right triangle ABC,  angle A = 90⁰ and AD is perpendicular to BC. If areas of the triangles ABC = 40cm² and triangle ACD = 10cm² with AC = 9cm, the length of BC is,

a.4cm b.12cm  c.18cm  d.6cm

Q7.P and Q are centres of two circles of radii 9cm and 2cm respectively. PQ is 17cm and R is the centre of a third circle that touches the other two circles externally. If ∠PRQ=90⁰,then radius of the third circle is, a.7cm  b.4cm  c.8cm  d.6cm

Q8.In a circle with centre at O and radius 5 cm, the length of a chord AB is 8 cm. If two tangents at A and B meet at C length of tangent section AC is

a.20/3cm.  b.15/4cm  c.10/3  cm. d.21/4 cm.

Q9.The units digit of 2⁷⁹+7³⁵ is

a.1  b.3  c.5  d.7

Q10. A tank is losing water 50% per hour. The percentage of water left after 2 hour will be

a.50% b.0%  c.25%  d.75%

Quant mock(Speed test-17) for Govt. exams(15 qns)

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Q1. If 0^o<θ<90⁰ and 2sin²θ+3cosθ=3 then the value of θ is

a.30⁰  b. 60⁰  c. 45⁰  d.75⁰

Q2. If cosθ+secθ=2 (0⁰≤θ≤90⁰) then the value of cos10θ+sec11θ is

a.0  b.1  c.2  d.-1

Q3. The minimum value of 2sin²θ+3cos²θ is

a.0  b.3  c.2  d.1

Q4. If two bells chime at intervals of 4 mins and 15 mins, after how long would they chime together first if they had chimed together in the beginning?

a.26 mins  b.52 mins  c.1 hour 18 minutes  d.1 hour

 Q5. (y−z)³+(z−x)³+(x−y)³  is equal to

a.(x−y)(y+z)(x−z)     b.(y−z)(z+x)(y−x)     c.(y−z)(z−x)(x−y)     d.3(y−z)(z−x)(x−y)

Q6. If x=b+c−2a, y=c+a−2b and z=a+b−2c, then the value of x²+y²−z²+2xy is, 

a.a+b+c     b. 0    c.a−b+c    d.a+b−c

Q7.A circular wire of radius 42 cm is bent in the form of a rectangle whose sides are in a ratio of 6 : 5. The smaller side of the rectangle is

a.30 cm  b.60 cm  c.36 cm  d.25 cm

Q8.From a point in the interior of an equilateral triangle, the perpendicular distances of the sides are, √3 cm, 2√3 cm and 5√3 cm. The perimeter (in cm) of the triangle is

a.48  b.64  c.24  d.32

Q9.The ratio of sides of a triangle is 3 : 4 : 5 and area of the triangle is 72 square units. Then the area of an equilateral triangle with same perimeter as the first triangle (in square units) is, a.48√3  b. 96  c. 60√3  d.32√3

Q10.If a train runs at 40km/hr, it reaches its destination 11 minutes late and if it runs at a speed of 50km/hr, it reaches the destination only 5 minutes late. Find the right time by which the train was to reach its destination

a.20 min  b.19 min  c.21 min  d.18 min

Q11.The sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of the diagonal is 15 cm. Then its total surface area is

a.351 cm²   b. 256 cm²    c. 265 cm²  d. 315 cm²

Q12.If sinθ+cosecθ=2, then the value of sin¹⁰⁰θ+cosec¹⁰⁰θ  is

a.100  b.3  c.2  d.1

Q13.The greatest value of sin⁴θ+cos⁴θ  is

a.1  b.12  c.3  d.2

Q14.If (1+sinA)(1+sinB)(1+sinC)=(1−sinA)(1−sinB)(1−sinC) , then the expression on each side of the equation equals,  a.1  b.tanA.tanB.tanC  c.cosA.cosB.cosC  d. sinA.sinB.sinC

Q15.If tanθ−cotθ=0 find the value of sinθ+cosθ

a. √2  b.0  c.1  d.2

Quant(Geometry) mock(Speed test-16) for Govt. exams(10 qns)

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Q1. The ratio between the number of sides of two regular polygons is 1:2 and the ratio between their interior angles is 2:3. The number of sides of the polygons are respectively  a. 5, 10    b.6, 12    c.7, 14    d.4, 8

 Q2. The length of the diagonal BD of the parallelogram ABCD is 18cm. If P and Q are the centroids of △ABC and △ADC respectively, length of PQ  is

a.4cm     b.12cm    c.6cm   d.9cm

Q3. A, B and C are three points on the circumference of a circle. If AB=AC=52√cm and ∠BAC=90⁰. the length of radius is

a. 15cm  b.5cm  c.10cm  d.20cm

Q4.AB and CD  are two parallel chords of respective lengths 8cm and 6cm on the same side of the center of a circle. The distance between them is 1cm. Then the radius of the circle is

a.4cm    b.5cm   c.3cm    d.2cm

Q5.△ABC is an isosceles triangle with AB=AC and AD as the median to base BC. If ∠ABC=35⁰, the ∠BAD is     a.70⁰    b. 35⁰   c. 55⁰   d. 110⁰ 

Q6.  If I is the incenter of △ABC,  ∠ABC=65⁰ and ∠ACB=55⁰, the ∠BIC is, 

a.110⁰   b. 120⁰  c. 130⁰  d. 140⁰

Q7. Sides of a right-angled triangle are in the ratio 4 : 5 : 6. If the in-radius of the triangle is 3 cm, the altitude of the triangle with base as the largest side is

a.7.5 cm  b.6 cm  c.8 cm  d.10 cm

Q8.The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is  a.7 cm  b.6 cm  c.5.5 cm  d.8 cm

Q9.A, B and C are three points on a circle such that angles subtended by the chords AB and AC at the centre are non-overlapping 90⁰ and 110⁰ respectively. ∠BAC is then equal to

a.80⁰  b.  90⁰  c 100⁰  d.70⁰

Q10.If the inradius of an equilateral triangle be 5 cm, its circumradius (in cm) is

a.10  b.15  c.25  d.30